Motion and Forces (Unit 1)

If a soccer player runs after his opponent 50m North, then turns around and chases him 20m south, what is his distance and displacement ?

Distance: 70m Displacement: 30m North

1NEWTON =

1KgxM/s squared

Free Fall

If the only force acting on an object is gravity then it is in free fall.

If an object travels at a right angle you use what?

Pythagorean theorem

Suppose you ran 2km in 10min. With what speed did you run?

S=d/t S=2/10 S=0.2km/min

The IMA of a wheel and axle could be increased by increasing the size of the and/or the size of the axle.

wheel decreasing

What is Air resistance (drag) determined by

1) Speed-Greater speed greater resistance 2) Size- larger object greater resistance (Moving a cargo plane through air) 3) Shape- Flatter object greater resistance (Frisbee)

the shaft on which a wheel turns

axle

What is the equation for a balanced lever

(W1)(D1) = (W2)(D2) LeftxRight

Net force

Combining all forces on an object. 2 N ---> /\ <-------5 N= 3 Newtons to the left.

Centripetal Acceleration

The Speed remains constant but it is accelerating because of its motion changes. The change in the direction of the horses' velocity is toward the center of the object. This is acceleration toward the center of a curved or circular path.

In a real system of levers, wheels, or pulleys, AMA is always less than IMA.

True

Horizontal and Vertical Motion

When you throw or shoot an object, such as a rubber band, the force exerted by your hand gives the band its horizontal velocit. Its horizontal velocity is constant, but the rubber band does not accelerate horizontally. If there was no gravity it would continue its movement along the dotted line. Gravity causes it to accelerate downward. It has an increasing vertical velocity.

It takes a person one half hour to run 6 kilometers at a constant rate along a straight-line path. What is the velocity of the person? A. 0 km/hr in the direction of the path B. 3 km/hr in the direction of the path C. 6 km/hr in the direction of the path D. 12 km/hr in the direction of the path

D. 12 km/hr in the direction of the path

What does IMA and AMA stand for?

IMA - Ideal Mechanical Advantage AMA - Actual Mechanical Advantage

What is force(F)

Push or Pull one object exerts on another F=ma

What is acceleration and how to calculate acceleration

a=vf-vi/t or change in velocity/time Rate of change of velocity over time m/s squared 1) It speeds up 2) It slows down 3) It changes direction -10m/s squared north is the same as 10m/s squared south.

How to calculate time

t=d/s

When using the wheel and axle, the input force moves through a greater distance than the output force.

true

What is distance and How to calculate distance

Total distance traveled. The SI Unit of distance is the meter(m). Longer distances are measured in Kilometers (km). One Kilometer is equal to 1,000 meters. One meter is equal to 100cm and to 1,000 mm d=ts

Give an example of when an object has the same speed but differnet velocity.

Two escalaors move at the same speed but in different directions. Also cars.

Newton's Third Law of Motion

What happens when you push against a wall? If the wall is sturdy, nothing happens. But if you pushed against a wall while wearing roller skates, you would go rolling backward. This is a demonstration of Newton's third law of motion. Newton's third law of motion states that when one object exerts a force on a second object, the second object exerts a force on the first that is equal in strength and opposite in direction. Sometimes, Newton's third law is written as "to every action force there is an equal and opposite reaction force." However, one force is not causing the second force. They occur at the same time. It does not matter which object is labeled Object 1 and which is labeled Object 2. Think about a boat tied to a dock with a taut rope. You could say that the action force is the boat pulling on the rope and the reaction force is the rope pulling on the boat. But it would be just as correct to say that the action force is the rope pulling on the boat and the reaction force is the boat pulling on the rope. Forces on different objects do not cancel If these two forces are equal in size and opposite in direction, you might wonder how some things ever happen. For example, if the box in Figure 13 pushes on the student when the student pushes on the box, why does the box move? According to the third law of motion, action and reaction forces act on different objects. Recall that the net force is the sum of the forces on a single object. The left picture in Figure 13 shows the forces on the student. The net force is zero and the student remains at rest. The right picture shows that there is a net force of 20 N to the right on the box and the box accelerates to the right.

Net force

When two or more forces act on an object at the same time, the forces combine to form the net force. The net force is the sum of all of the forces acting on an object. Forces have a direction, so they follow the same addition rules as displacement, as listed in Table 1. Forces are measured in the SI unit of newtons (N). A force of about 3 N is needed to lift a full can of soda at a constant speed. Unbalanced forces Look at Figure 2A. The students are each pushing on the box in the same direction. These forces are combined, or added together, because they are exerted on the box in the same direction. The students in Figure 2B are pushing in opposite directions. Here, the direction of the net force is the same as the direction of the larger force. In other words, the student who pushes harder causes the box to move in the direction of that push. The net force will be the difference between the two forces because they are in opposite directions. In Figure 2A and Figure 2B, the net force had a value that was not zero and the box moved. The forces that the students applied are considered unbalanced forces. Balanced forces Now suppose that the students were pushing with the same size force but in opposite directions, as shown in Figure 2C. The net force on the box is zero because the two forces cancel each other. Forces on an object that are equal in size and opposite in direction are called balanced forces. Unbalanced forces cause changes in motion. Balanced forces do not cause a change in motion

Law of Inertia

Tendency of an object to resist change in motion The more mass an objects has the more inertia it has. Inertia is not overcome as long as an object has mass.

A delivery truck drives 4 miles west before turning right and driving 6 miles north to make a delivery. Find distance and displacement?

Distance: 10miles Displacement: 7.21 miles NW

Graphing Motion

The motion of an object over a period of time can be shown on a distance-time graph. For example, the graph in Figure 7 shows the distance traveled by three swimmers during a 30-minute workout. Time is plotted along the horizontal axis of the graph, and the distance traveled is plotted along the vertical axis of the graph. Each axis must have a scale that covers the range of numbers to be plotted. In Figure 7, the distance scale must range from 0 to 2,400 m and the time scale must range from 0 to 30 min. Next, the x-axis is divided into equal time intervals, and the y-axis is divided into equal distance intervals. Once the scales for each axis are in place, the data points can be plotted. In Figure 7, there is a data point plotted for each swimmer every two and a half minutes. After plotting the data points, a line is drawn connecting the points. Speed on distance-time graphs If an object moves with constant speed, the increase in distance over equal time intervals is the same. As a result, the line representing the object's motion is a straight line. For example, look at the graph of the swimmers' workouts in Figure 8. The straight red line represents the motion of Mary, who swam with a constant speed of 80 m/min. The green line represents the motion of Julie, who did not swim with a constant speed. She swam with a constant speed of 40 m/min for 10 minutes, rested for 10 minutes, and then swam with a constant speed of 80 m/min for 10 minutes. The graph shows that the line representing the motion of the faster swimmer is steeper. The steepness of a line on a graph is the line's slope. The slope of a line on a distance-time graph equals the object's speed. Because Mary has a greater speed (80 m/min) than Kathy (60 m/min), the line representing her motion has a larger slope. Now look at the green line representing Julie's motion. During the time she is resting, her line is horizontal. A horizontal line on a distance-time graph has zero slope and represents an object at rest.

