Physics Exam II
From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only F, how long would it have to be applied to reach the same final speed?
8 seconds. In the first case, the acceleration acts over time T = 4 s to give velocity v = aT. In the second case, the force is half, therefore the acceleration is also half, so to achieve the same final speed, the time must be doubled.
My weight is 800 Newtons... When I jump up, what is the force that I exert on the earth while I am in the air?
800 Newtons, up toward me.
Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart?
After the cart is released, there is no longer a force in the x-direction. This does not mean that the cart stops moving!! It simply means that the cart will continue moving with the same velocity it had at the moment of release. The initial push got the cart moving, but that force is not needed to keep the cart in motion.
A box sits on a flat board. You lift one end of the board, making an angle with the floor. As you increase the angle, the box will eventually begin to slide down. Why?
As the angle increases, the component of weight parallel to the plane increases and the component perpendicular to the plane decreases (and so does the normal force). Because friction depends on the normal force, we see that the friction force gets smaller and the force pulling the box down the plane gets bigger.
A child whirls a ball in a vertical circle. Assuming the speed of the ball is constant (an approximation) , when would the tension in the cord connected to the ball be greatest?
At the bottom of the circle.
When I stand on a scale, is the normal force, which is equal and opposite to the gravitational force, an example of NIII law forces?
Yes
You're on a Ferris wheel moving in a vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. How does N change at the top of the Ferris wheel when you are in motion?
You are in circular motion, so there has to be a centripetal force pointing inward. At the top, the only two forces are mg (down) and N (up), so N must be smaller than mg.
Suppose an object is accelerated by a force of 100 N. Suddenly a second force of 100 N in the opposite direction is exerted on the object, so that the forces cancel. The object...
Continues at the velocity it had before the second force was applied.
Earth's orbit around the Sun is slightly elliptical. Thus, Earth actually gets closer to the Sun during part of the year. What happens to Earth's orbital speed when it is closer to the Sun?
Earth's orbital speed is greater when it is closer to the Sun than when it is farther from the Sun.
Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. Who makes it to the bottom first? Kathleen starts at a lower height than Paul.
Even though they both have the same final velocity, Kathleen is at a lower height than Paul for most of her ride. Thus, she always has a larger velocity during her ride and therefor arrives earlier.
A force is required to keep an object moving in a straight line.
False. A force gives an acceleration and, in fact, an object in motion will stay in motion in a straight line without any other forces. This is N1.
An object receiving two equal and opposite vertical forces must be at rest.
False. The object is not necessarily at rest due to the vertical forces. It may have horizontal motion. This is N1.
You swing a ball at the end of string in a vertical circle. Because the ball is in circular motion there has to be a centripetal force. At the top of the ball's path, what is Fc equal to?
Fc points toward the center of the circle (i.e., downward in this case). The weight vector points down and the tension (exerted by the string) also points down. The magnitude of the net force, therefore, is Fc = T + mg.
A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?
Four.
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
Friction acts in the opposite direction to the displacement, so the work is negative.
A box sliding on a frictionless flat surface runs into a fixed spring, which compresses a distance x to stop the box. If the initial speed of the box were doubled, how much would the spring compress in this case?
If v doubles, x doubles
Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? Push from behind vs. pull from front.
In case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that frictional force is proportional to normal force.
We just decided that the cart continues with constant velocity. What would have to be done in order to have the cart continue with constant acceleration?
In order to achieve a non-zero acceleration, it is necessary to maintain the applied force. The only way to do this would be to continue pushing the cart as it moves down the track. This will lead us to a discussion of Newton's Second Law.
From rest, we step on the gas of our Ferrari, providing a force F for 40 m, speeding it up to a final speed of 50 km/hr. If the same force would be applied for 80 m, what final speed would the car reach?
In the first case, the acceleration acts over a distance x = 40 m, to give a final speed of v2 = 2ax. In the 2nd case, the distance is doubled, so the speed increases by a factor of sqrt 2.
