Phys 1010 Module 4

Consider the air track in Figure 6.16. Suppose a gliding cart of mass 0.5 kg bumps into, and sticks to, a stationary cart of mass 1.5 kg. If the speed of the gliding cart before the collision is (v*before* or v1) how fast will the coupled carts glide after the collision?

(0.5kg)v1 = (0.5kg + 1.5 kg)v2 v2 = (0.5kg)v1 / (0.5+1.5)kg = 0.5v1/2 = v2/4 the velocity will be 1/4 as fast

a plane flys east bound in 4 hours and 2 minutes. upon returning west-bound, it takes 4 hours and 49 minutes. the distance covered is 1969 miles. what is the jet stream? (the effect of the air on the jet?)

-east bound = 1969 / 4.03 hours = 488 mph -west bound= 1969 / 4.82 hours = 402 mph jet stream = (488 - 402) //2 = 39 mph (the difference between two speeds divided by 2 is what the speed would be without win bc the wind has pushed it east and fought against it west)

scalar quantity

-has magnitude ex: mass, weight, speed

momentum

-inertia in motion (the force or speed w/ which sthg moves) -mass x velocity

vector

-something that has magnitude and direction -can be represented by an arrow example: velocity, force, acceleration

resultant

-the sum of two or more vectors -for vectors in the same direction, add arithmetically -for vectors in oppositve directions, subtract arithmetically -two vectors that don't act in the same or opposite direction: use the parallelogram rule -two vectors at right angles to each other: use the Pythagorean Theorem

Freddy Frog drops vertically from a tree onto a horizontally-moving skateboard. The skateboard slows. Give two reasons for the slowing: one in terms of force and the other in terms of momentum conservation

1. Freddy exerts friction on the surface of the skateboard, and a briefly act of force of friction slows the board 2. of accord with the law of conservation, the momentum before freddy lands should be equal to the momenutm after freddy lands; since the mass increases when freedy lands, the velocity must decrease (mV = Mv)

A fish swims toward and swallows a smaller fish at rest, as shown in the sketch. If the larger fish has a mass of 5 kg and swims 1 m/s toward the 1-kg fish, what is the velocity of the larger fish immediately after lunch? Ignore the effects of water resistance. Suppose the small fish in this example is not at rest, but swims toward the left at a velocity of 4 m/s. It swims in a direction opposite that of the larger fish—a negative direction, if the direction of the larger fish is considered positive.

1. net momentum before = net momentum after (5kg)(1m/s) + (1kg)(0m/s) = (5kg + 1kg)v 5 kg x m/s = (6kg)v v = 5/6 m/s 2. (5kg)(1m/s) + (1kg)(-4m/s) = (5kg + 1kg)v (5 kg x m/s) + (-4 kg x m/s) = (6kg)v (1 kg x m/s) = (6kg)v v = 1/6 m/s

A 7-N vector at an angle of 45° to the horizontal has a vertical component that is about _______.

5 N

rule for identifying action and reaction forces

Action: Object A exerts a force on object B. Reaction: Object B exerts a force on object A.

1st law

An object at rest tends to remain at rest; an object in motion tends to remain in motion at constant speed along a straight-line path. This property of objects to resist change in motion is called inertia. Mass is a measure of inertia. Objects will undergo changes in motion only in the presence of a net force.

To increase the momentum of an object

Apply the greatest force possible for as long as possible

Why doesn't a book sitting on a table ever accelerate "spontaneously" in response to the trillions of interatomic forces acting within it?

Every one of these interatomic forces is part of an action-reaction pair within the book. These forces add up to zero, no matter how many forces there are. This is what makes Newton's first law apply to the book. The book has zero acceleration unless an external force acts on it.

Consider the system of a single football. If you kick it, is there a net force to accelerate the system? If a friend kicks it at the same time with an equal and opposite force, is there a net force to accelerate the system?

If you kick the football, there is a net force to accelerate the system; if you and your friend kick it, there is not.

law of conservation of momentum

In the absence of an external force, the momentum of a system remains unchanged. ex: A cue ball hits an 8 ball head-on. Consider this event in three systems: (a) An external force acts on the 8-ball system, and its momentum increases. (b) An external force acts on the cue-ball system, and its momentum decreases. (c) No external force acts on the cue-ball + 8-ball system, and momentum is conserved (simply transferred from one part of the system to the other).