Momentum practice

1.) How much force is needed to accelerate a 100 kg mass at a rate of 2.5 m/s2? 2.) What is the force acting on a 0.5 kg object moving at a rate of 100 m/s2? 3.) What is the mass of an object that is accelerating at a rate of 25 m/s2 and is using 15 N of force? 4.) Timmy pushes off of the pool wall with a force of 2300 N and accelerates at 15 m/s2, what is Timmy's mass? (ignore water resistance) 5.) Tonya uses a 418 N force to move a 56 kg mass, at what rate does the object accelerate? 6.) How much momentum does a 25 kg mass moving at 25 m/s have? 7.) How much momentum does a stationary 5500 kg mass have? 8.) What is the velocity of a 5.5 kg object that has a momentum of 550 kg·m/s? 9.) Compare the momentums of a 50 kg dolphin swimming at 16.4 m/s and a 4100 kg elephant walking 0.20 m/s. 10.) An object has a momentum of 55 kg·m/s and hits a stationary object making the second object starts to move. If the first object ends with a momentum of 13 kg·m/s, what is the momentum of the second object?

Gravity

Attractive force between two objects that depends on mass and distance. Acts on all objects with mass. Law of Universal Gravitation: Any two masses exert an attractive force on each other -Depends on mass: greater mass, greater gravitational attraction. - Distance: lower the distance greater gravitational attraction (Gravity: Attraction to earth that pulls downward) This force causes all falling objects to have an acceleration due to gravity of 9.8m/s squared regardless of mass and air resistance You feel Earth's pull beause it is closer and larger. Because the gravitational force btween two objects never disappears, gravity is called a long range force. Gravity is sometimes called a field because it requires no contact. A field is a region of space that has a physical quantity (such as a force) at every pont.

Three factors of friction

1) Rougher the surface= more friction(Have micro welds, microscopes bumps that cause friction) increase resistance between object 2) The Greater the force pushing objects = greater friction -increases opposition of micro welds between objects 3) The greater surface area of two objects touching, greater friction (Surface area=space of plan)

Weight

the force of gravity on an object - Because its force you can use F=ma - When finding weight, acceleration due to gravity is 9.8 m/s squared Weight(N)= mass(kg) x gravitational strength (N/kg) Weight increass as mass does.

What is a projectile

Anything shot through the air. Objects curve downwards, Earth's gravity causes projectiles to follow a curved path.

Gravity and you

The law of universal gravitation explains why you feel Earth's gravity but not the Sun's gravity or this book's gravity. While the Sun has much more mass than Earth, the Sun is too far away to exert a noticeable gravitational attraction on you. And while this book is close, it does not have enough mass to exert an attraction that you can feel. Only Earth is both close enough and has a large enough mass that you can feel its gravitational attraction. The range of gravity According to the law of universal gravitation, the gravitational force between two masses decreases rapidly as the distance between the masses increases. For example, if the distance between two objects increases from 1 m to 2 m, the gravitational force between them becomes one fourth as large. If the distance increases from 1 m to 10 m, the gravitational force between the objects is one-hundredth as large. However, no matter how far apart two objects are, the gravitational force between them never completely goes to zero. Because the gravitational force between two objects never disappears, gravity is called a long-range force. Reading Check Explain why gravity is called a long-range force. The gravitational field Because contact between objects is not required, gravity is sometimes discussed as a field. A field is a region of space that has a physical quantity (such as a force) at every point. All objects are surrounded by a gravitational field. Figure 8 shows that Earth's gravitational field is strongest near Earth and becomes weaker as the distance from Earth increases. The strength of the gravitational field, represented by the letter g, is measured in newtons per kilogram (N/kg).

displacement(change in x)

distance and direction of an object's change in position difference from start and end point

Speed, Velocity, and Acceleration Problems

correct units. 1. Pete is driving down 7th street. He drives 150 meters in 18 seconds. Assuming he does not speed up or slow down, what is his speed in meters per second? 2. A person jogs 4.0 km in 32 minutes, then 2.0 km in 22 minutes, and finally 1.0 km in 16 minutes. What is the jogger's average speed in km per minute? 3. A train travels 120 km in 2 hours and 30 minutes. What is its average speed? 4. A plane's average speed between two cities is 600 km/hr. If the trip takes 2.5 hrs. how far does the plane fly? 5. George walks to a friend's house. He walks 750 meters North, then realizes he walked too far. He turns around and walks 250 meters South. The entire walk takes him 13 seconds. What is his speed per second? 6. In problem #5, what was George's velocity in meters per second? (hint: draw a picture to find his displacement) 7. A roller coaster's velocity at the top of a hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26 m/s. What was the acceleration of the coaster? 8. A roller coaster is moving at 25 m/s at the bottom of a hill. Three seconds later it reaches the top of the hill moving at 10 m/s. What was the acceleration of the coaster? 9. A car traveling at 15 m/s starts to decelerate steadily. It comes to a complete stop in 10 seconds. What is it's acceleration? 10. A child drops a ball from a window. The ball strikes the ground in 3.0 seconds. What is the velocity of the ball the instant before it hits the ground? 11. A boy throws a ball straight up into the air. It reaches the highest point of its flight after 4 seconds. How fast was the ball going when it left the boy's hand? 12. A train moves from rest to a speed of 25 m/s in 30.0 seconds. What is its acceleration? 13. If a train going 60 m/s hits the brakes, and it takes the train 1 minute 25 seconds to stop, what is the train's acceleration? 14. How long will it take a car to go from a complete stop to 44 km/hr if they are accelerating at 5 km/hr2 ? 15. How long will it take a car to accelerate from 15.2 m/s to 23.5 m/s if the car has an average acceleration of 3.2 m/s2

Terminal Velocity

Maximum velocity a falling object will reach Occurs when the force of gravity and resistance become balanced Net force balanced= Zero acceleration

In a real pulley system, the work input must be the work output.

More then

Newtons Second Law of Motion

The second law explains how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. Newton also developed the calculus of mathematics, and the "changes" expressed in the second law are most accurately defined in differential forms. (Calculus can also be used to determine the velocity and location variations experienced by an object subjected to an external force.) For an object with a constant mass m, the second law states that the force F is the product of an object's mass and its acceleration a:

Velocity

1. A roller coasters velocity at the top of the hill is 10 m/s. Two seconds later it reaches the bottom of the hill with a velocity of 26m/s. What is the acceleration of the coaster? 2. A roller coaster is moving at 25 m/s at the bottom of a hill. Three seconds later it reaches the top of the hill moving at 10 m/s. What was the acceleration of the coaster? 3. A swimmer speeds up from 1.1 m/s to 1.3 m/s during the last 20 seconds of the race. What is the acceleration of the swimmer? 4. A cars velocity changes from o m/s to 30 m/s in 10 seconds. Calculate acceleration. 5. A satellite's original velocity is 10,000 m/s. After 60 seconds it s going 5,000 m/s. What is the acceleration 6. A car goes from a stop to 30 km/ss in 25 seconds. What is the acceleration? 7. If a speeding train hits the brakes and it takes the train 39 seconds to go from 54.8 m/s to 12 m/s what is the acceleration? 8. (Be careful!) How long will it take a car to go from 0 to 44 km/hr if they are accelerating at 5 km/hr2? 9. (Be careful!) How many minutes will it take a car to go from a stop to 33 km/hr if it accelerates at 10 km/hr2 10. Calculate acceleration of a turtle going from 0.3 m/s to 0.7 m/s in 30 seconds.

