Physics Chapter 6 Momentum
Suppose a ball of putty moving horizontally with 1 kg·m/s of momentum collides with and sticks to an identical ball of putty moving vertically with 1 kg·m/s of momentum. What is the magnitude of their combined momentum?
1.41 kg·m/s
A green truck is moving to the right. A red truck is moving to the left with a speed of 6 m/s. The mass of the red truck is 1,000 kg and the mass of the green truck is 3,000 kg. How fast must the green truck be moving such that ,if it collides head-on with the red truck and the two trucks stick together, the final velocity of the two trucks is zero?
2 m/s. Since the green truck is three times more massive, it needs a speed 1/3 that of the red truck in order for its momentum to be equal and opposite that of the red truck.
A green truck is moving to the right with an initial speed of 9 m/s. It collides head-on with a yellow truck, initially at rest. After the collision, the two trucks are stuck together. The green truck is twice as massive as the yellow truck. Immediately after the collision, what is the speed of the two trucks?
6 m/s. Since the final mass of the two trucks is three halves the mass of the green truck, the final speed of the two trucks needs to be two thirds of the initial speed of the green truck
A green truck is moving to the right with a speed of 10 m/s. A red truck is moving to the right with a speed of 2 m/s. The mass of the two trucks are equal. If the two trucks have an inelastic collision, what is the speed of the two trucks right after the collision?
6 m/s. The velocities don't add together. If they did, the total momentum would be much larger than the initial momentum of the system. Since momentum is conserved and the masses of the trucks are the same, the final velocity is equal to the average of the two velocities.
How much impulse stops a 60-kg carton sliding at 4.0 m/s when it meets a rough surface?
60 kg × 4 m/s = J = 240 N × s. The question is looking for the force of friction the carton receives upon meeting the rough surface.
Which undergoes the greatest change in momentum: A) a baseball that is caught, B) a baseball that is thrown, or C) a baseball that is caught and then thrown back, if all of the baseballs have the same speed just before being caught and just after being thrown?
A baseball that is caught then thrown back.
In which of these processes is the momentum of the object conserved? An asteroid (the object) accelerates steadily toward the moon. A car (the object) pulls away from a stop sign. A cyclist (the object) collides with a pedestrian. A train (the object) goes around a curve at a steady speed. A skydiver (the object) with her parachute deployed falls toward the ground at a steady speed.
A skydiver (the object) with her parachute deployed falls toward the ground at a steady speed. Having a quantity be conserved means that it doesn't change. In order for momentum to be conserved it must have an unchanging mass and velocity (including both speed and direction).
A moving object has: momentum. energy. speed. all of the above.
All of the above.
What is the relationship between impulse and momentum
An impulse indicates a change in momentum. Impulse = change in momentum. Ft = ∆(mv)
Which has more momentum: a 1-ton car moving at 100 km/h or a 2-ton truck moving at 50 km/h?
Both have the same momentum (1 ton × 100 km/h = 2 ton × 50 km/h).
elastic collision
Collision in which colliding objects rebound without lasting deformation or heat generation.
inelastic collision
Collision in which the colliding objects become distorted and/or generate heat during the collision and possible stick together.
Two hockey players collide on the ice. Which statement reflects how we can apply conservation of momentum to this situation?
During the very brief collision the total momentum of the two players (the system) is a conserved quantity. The momentum of each player is not itself a conserved quantity since they both experience a net force during the collision. It is the total momentum of the system (the two players, in this case) that can be considered to be conserved since the system experiences no net external force. However, we can only consider it to be conserved if we restrict ourselves to just the brief collision between the players. If we extend our time to include time before and after the collision, the players might use their skates to change speed or direction (using external forces) and the total momentum of the two skaters would no longer be conserved.
An ostrich egg of mass m is tossed at a speed v into a sagging bed sheet and is brought to rest in a time t. If the mass of the egg is 0.80 kg , its initial speed is 2.4 m/s , and the time to stop is 0.20 s, find the average force on the egg.
F = (.80 * .20) ÷ .20 Force = 9.6 N.
How is the impulse-momentum relationship related to Newton's second law?