A force F acts on mass M for a time interval T, giving it a final speed v. If the same force acts for the same time on a different mass 2M, what would be the final speed of the bigger mass?
In the first case, the acceleration acts over time T to give velocity v = aT. In the second case, the mass is doubled, so the acceleration is cut in half; therefore, in the same time T, the final speed will only be half as much.
A bear sling, is used in some national parks for placing backpackers' food out of the reach of bears. As the backpacker raises the pack by pulling down on the rope, the force F needed:
Increases but the rope always sags where the pack hangs.
A person stands on a scale in an elevator. His apparent weight will be the greatest when the elevator...
Is accelerating upward.
The Moon does not crash into the Earth because...
It is freely falling but it has a high tangential velocity.
A penny is placed on a turntable which is spinning clockwise. If the power to the turntable is turned off, which arrow best represents the direction of the acceleration of the penny at point P while the turntable is still spinning but slowing down?
It will continue in the same direction as the turntable
A space shuttle in orbit around the Earth carries its payload with its mechanical arm. Suddenly, the arm malfunctions and releases the payload. What will happen to the payload?
It will remain in the same orbit with the shuttle.
A truck is traveling horizontally to the right. When the truck starts to slow down, the crate on the (frictionless) truck bed starts to slide.
No direction. The net force is zero.
Tension and Work A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?
No work is done because the force acts in a perpendicular direction to the displacement.
A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible?
No work is done if the direction of motion is perpendicular to the force.
Engine #1 produces twice the power of engine #2. Can we conclude that engine #1 does twice as much work as engine #2?
No!! We cannot conclude anything about how much work each engine does. Given the power output, the work will depend upon how much time is used. For example, engine #1 may do the same amount of work as engine #2, but in half the time.
Therefore, when you go from the 1st floor up to the 3rd floor, does your weight get a lot smaller (~1/10th as big)?
No, because the distance from the earth's surface isn't what matters.
There is a gravitational force exerted on me, by the earth, directed down. According to Newton's 3rd law, there is also a force exerted...
On the earth, by me, directed up.
A Ping-Pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the Ping-Pong ball leaves the track, which path will it follow?
Once the ball leaves the tube, there is no longer a force to keep it going in a circle. Therefore, it simply continues in a straight line, as Newton's First Law requires!
You push very hard on a heavy desk, trying to move it. You do work on the desk:
Only if it starts moving.
Antilock brakes keep the car wheels from locking and skidding during a sudden stop. Why does this help slow the car down?
Static friction is greater than sliding friction, so by keeping the wheels from skidding, the static friction force will help slow the car down more efficiently that the sliding friction that occurs during a skid.
A hypothetical planet has a mass one-third of and a radius three times that of Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity on Earth?
The acceleration due to gravity is g/27.
In the collision between the car and the truck, which has the greater acceleration?
The acceleration is given by F/m so the car has the larger acceleration, because it has the smaller mass.
The same net force is applied to two different objects. The second object has twice the mass of the first object. Compare the acceleration of the two objects.
The acceleration of object 1 is twice the acceleration of object 2.
In the International Space Station which orbits Earth, astronauts experience apparent weightlessness because...
The astronauts and the station are in free fall towards the center of the Earth.
A block of mass m rests on the floor of an elevator that is accelerating upward. What is the relationship between the force due to gravity and the normal force on the block?
The block is accelerating upward, so it must have a net upward force. The forces on it are N (up) and mg (down), so N must be greater than mg in order to give the net upward force!
Two equal-mass rocks tied to strings are whirled in horizontal circles. The radius of circle 2 is twice that of circle 1. If the period of motion is the same for both rocks, what is the tension in cord 2 compared to cord 1?
The centripetal force in this case is given by the 1 tension, so T = mv2/r. For the same period, we find that v2 = 2v1 (and this term is squared). However, for the denominator, we see that r2 = 2r1 which gives us the relation T2 = 2T1.