ACCELERATION PRACTICE PROBLEMS

1. Does the speedometer of a car read average speed or instantaneous speed? How do you know? 2. If the speedometer of your car reads a constant speed of 40km/hr, can you say 100% for sure that the car has a constant velocity? Explain your answer. 3. What two controls on a car cause a change in speed? 4. What control causes a change in velocity? 5. What is the acceleration of a car that travels in a straight line at a constant speed? 6. Describe a situation in which you can accelerate even though your speed doesn't change. 7. A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration? 8. A cyclist accelerates from 0 m/s to 8 m/s in 3 seconds. What is his acceleration ? Is this acceleration higher than that of a car which accelerates from 0 to 30 m/s in 8 seconds? 9. A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Find the car's average acceleration. 10. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average acceleration? 11. A runner covers the last straight stretch of a race in 4 s. During that time, he speeds up from 5 m/s to 9 m/s. What is the runner's acceleration in this part of the race? 12. You are traveling in a car that is moving at a velocity of 20 m/s. Suddenly, a car 10 meters in front of you slams on it's brakes. At that moment, you also slam on your brakes and slow to 5 m/s. Calculate the acceleration if it took 2 seconds to slow your car down. 13. A ball is dropped from the top of a building. After 2 seconds, it's velocity is measured to be 19.6 m/s. Calculate the acceleration for the dropped ball. Time FinalVelocity InitialVelocity Acceleration 14. If a Ferrari, with an initial velocity of 10 m/s, accelerates at a rate of 50 m/s/s for 3 seconds, what will its final velocity be? 15. Falling objects drop with an average acceleration of 9.8 m/s2 . If an object falls from a tall building, how long will it take before it reaches a speed of 49 m/s? 16. Josh rolled a bowling ball down a lane in 2.5 s. The ball traveled at a constant acceleration of 1.8 m/s2 down the lane and was traveling at a speed of 7.6 m/s by the time it reached the pins at the end of the lane. How fast was the ball going when it left Tim's hand?

Calculate Force

1. How much force is needed to accelerate a 66 kg skier at 2 m/sec2? 2. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec2? 3. What is the acceleration of a 50 kg object pushed with a force of 500 newtons? 4. The mass of a large car is 1000 kg. How much force would be required to accelerate the car at a rate of 3 m/sec2? 5. A 50 kg skater pushed by a friend accelerates 5 m/sec2. How much force did the friend apply? 6. A force of 250 N is applied to an object that accelerates at a rate of 5 m/sec2. What is the mass of the object? 7. A bowling ball rolled with a force of 15 N accelerates at a rate of 3 m/sec2; a second ball rolled with the same force accelerates 4 m/sec2. What are the masses of the two balls? 8. If a 60 kg person on a 15 kg sled is pushed with a force of 300 N, what will be person's acceleration? 9. A force of 20 N acts upon a 5 kg block. Calculate the acceleration of the object. 10. An object of mass 300 kg is observed to accelerate at the rate of 4 m/s2. Calculate the force required to produce this acceleration. 11. A 5 kg block is pulled across a table by a horizontal force of 40 N with a frictional force of 8 N opposing the motion. Calculate the acceleration of the object. 12. An object of mass 30 kg is in free fall in a vacuum where there is no air resistance. Determine the acceleration of the object. 13. An object of mass 30 kg is falling in air and experiences a force due to air resistance of 50 newtons. a. Determine the net force acting on the object and b. calculate the acceleration of the object. 1. A man hits a golf ball (0.2 kg) which accelerates at a rate of 20 m/s2. What amount of force acted on the ball? 2. You give a shopping cart a shove down the isle. The cart is full of groceries and has a mass of 18 kg. The cart accelerates at a rate of 3 m/s 2. How much force did you exert on the cart? 3. The wind pushes a paper cup along the sand at a beach. The cup has a mass of 25 grams ( = ? kg) and accelerates at a rate of 5 m/s 2. How much force (in Newtons) is the wind exerting on the cup? 4. You push a friend sitting on a swing. She has a mass of 50 kg and accelerates at a rate of 4 m/s2. Find the force you exerted. 5. How much force would it take to push another, larger friend who has a mass of 70 kg to accelerate at the same rate of 4 m/s2? 6. A worker drops his hammer off the roof of a house. The hammer has a mass of 9 kg, and gravity accelerates it at the usual 9.8 m/s2. How much force does the earth apply to the hammer? 7. A car whose mass is 1000 kg is traveling at a constant speed of 10 m/s. Neglecting any friction, how much force will the engine have to supply to keep going the same speed?

Newton's Second Law and Gravitational

Acceleration Recall that the gravitational force exerted on an object is equal to the object's mass times the strength of gravity ( F g = mg). If gravity is the only force acting on an object ( F net = F g ), then Newton's second law states that the object's acceleration is the force of gravity divided by the object's mass. Notice that the mass cancels and the object's acceleration due to gravity is equal to the strength of gravity. a = _ F net m = F _g m = _ mg m = g When discussing the acceleration due to gravity, g is written with the units m/s2 . On Earth, any falling object with only gravity acting on it will accelerate at 9.8 m/s2 toward Earth. Air resistance The gravitational force causes objects to fall toward Earth. However, objects falling in the air experience air resistance. Air resistance is a friction-like force that opposes the motion of objects that move through the air. Air resistance acts in the direction opposite to the motion of an object moving through air. If the object is falling downward, air resistance exerts an upward force on the object. The amount of air resistance on an object depends on the size, shape, and speed of the object, as well as the properties of the air. Air resistance, not the object's mass, is the reason feathers, leaves, and pieces of paper fall more slowly than pennies, acorns, and billiard ball. If there were no air resistance, then all objects, including the feather and the billiard ball, would fall with the same acceleration, as shown in Figure 16.

Momentum

An object is moving at 2 m/s toward a glass vase. Will the vase be damaged in the collision? If the object has a small mass, like a bug, a collision will not damage the vase. But if the object has a larger mass, like a car, a collision will damage the vase. A useful way of describing both the velocity and mass of an object is to state its momentum. The momentum of an object is the product of its mass and velocity. Momentum is usually represented by the symbol p. The unit for momentum is kg·m/s. Like velocity, momentum has a size and a direction. An object's momentum is always in the same as the direction as its velocity. Table 3 shows the sizes of the momentums of some common objects. Comparing momentums Think about the car and the truck in Figure 14. Which has the larger momentum? The truck does because it has more mass. When two objects travel at the same velocity, the object with more mass has a greater momentum. A difference in momentums is why a car traveling at 2 m/s might damage a porcelain vase, but an insect flying at 2 m/s will not. Now consider two 1-mg insects. One insect flies at a speed of 2 m/s, and the other flies at a speed of 4 m/s. The second insect has a greater momentum. If two objects have the same mass, the object with the larger velocity has the larger momentum