On a cold, rainy day, you find yourself in a car with a dead battery. You must push the car to move it and get it started. Why can't you move the car by remaining comfortably inside and pushing against the dashboard?

In this case, the system to be accelerated is the car. If you remain inside and push on the dashboard, the force pair you produce acts and reacts within the system. These forces cancel out as far as any motion of the car is concerned. To accelerate the car, there must be an interaction between the car and something external—for example, you on the outside pushing against the road and on the car.

A car accelerates along a road. Identify the force that moves the car.

It is the road that pushes the car along. Really! Only the road provides the horizontal force to move the car forward. How does it do this? The rotating tires of the car push back on the road (action). The road simultaneously pushes forward on the tires (reaction). Evidence for this is shown by the wavy pattern of bricks in Figure 5.20. The originally straight-lined bricks at the crosswalk of the two-lane road have been pushed backward to the right when cars accelerate forward to the left. How would the wave pattern of the bricks differ if cars braked to a rapid stop on them? We see physics everywhere!

How does the concept of inertia relate to the concept of momentum?

Momentum can be considered "inertia in motion."

Is it possible to push on something without that same something pushing back on you? Defend your answer.

No, because every push is one part of a two-push interaction. You can only push on something if that something pushes back on you. If it doesn't push back, you have not exerted a force on it!

Does a moving object have impulse?

No, impulse is not something an object has, like momentum. Impulse is what an object can provide or what it can experience when it interacts with some other object. An object cannot possess impulse just as it cannot possess force.

Does a high-speed baseball possess force?

No. A speeding baseball may exert a force on something when an interaction occurs, but it does not possess force as an entity in itself. In following chapters we'll learn that a speeding object possesses kinetic energy and momentum—but not force.

A classmate refers to the big fish swallowing a small fish at rest in the Problem Solving box and says that immediately after lunch the fattened fish has a change in both speed and momentum. Do you agree?

No. Agree about a change in speed, but NOT a change in momentum. In accord with all of the previous examples, the momentum of the two-fish system is the same before and after lunch. The lower speed of the big fish is compensated by its fatter belly, still maintaining its same momentum before lunch. Without careful thought, many readers miss this question.

When tossing a ball, you exert a force on the ball. Does part of that force remain with the ball after it leaves your hand?

No. In tossing a ball your hand presses on the ball while the ball presses on your hand (which is why tossing a ball with a sore hand can be painful). As soon as contact between your hand and the ball ceases, all force by your hand ceases also. From that point on, the ball encounters forces due to gravity and air resistance—but no part of a former force by your hand.

If you toss a ball horizontally while standing on a skateboard, you'll roll backward with as much momentum as you impart to the ball. Will you roll backward if you instead hold onto the "tossed ball" while going through the motions of tossing it?

No. Without an external impulse acting on you and the skateboard, you will not roll backward. You may jiggle a bit with the motions, but no net backward motion will occur. In terms of momentum, if no momentum is imparted to the ball, no net momentum will be imparted to you and your board.

If the forces that act on a cannonball and the recoiling cannon from which it is fired are equal in magnitude, why do the cannonball and cannon have very different accelerations?

Remember F = ma, and note that the cannon has a much greater mass than the cannon ball, so the cannon accelerates less for the same force.

(a) The force due to gravity on Nellie is shown by the downward vertical vector. An equal and opposite vector is needed for equilibrium, shown by the dashed vector. (b) This dashed vector is the diagonal of a parallelogram defined by the green lines. (c) Both rope tensions are shown by the constructed vectors. Tension is greater in the right rope, the one more likely to break. If the ropes are wider apart with less steep angles, how will rope tensions be affected?

Rope tensions will be greater. For example, when the ropes are at to the dashed line (the vertical), tension in each rope equals Nellie's weight. Beyond , tensions become greater. As the ropes approach being horizontal, tension increases toward a breaking point, no longer supporting Nellie's weight. (A child can safely hang on a sagging clothesline, but not on a tight nearly horizontal line—snap!)

For the same force, which cannon imparts a greater speed to a cannonball: a long-barreled cannon or a short-barreled cannon?

Speed will be greater for a cannonball fired from a long-barreled cannon because the force on the cannonball is exerted over a longer time, a greater impulse, which produces a greater change in the cannonball's momentum.

If a boxer is able to increase the duration of impact to three times as long by riding with the punch, by how much will the force of impact be reduced?

The force of impact will be only a third of what it would have been if he hadn't pulled back.