F net=ma ma=mΔv/Δt so Ft=Δmv
True or False: The momentum of a big, massive truck is always greater than the momentum of a person riding a bicycle.
False. Since momentum is mass times velocity, the truck could have very little momentum if it is moving very, very slowly.
Distinguish between force and impulse.
Force is a push or pull. An impulse is the product of the force acting on an object and the time during which it acts.
Impulse formula
Force × time = m∆v
An ostrich egg of mass m is tossed at a speed v into a sagging bed sheet and is brought to rest in a time t. Find the force acting on the egg when it hits the sheet.
From Ft = mv. F = mv/t
When does impulse equal momentum?
Generally, impulse equals a change in momentum. If the initial momentum of an object is zero when the impulse is applied, final momentum = impulse applied. And, if an object is brought to rest, initial momentum = impulse delivered.
Imagine that you replace the block in the video with a happy or sad ball identical to the one used as a pendulum, so that the sad ball strikes a sad ball and the happy ball strikes a happy ball. The target balls are free to move, and all the balls have the same mass. In the collision between the sad balls, how much of the balls' kinetic energy is dissipated?
Half of it. The collision between the sad balls is completely inelastic, and due to the conservation of momentum, the velocity of the balls after the collision will be half the velocity of the incoming ball before the collision. The expression for kinetic energy is ½mv², and while there is double the mass moving after the collision as before, the decrease in velocity by a factor of two results in the overall kinetic energy being half its initial value.
How does Dr. Hewitt break the piece of wood?
He causes a change in momentum of his hand over a short period of time.
How is Dr. Hewitt able to break a piece of wood in his demonstration?
He moves his hand very quickly.
relationship of impulse and momentum
Impulse is equal to the change in the momentum of the object that impulse acts upon. In symbol notion, Ft = ∆mv
Cassy breaks a stack of bricks with her hand. How does the force that Cassy exerts on the bricks compare with the force exerted on her hand?
In accord with Newton's third law, the forces are equal. Only the resilience of the human hand and the training she has undergone to toughen her hand allow this feat to be performed without broken bones.
Conservation of momentum
In the absence of a net external force, the momentum of ab object or system of objects is unchanged. mv (before event) = mv(after event)
law of conservation of momentum
In the absence of an external force, the momentum of a system remains unchanged. Hence, the momentum before an event involving only internal forces is equal to the momentum after the event. mass × velocity (before event) = mass × velocity (after event)
What would Dr. Hewitt need to have done to exert an even greater force than he did in his karate demonstration?
Increase the change in momentum, and decrease the time duration.
momentum
Inertia in motion. The product of the mass and the velocity of an object (provided the speed is much less than the speed of light). Has magnitude and direction and therefore is a vector quantity. Also called linear momentum, and abbreviated p. p = mv
What does it mean to say that momentum (or any quantity) is conserved?
It means that momentum doesn't change. Momentum before an event = momentum after an event.
When you are struck by a moving object, is it favorable that the object makes contact with you over a short time or over a long time? Explain.
Long contact time decreases the magnitude of the average force and is favorable.
In which is momentum conserved: an elastic collision or an inelastic collision?
Momentum is conserved for both. Net mv(before) = Net mv (after)
Can you produce a net impulse on an automobile if you sit inside and push on the dashboard? Can the internal forces within a soccer ball produce an impulse on the soccer ball that will change its momentum?
No impulses must be exerted from outside of the system. Internal impulses do not cause momentum.
Can an object have more than one momentum at a given moment?
No, an object always has one unique velocity and one unique mass at any given moment.
When a dish falls, will the change in momentum be less if it lands on a carpet than if it lands on a hard floor?
No, both are the same. the momentum becomes zero in both cases, so both change by the same amount. Although the momentum change and impulse are the same, the force is less when the time of momentum change is extended.
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.
When a cannonball is fired, momentum is conserved for the system cannon + cannonball. Would momentum be conserved for the system if momentum were not a vector quantity? Explain.