Gravity

At this moment, you are exerting an attractive force on everything around you—your desk, your classmates, and even the planet Jupiter, millions of kilometers away. This attractive force acts on all objects with mass and is called gravity. Gravity is an attractive force between any two objects that depends on the masses of the objects and the distance between them. Gravity is one of the four basic forces. These forces are called the fundamental forces. The other basic forces are the electromagnetic force, the strong nuclear force, and the weak nuclear force. Gravity acts on all objects with mass, and the electromagnetic force acts on all charged particles. Both gravity and the electromagnetic force have an infinite range. The nuclear forces only affect particles in the nuclei of atoms. The law of universal gravitation In the 1660s, British scientist Isaac Newton used data on the motions of the planets to find the relationship between the gravitational force between two objects, the objects' masses, and the distance between them. This relationship is called the law of universal gravitation and can be written as the following equation. F = G m 1m _2 d 2 In this equation, G is the universal gravitational constant, and d is the distance between the centers of the two masses, m 1 and m 2. The law of universal gravitation states that the gravitational force increases as the mass of either object increases and as the objects move closer, as shown in Figure 7. The force of gravity between any two objects can be calculated if their masses and the distance between them are known. This relationship is called the law of universal gravitation and can be written as the following equation. F = G x m¹m²/d² If the mass of either of the objects increases, the gravitational force between them increases. If the objects are closer together, the gravitational force between them increases.

Newtons Second Law of Motion

F=ma -The net force acting on an object causes the object to accelerate in direction of net force. -The greater the mass the greater force needed to accelerate -the greater net force, the greater acceleration You push with a force of

Motion of Earth's Crust

Can you think of something that is moving so slowly that you cannot detect its motion, but you can see evidence of its motion over long periods of time? As you look around the surface of Earth from year to year, its basic structure seems the same. Mountains, plains, and oceans seem to remain unchanged. Yet, if you examined geologic evidence of what Earth's surface looked like over the past 250 million years, you would see that large changes have occurred. Figure 11 shows how, according to the theory of plate tectonics, the positions of landmasses have changed during this time. Changes in the landscape occur constantly as continents drift slowly over Earth's surface. These moving plates cause geologic changes, such as the formation of mountain ranges, earthquakes, and volcanic eruptions. The movement of the plates changes the size of the oceans. The Pacific Ocean is getting smaller, and the Atlantic Ocean is getting larger. The plates' movement also changes the shape of the continents as they collide and spread apart. Plates move so slowly that their speeds are given in units of centimeters per year. Along the San Andreas Fault in California, two plates move past each other with an average speed of about 1 cm per year. The Australian Plate moves faster and pushes Australia north at an average speed of about 17 cm/y. Therefore, the velocity of the Austrailian plate is 17 cm/y north.

What is force?

Catching a basketball and hitting a baseball with a bat are examples of applying force to an object. A force is a push or a pull. In both examples, the applied force changes the movement of the ball. Sometimes, it is obvious that a force has been applied. But other forces are not as noticeable. For instance, are you conscious of the force that the floor exerts on your feet? Can you feel the force of the atmosphere pushing against your body or gravity pulling on your body? Think about all of the forces that you exert in a day. Every push, pull, stretch, or bend results in a force being applied to an object. Changing motion What happens to the motion of an object when you exert a force on it? A force can cause the motion of an object to change. Think of kicking a soccer ball, as shown in Figure 1. The player's foot strikes the ball with a force that causes the ball to stop and then move in the opposite direction. If you have played billiards, you know that you can force a ball at rest to roll into a pocket by striking it with another ball. The force of the moving ball causes the ball at rest to move in the direction of the force. In each case, the velocity of the ball was changed by a force.

Inertia and mass

Does a bowling ball have the same inertia as a table-tennis ball? Why is there a difference? You could not change the motion of a bowling ball much by swatting it with a table-tennis paddle. But you could easily change the motion of the table-tennis ball. A greater force would be needed to change the motion of the bowling ball because it has greater inertia. Recall that mass is the amount of matter in an object. An object's inertia is related to its mass. The greater an object's mass is, the greater its inertia is. A bowling ball has more mass than a table-tennis ball has, so the bowling ball has a greater inertia. You will sometimes hear people say that when an object begins to move, inertia is overcome. This is not true. The object still has mass when it is moving, so it still has inertia. As long as the mass is the same, the object has the same inertia.

Coordinate systems

Figure 2 shows a map of the city where the mail truck is delivering mail with a coordinate system drawn on it. The x-axis is in the east-west direction, the y-axis is in the north-south direction, and each division represents a city block. The post office is located at the origin. The mail truck is located at 3 blocks east (x = 3) and 2 blocks north (y = 2) of the post office. Change in Position Have you ever run a 50-m dash? Describing how far and in what direction you moved was an important part of describing your motion. Distance In a 50-m dash, each runner travels a total distance of 50 m. The SI unit of distance is the meter (m). Longer distances are measured in kilometers (km). One kilometer is equal to 1,000 m. Shorter distances are measured in centimeters (cm) or millimeters (mm). One meter is equal to 100 cm and to 1,000 mm. Displacement Suppose a runner jogs to the 50-m mark and then turns around and runs back to the 20-m mark, as shown in Figure 3. The runner travels 50 m in the original direction (east) plus 30 m in the opposite direction (west), so the total distance that she ran is 80 m. How far is she from the starting line? The answer is 20 m. Sometimes, you may want to know the change in an object's position relative to the starting point. An object's displacement is the distance and direction of the object's change in position. In Figure 3, the runner's displacement is 20 m east. The length of the runner's displacement and the total distance traveled would be the same if the runner's motion were in a single direction. For example, if the runner ran east from the starting line to the finish line without changing direction, then the distance traveled would be 50 m and the displacement would be 50 m east Adding displacements You know that you can add distances together to get the total distance. For example, 2 m + 3 m = 5 m. But how would you add the displacements 5 m east and 10 m east? Directions in math problems are much like units: you can add numbers with like directions. For example, suppose a student walks 5 m east, stops at a crosswalk, and then walks another 5 m east, as shown on the left in Figure 4. His displacement is 5 m east + 5 m east = 10 m east But what if the directions are not the same? Then compare the two directions. If the directions are exactly opposite, the distances can be subtracted. Suppose a student walks 10 m east, turns around, and walks 5 m west, as shown in the center of Figure 4. The size of the displacement would be 10 m − 5 m = 5 m The direction of the total displacement is always the direction of the larger displacement. In this case, the larger displacement is east, so the total displacement is 5 m east. Now suppose the two displacements are not in the same direction or in opposite directions, as illustrated on the right in Figure 4. Here, the student walks 4 m east and then 3 m north. The student walks a total distance of 7 m, but the displacement is 5 m in a roughly northeast direction. 4 m east and 3 m north cannot be directly added or subtracted, and they should be discussed separately. The rules for adding displacements are summarized in Table 1. 1) Add displacements in the same direction. 2. Subtract displacements in opposite directions. 3. Displacements that are not in the same or in opposite directions cannot be directly added together.