In general, how does the coefficient of static friction compare to the coefficient of kinetic friction for the same two materials?
The coefficient of static friction is greater than the coefficient of kinetic friction.
A mass m is placed on an inclined plane (m > 0) and slides down the plane with constant speed. If a similar block (same m) of mass 2m were placed on the same incline, it would:
The component of gravity acting down the plane is double for 2m. However, the normal force (and hence the friction force) is also doubled (the same factor). This means the two forces still cancel to give it a net force of zero.
While driving fast around a sharp right turn, you find yourself pressing against the car door. What is happening?
The door is exerting a rightward force on you.
Elastic Potential Energy How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm?
The elastic potential energy is 1/2kx2. The elastic PE is four times greater than in the first case. Thus, the work required to stretch the spring is also four times greater.
You are trying to push your stalled car. Although you apply a horizontal force of 400 N to the car, it doesn't budge, and neither do you. Which force(s) must also have a magnitude of 400 N?
The force exerted by the car on you, the friction force exerted by the road on you, and the friction force exerted by the car on the road.
What can you say about the force of gravity Fg acting on a stone and a feather?
The force of gravity (weight) depends on the mass of the object!! The stone has more mass, and therefore more weight.
A golf ball is hit with a golf club. While the ball flies through the air, which forces act on the ball? Neglect air resistance.
The force of gravity acting on the ball.
A planet of mass m is a distance d from Earth. Another planet of mass 2m is a distance 2d from Earth. Which force vector best represents the direction of the total gravitation force on Earth?
The force of gravity on the Earth due to m is greater than the force due to 2m, which means that the force component pointing down in the figure is greater than the component pointing to the right.
A large truck collides head-on with a small car. The car is severely damaged as a result of the collision. According to Newton's third law, how do the forces acting between the truck and car compare during the collision?
The force on the truck is equal to the force on the car.
What causes the row boat to move forward?
The force the water exerts on the paddle.
You are pushing a heavy box across a rough floor. When you are initially pushing the box and it is accelerating...
The force you exert on the box is equal to the force of the box pushing back on you.
In outer space, a bowling ball and a Ping-Pong ball attract each other due to gravitational forces. How do the magnitudes of these attractive forces compare
The forces are equal and opposite by Newton's Third Law!
In outer space, gravitational forces exerted by a bowling ball and a Ping-Pong ball on each other are equal and opposite. How do their accelerations compare?
The forces are equal and opposite—this is Newton's Third Law!! But the acceleration is F/m and so the smaller mass has the bigger acceleration.
You drive your dad's car too fast around a curve and the car starts to skid. What is the correct description of this situation?
The friction force between tires and road provides the centripetal force that keeps the car moving in a circle. If this force is too small, the car continues in a straight line!
Two objects attract each other gravitationally. If the distance between their centers decreases by a factor of 2, how does the gravitational force between them change?
The gravitational force increases by a factor of 4.
Ryan walked to a cliff and dropped a stone. Neglecting any effects due to the air as it falls vertically, which one of the following is the reaction force to the Earth's gravity on the stone?
The gravitational force of the stone on the Earth.
Matt, in the foreground of (Figure 1), is able to move the large truck because...
The ground exerts a greater friction force on Matt than it does on the truck.
A packing crate is sitting at rest on an inclined loading ramp. How does the magnitude of the force of static friction compare to the other forces acting on the crate?
The magnitude of the force of static friction is equal to the magnitude of the component of the weight of the crate parallel to the inclined ramp.
An object is hanging by a string from the ceiling of an elevator. The elevator is moving upward with a constant speed. What is the magnitude of the tension in the string?
The magnitude of the tension in the string is equal to the magnitude of the weight of the object.
An object is hanging by a string from the ceiling of an elevator. The elevator is slowing down while moving upward. What is the magnitude of the tension in the string?