If the boxer instead moves into the punch so as to decrease the duration of impact by half, by how much will the force of impact be increased?

The force of impact will be two times greater than it would have been if he had held his head still.

How does a helicopter get its lifting force?

The helicopter exerts downward forces on air; the reaction forces of the air on the helicopter are upward and called lift.

A high-speed bus and an innocent bug have a head-on collision. The force of impact splatters the poor bug over the windshield. Is the corresponding force that the bug exerts against the windshield greater, less, or the same? Is the resulting deceleration of the bus greater than, less than, or the same as that of the bug?

The magnitudes of both forces are the same because they constitute an action-reaction force pair that makes up the interaction between the bus and the bug. The accelerations, however, are very different because the masses are different. The bug undergoes an enormous and lethal deceleration, while the bus undergoes a very tiny deceleration—so tiny that the very slight slowing of the bus is unnoticed by its passengers. But, if the bug were more massive—as massive as another bus, for example—the slowing down would unfortunately be very apparent.

A Volkswagen Bug and a Volvo truck have a head-on collision. Which statement is true?? The greater force acts on the Volkswagen Bug. The greater force acts on the Volvo truck Both forces are identical. The magnitudes of both forces are the same.

The magnitudes of both forces are the same.

We all know that a safety net is important for circus acrobats. What physics accounts for this safety?

The physics of net safety is the impulse-momentum relationship. In an accidental fall, momentum gained by the acrobat in falling comes to a halt. On a solid floor this would be devastating. Falling into a net that sags upon impact, the same change in momentum is spread over an extended time and with a correspondingly small force. Be glad the net sags when contact is made!

A Mars rover in a trial run moves at 12 km/h on Earth. Later on Mars' surface it moves at the same speed. In which location is its momentum greater?

The rover's momentum (mass x speed) is the same in both locations. Its weight will differ, but not its mass or momentum at the same speed.

A boxer being hit with a punch contrives to extend time for best results, whereas a karate expert delivers a force in a short time for best results. Isn't there a contradiction here?

There is no contradiction because the best results for each are quite different. The best result for the boxer is reduced force, which is achieved by maximizing time, and the best result for the karate expert is increased force delivered in minimum time.

When can a 1000-kg car and a 2000-kg truck have the same momentum?

They will have the same momentum when the car travels twice as fast as the truck. Then (1000 kg x 2v) for the car equals (2000 kg x v) for the truck. Or, if they are both at rest, they have the same momentum: zero.

Can you identify the action and reaction forces in the case of an object falling in a vacuum?

To identify a pair of action-reaction forces in any situation, first identify the pair of interacting objects involved—body A and body B. Body A, the falling object, is interacting (gravitationally) with body B, the whole Earth. So Earth pulls downward on the object (call it action), while the object pulls upward on Earth (reaction).

What does it mean to say momentum is conserved?

To say momentum is conserved is to say that whatever momentum a system possesses, if no external forces act on that system, its momentum perseveres—without change.

2nd law

When a net force acts on an object, the object will accelerate. The acceleration is directly proportional to the net force and inversely proportional to the mass. Symbolically, a = F/m. Acceleration is always in the direction of the net force. When objects fall in a vacuum, the net force is simply the pull of gravity—and the acceleration is g (the symbol g denotes that acceleration is due to gravity alone). When objects fall in air, the net force is equal to gravity's pull minus the force of air resistance, and the acceleration is less than g. If and when the force of air resistance equals the gravitational force on a falling object, acceleration terminates, and the object falls at constant speed (called terminal speed ).

3rd law

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Forces occur in pairs, one action and the other reaction, which together constitute the interaction between one object and the other. Action and reaction always occur simultaneously and act on different objects. Neither force exists without the other.

Newton's Third Law

Whenever one object exerts a force on a second object, the second object simultaneously exerts an equal and opposite force on the first. -To every action there is always an opposed equal reaction.

Does a moving object have momentum?

Yes, a moving object can possess momentum but, like velocity, only in a relative sense—that is, with respect to a frame of reference such as Earth's surface. For example, a fly inside a fast-moving airplane cabin may have a large momentum relative to Earth below, but it has very little momentum relative to the cabin.

A friend remarks that the impulse that halts an acrobat's momentum of fall is the same whether by a floor or a safety net. Do you agree?

Yes, agree with your friend. Anyone in free fall gains momentum, which is soon stopped by an impulse below. The amount of impulse is the same whether the time of changing momentum is quick or prolonged. Of course the force is another story

Newton's second law states that, if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs?