What forces change motion

Friction: Resistance to motion when two objects are in contact Air resistance: Resistance objects has when in air Gravity: Attraction two objects have on each other

Relative Motion

Have you ever watched cars pass you on the highway? Cars traveling in the same direction often seem to creep by, while cars traveling in the opposite direction seem to zip by. This apparent difference in speeds is because the reference point— your vehicle—is also moving. The choice of a moving reference point affects how you describe motion. For example, the motion of a hurricane can be described using a stationary reference point, such as a house. Figure 12 shows the locations and velocities of a hurricane and a car relative to a house at 2:00 p.m. and 3:00 p.m. The distance between the hurricane and the house is decreasing at a rate of 20 km/h. The distance between the house and the car is increasing at a rate of 10 km/h. How would the description of the hurricane's motion be different if the reference point were a car traveling at 10 km/h west? Figure 13 shows the motion of the hurricane and the house relative to the car. A person in the car would say that the hurricane is approaching with a speed of 10 km/h and that the house is moving away at a speed of 10 km/h. It is important to notice that Figure 12 and Figure 13 show the same changes, but they use different reference points. Velocity and position always depend on the point of reference chosen.

Throwing and dropping

If you were to throw a ball as hard as you could in a perfectly horizontal direction, would it take longer to reach the ground than if you dropped a ball from the same height? Surprisingly, it will not. A thrown ball and a dropped ball will hit the ground at the same time. Both balls in Figure 19 travel the same vertical distance in the same amount of time. However, the ball thrown horizontally travels a greater horizontal distance than the ball that is dropped. Amusement park acceleration Riding roller coasters in amusement parks can give you the feeling of danger, but these rides are designed to be safe. Engineers use the laws of physics to design amusement park rides that are thrilling but harmless. Roller coasters are constructed of steel or wood. Because wood is not as strong as steel, wooden roller coasters do not have hills that are as high and as steep as some steel roller coasters have. The highest speeds and accelerations are usually produced on steel roller coasters. Steel roller coasters can offer multiple steep drops and inversion loops, which give the rider large accelerations. As riders move down a steep hill or an inversion loop, they will accelerate toward the ground due to gravity. When riders go around a sharp turn, they are also accelerated. This acceleration makes them feel as if a force is pushing them toward the side of the car

What happens in a crash?

Newton's first law of motion can explain what happens in a car crash. When a car traveling about 50 km/h collides head-on with something solid, the car crumples, slows down, and stops within approximately 0.1 s. According to Newton's first law, the passengers will continue to travel at the same velocity that the car was moving unless a force acts on them. This means that within 0.02 s after the car stops, any unbelted passengers will slam into the windshield, dashboard, steering wheel, or the backs of the front seats, as shown on the left in Figure 15. These unbelted passengers are traveling at the car's original speed of 50 km/h (about 30 miles per hour). Safety belts Passengers wearing safety belts, also shown in Figure 15, will be slowed down by the force of the safety belt. This prevents the person from being thrown out of the seat. Car-safety experts say that about half of the people who die in car crashes would survive if they wore safety belts. Thousands of others would suffer fewer serious injuries. The force needed to slow a person's speed from 50 km/h to 0 in 0.1 s is equal to 14 times the force of gravity on the person. Therefore, safety belts are designed to loosen a little as they restrain the passengers. The loosening increases the time it takes to slow the person down, meaning a smaller acceleration and a smaller force is exerted on the passenger. Air bags Air bags also reduce injuries in car crashes by providing a cushion that reduces the acceleration of the passengers and prevents them from hitting the dashboard. When impact occurs, a chemical reaction occurs in the air bag that produces nitrogen gas. The air bag expands rapidly and then deflates just as quickly as the nitrogen gas escapes out of tiny holes in the bag. The entire process is completed in about 0.04 s

Newton's Second Law of Motion

Newton's first law of motion states that the motion of an object changes only if an unbalanced force acts on the object. Newton's second law of motion describes how the forces exerted on an object, its mass, and its acceleration are related. Force and acceleration How are throwing a ball as hard as you can and tossing it gently different? When you throw hard, you exert a greater force on the ball. The ball has a greater velocity when it leaves your hand. The hard-thrown ball has a greater change in velocity, and the change occurs over a shorter period of time. Recall that acceleration equals the change in velocity divided by the time it takes for the change to occur. So, a hard-thrown ball is accelerated more than a gently thrown ball, as shown in Figure 11 Mass and acceleration If you throw a softball and a baseball as hard as you can, as shown in Figure 12, why do they not have the same speed? The difference is due to their masses. A softball has a mass of about 0.20 kg, but a baseball's mass is about 0.14 kg. The softball has less velocity after it leaves your hand than the baseball does, even though you exerted the same force. The softball has a smaller final speed because it experienced a smaller acceleration. The acceleration of an object depends on its mass as well as the force exerted on it. Force, mass, and acceleration are related. Reading Check Identify You apply a force of 2 N to a toy car and to a real car. Which car has the greater acceleration? Relating force, mass, and acceleration Newton's second law of motion states an object's acceleration is in the same direction as the net force on the object and is equal to the net force exerted on it divided by its mass. Newton's second law can be written as the following equation. In the above equation, acceleration has units of meters per second squared (m/s2 ) and mass has units of kilograms (kg). Recall that the net force is the sum of all of the forces on an object. Remember that the SI unit for force is a newton (N) and that 1 N = 1 kg∙m/s2 . Just like velocity and acceleration, force has a size and a direction. Calculating net force Newton's second law can also be used to calculate the net force if mass and acceleration are known. To do this, the equation for Newton's second law must be solved for the net force, F net . To solve for the net force, multiply both sides of the above equation by the mass For example, when a tennis player hits a ball, the racket and the ball might be in contact for only a few thousandths of a second. Because the ball's velocity changes over such a short period of time, the ball's acceleration could be as high as 5,000 m/s2 . The ball's mass is 0.06 kg, so the size of the net force exerted on the ball would be 300 N.

Newton First Law of Motion (Describe motion upon an object with motion)

Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia. The key point here is that if there is no net force acting on an object (if all the external forces cancel each other out) then the object will maintain a constant velocity. If that velocity is zero, then the object remains at rest. If an external force is applied, the velocity will change because of the force. -An object will move until acted on. -An object will move at a constant velocity until a net force acts on t. -An object will stay at rest until acted

Forces are interactions

Newton's third law states a very important fact: forces are interactions between objects. For example, it makes no sense to say, "The box has a force of 30 N." Is this force acting on the box? Is the box pushing on something? What is causing this force? It makes sense, however, to say, "The student applied a force of 30 N to the box." Furthermore, both objects experience a force from the interaction. Look at the skaters in Figure 14. The male skater is pulling upward on the female skater, while the female skater is pulling downward on the male skater. The two forces are equal in size but opposite in direction. Both skaters feel a pull of the same size. Even if the two objects have different masses, they will feel the same size force. For example, if a bug flies into the windshield of a truck, the bug and the truck exert forces on each other. According to Newton's third law, the bug and the truck experience the same size force even though their masses and accelerations are different

Centripetal Forces

Orbiting objects, such as space shuttles, are traveling in nearly circular paths. According to Newton's first law, this change in motion is caused by a net force acting on the object. Newton's second law states that because the object's acceleration is toward the center of the curved path, the net force is also toward the center. A centripetal force is a force exerted toward the center of a curved path. Anything that moves in a circle is doing so because a centripetal force is accelerating it toward the center. Many different forces can act as a centripetal force. Gravity is the centripetal force that keeps planets orbiting the Sun. On the amusement park ride in Figure 20, the push of the walls of the ride on the people is the centripetal force. When a car rounds a level curve on a highway, friction between the tires and the road acts as the centripetal force. If the road is slippery and the frictional force is small, it might not be large enough to keep the car moving around the curve. Then the car will slide in a straight line, as shown in Figure 21.