The magnitude of the tension in the string is less than the magnitude of the weight of the object.
Two planets, planet A and planet B, have the same surface gravity. However, planet B has twice the radius of planet A. How does the mass of planet B compare to the mass of planet A?
The mass of planet B is four times the mass of planet A.
An astronaut on Earth kicks a bowling ball and hurts his foot. A year later, the same astronaut kicks a bowling ball on the Moon with the same force. His foot hurts...
The masses of both the bowling ball and the astronaut remain the same, so his foot feels the same resistance and hurts the same as before.
An object is moving with constant velocity. Which of the following best describes the force(s) acting on the object?
The net force acting on the object is zero.
An object moves in a circular path at a constant speed. What is the direction of the net force acting on the object?
The net force is directed toward the center of the circular path.
A rider in a "barrel of fun" finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?
The normal force of the wall on the rider provides the centripetal force needed to keep her going around in a circle. The downward force of gravity is balanced by the upward frictional force on her, so she does not slip vertically.
A constant net force acts on an object. Which of the following best describes the object's motion?
The object is moving with a constant acceleration.
An object is at rest on a tabletop. Earth pulls downward on this object with a force equal in magnitude to mg. If this force serves as the action force, what is the reaction force in the action-reaction pair?
The object pulling upward on Earth.
An object is moving in the absence of a net force. Which of the following best describes the object's motion?
The object will continue to move with a constant velocity.
You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?
The passenger has the tendency to continue moving in a straight line. From your perspective in the car, it feels like you are being thrown to the right, hitting the passenger door.
During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?
The passenger has the tendency to continue moving in a straight line. There is a centripetal force, provided by the door, that forces the passenger into a circular path.
A Ping-Pong ball is shot into a circular tube that is lying flat (horizontal) on a table-top. When the Ping-Pong ball exits the tube, which path will it follow.
The ping pong ball will continue in a straight line after exit.
A planet is discovered orbiting around a star in the galaxy Andromeda at the same distance from the star as Earth is from the Sun. If that star has four times the mass of our Sun, how does the orbital period of the planet compare to Earth's orbital period?
The planet's orbital period will be one-half Earth's orbital period.
What would happen if you were to accelerate up in an elevator?
The scale's force would get bigger. This is because, To accelerate up requires... a net force directed up
What would happen if you were to accelerate down in an elevator?
The scale's force would get smaller. This is because, to accelerate down requires a net force directed down.
The normal force on an extreme skier descending a very steep slope can be zero if...
The slope is vertical (90º) and he leaves the slope (no longer touches the snow).
A box of weight 100 N is at rest on a floor where static friction = 0.4. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move?
The static friction force has a maximum of msN = 40 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction.
You tie a rope to a tree and you pull on the rope with a force of 100 N. What is the tension in the rope?
The tension in the rope is the force that the rope "feels" across any section of it (or that you would feel if you replaced a piece of the rope). Because you are pulling with a force of 100 N, that is the tension in the rope.
You lift a book with your hand in such a way that it moves up at constant speed. While it is moving, what is the total work done on the book?
The total work is zero because the net force acting on the book is zero. The work done by the hand is positive, and the work done by gravity is negative. The sum of the two is zero.
Two satellites orbit the Earth in circular orbits of the same radius. One satellite is twice as massive as the other. Which statement is true about the speeds of these satellites?
The two satellites have the same speed.
An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?
The velocity and acceleration vectors are perpendicular.
If you weigh yourself at the equator of Earth, would you get a bigger, smaller, or similar value than if you weigh yourself at one of the poles?
The weight that a scale reads is the normal force exerted by the floor (or the scale). At the equator, you are in circular motion, so there must be a net inward force toward Earth's center. This means that the normal force must be slightly less than mg. So the scale would register something less than your actual weight.