Yes, because no acceleration means that no change occurs in velocity or in momentum (mass x velocity). Another line of reasoning is simply that no net force means there is no net impulse and thus no change in momentum.

Newton's third law states that the force one body exerts on another is equal and opposite to the force the second body exerts on the first. Does it follow that the impulse one body exerts on another is equal and opposite to the impulse the second body exerts on the first?

Yes, because the interaction between both occurs during the same time interval. Because the times are equal and the forces are equal and opposite, the impulses Ft are also equal and opposite. Like force, impulse is a vector quantity and follows vector rules.

We know that Earth pulls on the Moon. Does it follow that the Moon also pulls on Earth?

Yes, both pulls make up an action-reaction pair of forces associated with the gravitational interaction between Earth and Moon. We can say that (a) Earth pulls on the Moon and (b) the Moon likewise pulls on Earth, but it is more insightful to think of this as a single interaction—both Earth and the Moon simultaneously pulling on each other, each with the same amount of force. You can't push or pull on something unless that something simultaneously pushes or pulls on you. That's the law!

Two kids blow peas from two drinking straws—a long straw and a short one. For the same breath, from which straw will a pea go farther?

a pea shot from a long straw should emerge at a greater speed and travel farther

a lunar vehicle is tested on earth at a aspeed of 10 km/h. when it travels at teh same speed on the moon, the momentum is a. the same b. less c. more d. zero

a. the same

Force vector components for a sled pulled at an upward angle _______.

are normally at right angles to each other

a ball is tossed into a bale of hay and comes to a stop; if instead it comes to a stop when hitting a sticky solid wall, the impulse needed to stop it is a. less b. the same

b

which of the following equatons most directly illustrates the safety value of automobile airbags? a. F = ma b. Ft = change in (mv) c. d = 1/2at^2 d. v = gt

b.

you run horizontally at 4 m/s in a vertically falling rain that falls at 4 m/s. relative to you, the raindrops are falling at an angle of a. 0 degrees b. 45 degrees c. 53 degrees d. 90 degrees

b. 45 degrees

If action is a foot kicking a soccer ball, the reaction is an equal force on the a. ball b. foot c. ground d. air drag of motion

b. foot

which will shoot farter w/ the same amount of powder? a. short cannon b. long cannon c. both the same

b. long cannon

A boulder falls due to gravity. The reaction to the force on the boulder is a. air resistance b. the boulder pulling up on earth c. the boulder being pulled downward by earth d. actually, all of these

b. the boulder pulling up on earth

a 1-kg ball has the same speed as a 10-kg ball, compared with the 1-kg ball, the 10-kg ball has a. less momentum b. the same momentum c. 10 times as much momentum

c.

if a car comes to a full stop when hitting a haystack and when hitting a stone wall, the change in momentum is greater for hitting the a. haystack b. stone wall c. same momentum change inboth cases d. none

c.

when a falling object bounces as it hits the ground a. the impulse on it is greater than for stopping it b. its change in momentum is greater than for stopping c. both of these d. none of these

c.

when the heck of an air-filled balloon is untied and air escapes, the balloon shoots through the air! the force that propels the balloon is provided by the a. surrounding air b. ejected air c. air still in the balloon d. ground beneath the balloon

c. air still in the balloon

When you jump vertically upward, strictly speaking, you cause Earth to a. also move upward with you b. remain stationary c. move downward d. move sideways

c. move downward

When both the force and time of contact are doubled, the impulse on an object is a. unchanged b. doubled c. quadrupled

c. quadrupled

Your friend says that impulse equals momentum. Your friend's statement is not correct, and the missing word is

change (in momentum)

impulse

change in momentum -force x time interval (impulese = Ft)

When momentum, or any quantity in physics, does not change, we say it is __________

conserved

when you jump from an elevate position to the ground below, the force you experience when landing does NOT depend on a. the jumping height b. the softness or hardness of the ground c. how much you bend your knees d. your attitude about jumping

d.

the resultant of a 30-N force and a 40-N force cannot possibly be a. 10 N b. 50 N c. 70 N d. 80 N

d. 80 N

What produces acceleration?

force

interaction forces depend on ______

friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force

Because impulses are ________ when an object bounces.

greater (The impulse required to bring an object to a stop and then to "throw it back again" is greater than the impulse required merely to bring the object to a stop)

A boxer's punch hits with more force when striking a heavier opponent. lighter opponent. same either way. none of the above

heavier opponent

The speed of an airplane caught in a right-angle crosswind decreases. remains unchanged. increases. cannot be estimated.

increases (Think vectors: Two velocity vectors at right angles to each other produce a resultant greater than either of the two vectors, just as the diagonal of a rectangle is longer than either of its two sides. The airplane will travel faster in a right-angle crosswind. In non-right-angle crosswinds, the resulting speed can be less.)