Force and Momentum

Recall that acceleration is the difference between the initial and final velocities, divided by the time. Therefore, we can write Newton's second law in the following way. F = ma = m × ( v f - v i )/t = ( mv f - mv i / t Recall that an object's momentum equals its mass multiplied by its velocity. In the equation above, m v f is the final momentum and mv i is the initial momentum. The equation states that the net force exerted on an object equals the change in its momentum divided by the time over which the change occurs. In fact, this is how Newton originally wrote the second law of motion . Conservation of momentum Newton's second and third laws of motion can be used to describe what happens when objects collide. For example, consider the collision of the balls in Figure 22. We will assume that friction is too small to cause a noticeable change in the balls' motion. In this ideal case, there are no external forces, but the balls exert forces on each other during the collision. According to Newton's third law, the forces are equal in size and opposite in direction. Therefore, the momentum lost by the first ball is gained by the second ball and the total momentum of the two balls is the same before and after the collision. This is the law of conservation of momentum—if no external forces act on a group of objects, their total momentum does not change. Collisions with multiple objects When a cue ball hits the group of motionless balls, as shown in Figure 23, the cue ball slows down and the rest of the balls begin to move. The momentum that the group of balls gained is equal to the momentum that the cue ball lost. Momentum is conserved.

Motion in Two Dimensions

So far, we have only discussed motion in a straight line. But most objects are not restricted to moving in a straight line. Recall that we cannot add measurements that are not in the same or opposite directions. So, we will discuss motion in each direction separately. For example, suppose a student walked three blocks north and four blocks east. The trip could be described this way: the student walked north for three blocks at 1 m/s and then walked east for four blocks east at 2 m/s. Recall that objects that change direction are accelerating. For an object that is changing direction, its acceleration is not in the same or opposite direction as its velocity. This means that we cannot use the acceleration equation. Just as with displacement and velocity, accelerations that are not in the same or opposite directions cannot be directly combined.

Free fall

Suppose an object were falling and there were no air resistance. Gravity would be the only force acting on the object. If gravity is the only force acting on an object, the object is said to be in free fall. For example, the feather and the billiard ball falling in a vacuum, previously shown in Figure 16, are in free fall. Another example is an object in orbit. Earth, for example, is in free fall around the Sun. If Earth did not have a velocity perpendicular to the gravitational force, it would fall into the Sun. Similarly, satellites are in free fall around Earth. Weightlessness You might have seen pictures of astronauts and equipment floating inside an orbiting spacecraft. They are said to be experiencing weightlessness. But, according the law of universal gravitation, the strength of Earth's gravitational field at a typical orbiting altitude is about 90 percent of its strength at Earth's surface. So, an 80-kg astronaut would weigh about 700 N in orbit and would not be weightless. What does it mean to say that something is weightless? Think about how you measure your weight. When you stand on a scale, as shown on the left of Figure 19, you are at rest. The net force on you is zero, according to Newton's second law of motion. The scale exerts an upward force that balances your weight. The dial on a scale shows the size of the upward force, which is the same size as your weight. Now suppose you stand on a scale in an elevator that is in free fall, as on the right in Figure 19. You would no longer push down on the scale at all. The scale dial would read zero, even though the force of gravity has not changed. An orbiting spacecraft is in free fall, and objects in it seem to float because they are all falling around Earth at the same rate.

Rocket propulsion

Suppose you are standing on skates holding a softball. You exert a force on the softball when you throw it. According to Newton's third law, the softball exerts a force on you. This force pushes you backward in the direction opposite the softball's motion. Rockets use the same principle to move, even in the vacuum of outer space. In the rocket engine, burning fuel produces hot gases. The rocket engine exerts a force on these gases and causes them to escape out the back of the rocket. By Newton's third law, the gases exert a force on the rocket and push it forward. Figure 24 shows one of the Apollo rockets that traveled to the Moon. Notice that the force of the rocket on the gases is equal in size to the force of the gases on the rocket. Momentum is conserved when a rocket ejects the hot gas. If the rocket is initially at rest, then the total momentum of the rocket and the fuel is zero. After the fuel is burned and the hot gas is expelled, the gas travels backward with a momentum of m gasv gas and the rocket travels forward with a momentum of m rocketv rocket . These momentums are equal in size, but opposite in direction. By controlling how much gas is ejected and the gas's velocity, the rocket's motion can be controlled

Which observation BEST demonstrates Newton's first law of motion? A. An astronaut weighs more on Earth than he does on the Moon, but his mass does not change. B. A baseball thrown by a professional player has greater acceleration than a baseball you throw. C. A book placed beside you on the back seat of a car slides to the floor as the car stops suddenly. D. A stone thrown at a trashcan cannot knock it over, but a stone with more mass can knock it over

The correct answer is choice (C) A book placed beside you on the back seat of a car slides to the floor as the car stops suddenly. Newton's first law of motion can be stated as an object in motion tends to stay in motion and an object at rest tends to stay at rest. When the car stops suddenly, the book continues to move forward and falls to the floor. Choice (A) is an example of unbalanced forces. Choice (B) is an example of Newton's second law of motion. The professional baseball player uses more force and so the acceleration of the ball is greater. Choice (D) is an example of Newton's third law. The force of the stone with greater mass is greater than that of the less massive stone.

Friction

Suppose you give a skateboard a push with your hand. After you let go, the skateboard slows down and eventually stops. Because the skateboard's motion is changing as it slows down, there must be a force acting on it. The force that slows the skateboard is called friction. Friction is the force that opposes the sliding motion of two surfaces that are touching each other. What causes friction? Would you believe that the surface of a highly polished piece of metal is rough? Surfaces that appear smooth actually have many bumps and dips. These bumps and dips can be seen when the surface is examined under a microscope, as shown in Figure 3. If two surfaces are in contact, welding or sticking occurs where the bumps touch each other. These microwelds are the source of friction. To move one surface over the other, a force must be applied to break the microwelds. Reading Check Describe the source of friction. The amount of friction between two surfaces depends on the kinds of surfaces and the force pressing the surfaces together. Rougher surfaces have more bumps and can form more microwelds, increasing the amount of friction. In addition, a larger force pushing the two surfaces together will cause more of the bumps to come into contact, as shown in Figure 4. The microwelds will be stronger, and a greater force must be applied to the object to break the microwelds. Static friction Suppose you have a cardboard box filled with books, such as the one in Figure 5, and want to move that box. The box is resting on what seems to be a smooth floor, but when you push on the box, it does not budge. The box experiences no change in motion, so the net force on the box is zero. The force of friction cancels your push. This type of friction is called static friction. Static friction prevents two surfaces from sliding past each other and is due to the microwelds that have formed between the bottom of the box and the floor. Your push is not large enough to break the microwelds, and the box does not move, as shown in Figure 5. Sliding friction If you and a friend push together, as shown on the right in Figure 5, the box moves. Together, you and your friend have exerted enough force to break the microwelds between the floor and the bottom of the box. But if you stop pushing, the box quickly comes to a stop. To keep the box moving, you must continually apply a force. This is because sliding friction opposes the motion of the box as the box slides across the floor. Sliding friction opposes the motion of two surfaces sliding past each other and is caused by microwelds constantly breaking and forming as the objects slide past each other. The force of sliding friction is usually smaller than the force of static friction. Rolling friction You may think of friction as a disadvantage. But wheels, like the ones shown in Figure 6, would not work without friction. As a wheel rolls, static friction acts over the area where the wheel and surface are in contact. This special case of static friction is sometimes called rolling friction. You may have seen a car that was stuck in snow, ice, or mud. The driver steps on the gas, but the wheels just spin without the car moving. The force used to rotate the tires is larger than the force of static friction between the wheels and the ground, so the tires slide instead of gripping the ground. Spreading sand or gravel on the surface increases the friction until the wheels stop slipping and begin rolling. When referring to tires on vehicles, people often use the term traction instead of friction.