A book is lying at rest on a table. The book will remain there at rest because:
There are forces acting on the book, but the only forces acting are in the y-direction. Gravity acts downward, but the table exerts an upward force that is equally strong, so the two forces cancel, leaving no net force.
Why does a satellite in a circular orbit travel at a constant speed?
There is no component of force acting along the direction of motion of the satellite.
Two tug-of-war opponents each pull with a force of 100 N on opposite ends of a rope. What is the tension in the rope?
This is literally the identical situation to the previous question. The tension is not 200 N !! Whether the other end of the rope is pulled by a person, or pulled by a tree, the tension in the rope is still 100 N !!
Forces always come in pairs.
True. The pair of forces are always action and reaction force pairs. This is N3.
An objects acceleration is proportional to the forces acting on it.
True. This is N2.
A very large truck sits on a frozen lake. Assume there is no friction between the tires and the ice. A fly suddenly smashes against the front window. What will happen to the truck?
When the fly hit the truck, it exerted a force on the truck (only for a fraction of a second). So, in this time period, the truck accelerated (backward) up to some speed. After the fly was squashed, it no longer exerted a force, and the truck simply continued moving at constant speed.
When you climb up a rope, the first thing you do is pull down on the rope. How do you manage to go up the rope by doing that?
When you pull down on the rope, the rope pulls up on you! It is actually this upward force by the rope that makes you move up! This is the "reaction" force (by the rope on you) to the force that you exerted on the rope. And voilá, this is Newton's Third Law.
A 50-N crate sits on a horizontal floor where the coefficient of static friction between the crate and the floor is 0.50 . A 20-N force is applied to the crate acting to the right.
20 N to the left.
From rest, we step on the gas of our Ferrari, providing a force F for 4 secs. During this time, the car moves 50 m. If the same force would be applied for 8 secs, how much would the car have traveled during this time?
200 meters. In the first case, the acceleration acts over time T = 4 s to give a distance of x = aT2 (why is there no v0T term?). In the 2nd case, the time is doubled, so the distance is quadrupled because it goes as the square of the time.
We step on the brakes of our Ferrari, providing a force F for 4 secs. During this time, the car moves 25 m but does not stop. If the same force would be applied for 8 secs, how far would the car have traveled during this time?
25 < x <50 meters. In the first 4 secs, the car has still moved 25 m. However, because the car is slowing down, in the next 4 secs it must cover less distance. Therefore, the total distance must be more than 25 m but less than 50 m.
Which of the following point towards the center of the circle in uniform circular motion?
Acceleration and net force.
A small car collides with a large truck. Which experiences the greater impact force?
According to Newton's Third Law, both vehicles experience the same magnitude of force.
Paul and Kathleen start from rest at the same time on frictionless water slides with different shapes. At the bottom, whose velocity is greater?Kathleen starts at a lower height than Paul.
Because both start from the same height, they have the same velocity at the bottom.
Mike performed 5 J of work in 10 secs. Joe did 3 J of work in 5 secs. Who produced the greater power?
Because power = work / time, we see that Mike produced 0.5 W and Joe produced 0.6 W of power. Thus, even though Mike did more work, he required twice the time to do the work, and therefore his power output was lower.
Mike applied 10 N of force over 3 m in 10 seconds. Joe applied the same force over the same distance in 1 minute. Who did more work?
Both exerted the same force over the same displacement. Therefore, both did the same amount of work. Time does not matter for determining the work done.
A car drives at steady speed around a perfectly circular track. What is pointed inward?
Both the acceleration and net force on the car point inward.
Which pulls harder gravitationally, the Earth on the Moon, or the Moon on the Earth? Which accelerates more?
Both the same; the Moon.
To pull an old stump out of the ground, you and a friend tie two ropes to the stump. You pull on it with a force of 500 N to the north while your friend pulls with a force of 450 N to the northwest. The total force from the two ropes is...
Less than 950 N.
When a skier skis down a hill, the normal force exerted on the skier by the hill is...
Less than the weight of the skier.