The force that propels a rocket is provided by gravity. Newton's laws of motion. its exhaust gases. the atmosphere against which the rocket pushes.

its exhaust gases

apply an impulse to an object and there will occur a change in _____

momentum

how difficult it is for something to change its motion

momentum

The idea of a short time of contact explains how a karate expert can split a stack of bricks with the blow of her bare hand. She brings her arm and hand swiftly against the bricks with considerable momentum. This momentum is quickly reduced when she delivers an impulse to the bricks. The impulse is the force of her hand against the bricks _________ by the time during which her hand makes contact with the bricks. By swift execution, she makes the time of contact very brief and correspondingly makes the force of impact huge.

multiplied

inelastic collision

one in which colliding objects become distorted and/or generate heat during the collision, and possibly stick together

elastic collision

one in which colliding objects rebound without lasting deformation or heat generation

If you were in a car that was out of control and you had to choose between hitting a concrete wall or a haystack, you wouldn't have to call on your knowledge of physics to make up your mind. Common sense tells you to choose the haystack. But, knowing the physics helps you to understand why hitting a soft object is entirely different from hitting a hard one. In the case of hitting either the wall or the haystack, your momentum is brought to zero by the same impulse. The same impulse does not mean the same amount of force or the same amount of time; rather, it means the same ________of force and time. A longer time interval reduces the force and decreases the resulting deceleration.

product

the process of determining the components of a vector is called ______

resolution

momentum conservation

states that when two objects collide in a isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object1 is equal to the momentum gained by object 2.

the relationship between the diagonal of a square and the length of one of its sides

the diagonal is the (square root of 2) times the length of the side of the square

The force that propels a rocket is that provided by _______.

the expelled gas pushing on the rocket

compared w/ the momentum of a 200 lb man running 10 mph, the momentum of a 2000-lb car moving 1 mph is a. zero b. the same c. greater d. less

the same P = mv

A mosquito has a collision with the windshield of a massive high-speed truck. The force of impact on the mosquito is ________ the force on the truck, and the acceleration of the mosquito is ________ the deceleration of the truck.

the same as, more than

A massive truck and a golf cart have a head-on collision with equal amounts of force. The least amount of acceleration occurs for a. the truck b. the cart, if it is initially at rest c. the cart, whether at rest or moving d. neither, for they undergo the same acceleration

the truck

Who wins a tug-of-war: those who pull harder on the rope or those who push harder against the floor?

those who push harder against the floor

to decrease the force during momentum, you have to increase the

time interval

t o f: A force sustained for a long time produces more change in momentum than does the same force applied briefly.

true

t o f: a moving boulder has more momentum than a stone rolling at the same speed

true

true or false: a fast boulder has more momentum than a slow boulder

true

true or false: every force is part of an interaction between one thing and another; These forces are equal in magnitude (have the same strength) and opposite in direction, and they constitute a single interaction.

true

true or false: forces only exist in pairs, equal and opposite

true

true or false: if no net force or net impulse acts on a system, the momentum of that system cannot change.

true

true or false: internal impuleses always cancel out, only external impuleses change momentum

true

true or false: you can't push something unless that something pushes back on you!

true

true or false: for an object to accelerate, it needs an external force (a force not apart of the system)

true! Inside a football are trillions and trillions of interatomic forces at play. They hold the ball together, but they play no role in accelerating the ball. Although every one of the interatomic forces is part of an action-reaction pair within the ball, they combine to zero, no matter how many of them there are. A force external to the football, like a kick, is needed to accelerate it.

true or false: The greater the impulse exerted on something, the greater will be its change in momentum.

true! impulse = change in momentum (F)(change of time) = (change of (mass)(velocity))

true or false: momentum is conserved in collisions

true! net momentum before = net momentum after

Is momentum a vector or scalar quantity?

vector quantity

component vector

when given a diagonal vector, it can be resolved into 2 component vectors perpendicular to each other (a horizontal and vertical)