A small marble is dropped to the floor. Assume that as the marble falls, the only force exerted on it is the force of gravity. How do the speed and acceleration of the marble change with time? A. speed increases, acceleration increases B. speed remains constant, acceleration increases C. speed increases, acceleration remains constant D. speed remains constant, acceleration remains constant

The correct answer is choice (C) speed increases, acceleration remains constant. Since the only force acting on the marble is the constant force of gravity, the acceleration of the object will also be constant. A constant acceleration causes the speed to increase at a constant rate. Choices (A) and (B) are incorrect because a constant force will result in a constant acceleration. Choice (D) is incorrect because only the acceleration remains constant, while the speed increases.

Weight

The gravitational force exerted on an object is the object's weight. The universal law of gravitation can be used to calculate weight, but scientists use a simplified version of this equation that combines m 1 , d 2 , and G into a single number called the gravitational strength, g. Weight Equation weight (N) = mass (kg) × gravitational strength (N/kg) F g = mg We use F g for weight because weight is the force due to gravity. Weight has units of newtons (N) because it is a force. The g in the subscript stands for gravity. The gravitational strength, g, has the units N/kg. Recall that 1 N = 1 kg ∙ m/s2 . So, g can also be written with units of m/s2 . Weight and mass Weight and mass are not the same. Weight is a force, and mass is a measure of the amount of matter an object contains. But, according to the weight equation, weight and mass are related. Weight increases as mass increases. Weight on Earth We often need to know an object's weight on Earth. Near Earth's surface, m 1 , from the law of universal gravitation, is Earth's mass and d is Earth's radius. As a result, g = 9.8 N/kg. Table 2 lists the weights of some objects on Earth Weight away from Earth An object's weight usually refers to the gravitational force between the object and Earth. But the weight of an object can change, depending on the gravitational force on the object. For example, the gravitational strength on the Moon is 1.6 N/kg, about one-sixth as large as Earth's gravitational strength. As a result, a person, such as the astronaut in Figure 9, would weigh only about one-sixth as much on the Moon as on Earth. Finding other planets Earth's motion around the Sun is affected by the gravitational pulls of the other planets in the solar system. In the same way, the motion of every planet in the solar system is affected by the gravitational pulls of all of the other planets. In the 1840s, the most distant planet known was Uranus. The motion of Uranus calculated from the law of universal gravitation disagreed slightly with its observed motion. Some astronomers suggested that there must be an undiscovered planet affecting the motion of Uranus. Using the law of universal gravitation and the laws of motion, two astronomers independently calculated the orbit of this planet. As a result of these calculations, the planet Neptune was found in 1846

Size and shape

The more spread out an object is, the more air resistance it will experience. Picture dropping two plastic bags, as shown in Figure 17. One is crumpled into a ball and the other is spread out. When the bags are dropped, the crumpled bag falls faster than the spread-out bag. The downward force of gravity on both bags is the same, but the upward force of air resistance on the crumpled bag is less. As a result, the net downward force on the crumpled bag is greater. Speed and terminal velocity The amount of air resistance also increases as the object's speed increases. As an object falls, gravity causes it to accelerate downward. But, as an object falls faster, the upward force of air resistance increases. So, the net force on the object decreases as it falls, as shown with the sky diver in Figure 18. Eventually, the upward air resistance force becomes large enough to balance the downward force of gravity and the net force on the object is zero. Then the acceleration of the object is zero, and the object falls with a constant speed called the terminal velocity. Terminal velocity is the maximum speed an object will reach when falling through a substance, such as air. A falling object's terminal velocity depends on its size, shape, and mass. For example, the air resistance on an open parachute is much larger than the air resistance on the sky diver alone. With the parachute open, the sky diver's terminal velocity is small enough that she can land safely.

Weightlessness

The phenomenon of "weightlessness" occurs when there is no force of support on your body. When your body is effectively in "free fall", accelerating downward at the acceleration of gravity, then you are not being supported. The sensation of apparent weight comes from the support that you feel from the floor, from the seat, etc. Different sensations of apparent weight can occur on a roller-coaster or in an aircraft because they can accelerate either upward or downward. If you travel in a curved path in a vertical plane, then when you go over the top on such a path, there is necessarily a downward acceleration. Taking the example of the roller-coaster which is constrained to follow a track, then the condition for weightlessness is met when the downward acceleration of your seat is equal to the acceleration of gravity. Considering the path of the roller-coaster to be a segment of a circle so that it can be related to the centripetal acceleration, the condition for weightlessness is. Think about standing on a scale and it is exerting an upward force on you that is the same as your weight. while standing on a scale in a elevator that moving exerts no force so the scale reads zero.

Newton Third Law of Motion

The third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal force on object A. Notice that the forces are exerted on different objects. The third law can be used to explain the generation of lift by a wing and the production of thrust by a jet engine.

Joe drives 120 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour? A) 42 B) 48 C) 50 D) 54 E) 56

The total distance is easy to compute: first 120 miles, and then another 120 miles, which gives us a total distance of 240 miles. Total time will take a few more steps. We'll use the formula: time = distance/speed Joe drives at two different speeds: 60 mph and 40 mph. Time spent driving 60 mph = 120 miles/60 mph = 2 hours Time spent driving 40 mph = 120 miles/40 mph = 3 hours As we said at the start of the problem, it will take less time to drive 120 miles at 60 mph than it will to drive that same distance at 40 mph, and we were right. It took Joe 2 hours to drive 120 miles at 60 mph, and it took 3 hours at 40 mph, giving us a total time of 5 hours. Putting it all Together: In the steps above we calculated total distance (120 miles + 120 miles = 240 miles), and we just found total time (5 hours). Average Speed = 240 miles/5 hours = 48 mph

In space how do two different objects vary in their drop

They drop at the same rate because there is no gravity or mass

Difference between throwing something in a horzional diection and dropping an object.

They hit the ground at the same time, both travel same vertical distance, but the ball thrown horizonallty travles a greater horizontal distanc than the ball dropped.

Circular motion

Think about a horse's horizontal motion on a carousel, such as the one in Figure 17. The horse moves in a circular path. Its speed remains constant, but it is accelerating because its direction of motion changes. The change in the direction of the horse's velocity is toward the center of the carousel. The horse's velocity is perpendicular to the inward acceleration. Acceleration toward the center of a curved or circular path is called centripetal acceleration. In the same way, Earth experiences centripetal acceleration as it orbits the Sun in a nearly circular path. Reading Check Define the term centripetal acceleration. Projectile motion If you have tossed a ball to someone, you have probably noticed that thrown objects do not travel in straight lines. They curve downward. That is why quarterbacks, dart players, and archers aim above their targets. Anything that is thrown or shot through the air is called a projectile. Earth's gravity causes projectiles to follow a curved path. Horizontal and vertical motion When you throw or shoot an object, such as the rubber band in Figure 18, the force exerted by your hand gives the object a horizontal velocity. For example, after releasing the rubber band, its horizontal velocity is constant. The rubber band does not accelerate horizontally. If there were no gravity, the rubber band would move along the straight dotted line in Figure 18. However, when you release a rubber band, gravity causes it to accelerate downward. The rubber band has an increasing vertical velocity. The result of these two motions is that the rubber band travels in a curve, even though its horizontal and vertical motions are completely independent of each other.

Speed

Think back to the mail truck moving down the street. You could describe the movement by the distance traveled or by the displacement. You might also want to describe how fast the truck is moving. To do this, you need to know how far it travels in a given amount of time. To describe how fast an object moves, scientist use the object's speed. Speed is the distance an object travels per unit of time. Calculating speed Any change over time is called a rate. For example, you could describe how quickly water is leaking from a tank by stating how many liters are lost each hour. This would be the rate of water leakage. If you think of distance as the change in position, then speed is the rate of change in position. Speed can be calculated from this equation. Speed Equation speed (in meters/second) = __ distance (in meters) time (in seconds) s = _ d t In SI units, distance is measured in meters and time is measured in seconds. Therefore, the SI unit for speed is meters per second (m/s). Sometimes, it is more convenient to express speed in other units, such as kilometers per hour (km/h). Table 2 shows the speeds of some common objects. Constant speed Suppose you are in a car traveling on a nearly empty freeway. You look at the speedometer and see that the car's speed hardly changes. If the car neither slows down nor speeds up, the car is traveling at a constant speed. If you are traveling at a constant speed, you can calculate your speed by dividing any distance interval over the time it took you to travel that distance. The speed you calculate will be the same regardless of the interval you choose. Changing speed Usually, speed is not constant. Think about riding a bicycle for a distance of 5 km. The bicycle's speed will vary, as in Figure 5. As you start out, your speed increases from 0 km/h to 20 km/h. You slow down to 10 km/h as you pedal up a steep hill and speed up to 30 km/h going down the other side of the hill. You stop for a red light, speed up again, and move at a constant speed for a while. Finally, you slow down and come to a stop. Checking your watch, you find that the trip took 15 min. How would you express your speed on such a trip? Would you use your fastest speed, your slowest speed, or some speed between the two? Two common ways of expressing a changing speed are average speed and instantaneous speed. Average speed Average speed is one way to describe the speed of the bicycle trip. Average speed is the total distance traveled divided by the total time of travel. It can be calculated using the relationships between speed, distance, and time. For the bicycle trip just described, the total distance traveled was 5 km and the total time was _1 4 h, or 0.25 h. Therefore, the average speed was Instantaneous speed Suppose you watch a car's speedometer, like the one in Figure 6, go from 0 km/h to 80 km/h. A speedometer shows how fast a car is going at one point in time, or at one instant. The speed shown on a speedometer is the instantaneous speed. Instantaneous speed is the speed at a given point in time. When something is speeding up or slowing down, its instantaneous speed is changing. The speed is different at every point in time. If an object is moving with constant speed, the instantaneous speed does not change. The speed is the same at every point in time.

Velocity and Acceleration

You are sitting in a car at a stoplight when the light turns green. The driver steps on the gas pedal and the car starts moving faster and faster. Just as speed is the rate of change of position, acceleration is the rate of change of velocity. When the velocity of an object changes, the object is accelerating. Remember that velocity includes the speed and direction of an object. Therefore, a change in velocity can be either a change in speed or a change in direction. Acceleration occurs when an object changes its speed, its direction, or both. When you think of acceleration, you probably think of something speeding up. However, an object that is slowing down also is accelerating, as is an object that is changing direction. Figure 15 shows the three ways an object can accelerate. Reading Check Identify three ways that an object can accelerate. Like velocity and momentum, acceleration has a direction. If you look at the car in Figure 15, you will see that when it is speeding up, its acceleration and velocity are in the same direction. When the car is slowing down, its acceleration is in the opposite direction of its velocity. When the car changes direction, the acceleration is not in the same direction or opposite direction as the car's velocity Speed-time graphs and acceleration When an object travels in a straight line and does not change direction, a graph of speed versus time can provide information about an object's acceleration. Figure 16 shows the speed-time graph of Tamara's car as she drives to the store. Just as the slope of a line on a distance-time graph is the object's speed, the slope of a line on a speed-time graph is the object's acceleration. For example, when Tamara pulls out of her driveway, the car's acceleration is 0.33 km/min2 , which is equal to the slope of the line from t = 0 to t = 0.5 min. Calculating acceleration Acceleration is the rate of change in velocity. To calculate the acceleration of an object, the change in velocity is divided by the length of the time interval over which the change occurred. The change in velocity is final velocity minus the initial velocity. If the direction of motion does not change and the object moves in a straight line, the size of the change in velocity can be calculated from the change in speed. Then, the acceleration of an object can be calculated from the following equation.

Motion and Position

You do not always need to see something move to know that motion has taken place. For example, suppose you look out a window and see a mail truck stopped next to a mailbox, as shown in Figure 1. One minute later, you look out again and see the same truck stopped farther down the street. Although you did not see the truck move, you know it moved because its position relative to the mailbox changed. Reference points A reference point is needed to determine the position of an object. In Figure 1, the reference point might be a mailbox. Motion is a change in an object's position relative to a reference point. How you describe an object's motion depends on the reference point that is chosen. For example, the description of the mail truck's motion in Figure 1 would be different if the reference point were a tree instead of a mailbox. After a reference point is chosen, a frame of reference can be created. A frame of reference is a coordinate system in which the position of the object is measured. The x-axis and y-axis of the reference frame are drawn so that they are perpendicular to each other and intersect the reference point.

Velocity

You turn on the radio and hear a news story about a hurricane. The storm, traveling at a speed of 20 km/h, is located 500 km east of your location. Should you worry? Unfortunately, you do not have enough information to answer that question. Knowing only the speed of the storm is not much help. Speed describes only how fast something is moving. To decide whether you need to move to a safer area, you also need to know the direction that the storm is moving. In other words, you need to know the velocity of the storm. Velocity includes the speed of an object and the direction of its motion. Velocity has the same units as speed, m/s. If you had been told that the hurricane was traveling straight toward your house at 20 km/h, you would have known to evacuate. Velocity and speed Because velocity depends on direction as well as speed, the velocity of an object can change even if the speed of the object remains constant. For example, the race cars in Figure 9 have constant speeds through the turn. Even though the speeds remain constant, their velocities changes because they change direction thoughout the turn. Same speed, different velocities It is possible for two objects to have the same speed but different velocities. For example, the two escalators pictured in Figure 10 are moving at the same speed but in opposite directions. The speeds of the two sets of passengers are the same, but their velocities are different because they are moving in different directions. Cars traveling in opposite directions on a road with the same speed also have different velocities.