No. If velocity was not a vector quantity, then it would always have a positive value. So when the cannon and the cannonball went in opposite directions, their momentums would not cancel each other out, but would instead double the overall momentum of the system.
Now, consider the collision between two happy balls described in Part A. How much of the balls' kinetic energy is dissipated?
None of it. In this scenario, since the collision between the happy balls is elastic, the kinetic energy will be conserved, and thus none will be dissipated.
During a complex collision between many objects, including object A and object C, the impulse exerted on object A by object C is equal to __________. the impulse exerted on object C by object A None of the listed responses is correct. the change in the momentum of object A the change in the momentum of object C
None of these are correct. Impulse is a vector quantity. Because of Newton's third Law the two objects must exert equal and opposite forces on each other. Since they will do so for equal amounts of time they will exert impulses with equal magnitudes but opposite directions on each other. The change in momentum of an object equals the net impulse exerted on it during the collision, which is not the same as any single impulse it experiences.
Impulse units
N×s
cyclotron
Particle accelerator that imparts high energy to charged particles such as protons, deuterons, and helium ions.
impulse
Product of force and the time interval during which the force acts. Impulse produces change in momentum. Impulse = Ft = ∆(mv)
Relative
Regarded in relation to something else, depending on point of view or frame of reference. Sometimes referred to as "with respect to".
Why is it advantageous to roll with the punch in boxing?
Rolling with the punch increases contact time, which decreases the force.
Railroad car A rolls at a certain speed and makes a perfectly elastic collision with car B of the same mass. After the collision, car A is observed to be at rest. How does the speed of car B compare with the initial speed of car A?
Since the cars have the same mass, Car B must have the same velocity as Car A did by conservation of momentum.
Suppose a ball of putty moving horizontally with 1 kg⋅m/s of momentum collides with and sticks to an identical ball of putty moving vertically with 1 kg⋅m/s of momentum. What is the magnitude of their combined momentum?
Since the two masses stick together, they will move at a diagonal direction of 45°, at a rate of √2 kg⋅m/s
Playing in the rain, a little girl tackles a little boy. Just before she tackles him, the boy is running east at 3 m/s and the girl is running south at 4 m/s. After the tackle, the girl holds on and the two slide on the wet grass. Our system consists of just the two children. Before the tackle, in roughly what direction does the total momentum of the system point?
Somewhere south of east, but we can't be any more specific than that because the mass of the children are not specified. If one is larger than the other it would affect the momentum of the tackle.
neutron star
Star that has undergone a gravitational collapse in which electrons are compressed into protons to form neutrons.
inelastic
Term applied to a material that does not return to its original shape after it has been stretched or compressed.
conserved
Term applied to a physically quantity such as momentum, energy, or electric charge, that remains unchanged during interactions.
Why is a force that is applied for a short time more effective in karate?
The average force is increased. A force that is applied for a short time is able to deliver a high impact force for the same change in momentum. If the time is small the force will be greater Ft=mv.
For the same force, why does a long cannon impart more speed to a cannonball than a short cannon?
The force is applied for a longer time in the long cannon.
What occurs when there is less time in an impulse?
The force of impact is large.
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. Impacts of this kind account for many knockouts.
How will the impulse resulting from the impact differ if her hand bounces back upon striking the bricks?
The impulse will be greater if her hand bounces from the bricks upon impact. If the time of impact is not correspondingly increased, a greater force will then be exerted on the bricks (and her hand!).
For the same force, which cannon imparts a greater impulse to a cannonball: a long cannon or a short one?
The long cannon imparts a greater impulse because the force acts over a longer time. (A greater impulse produces a greater change in momentum, so a long cannon imparts more speed to a cannonball than a short cannon.)
Suppose a gliding cart of mass .5kg bumps into and sticks to a stationary cart of a mass 1.5 kg. If the speed of the gliding cart before the collision is Vbefore, how fast will the coupled carts glide after the collision.
The momemtum of the .5kg cart will = the momentum of the carts stuck together. So .5kg × V₁ = (.5kg + 1.5kg) × V₂. You're searching for V₂, so therfore: V₂ = .5kg × .5kg × V₁ / 2kg. = .25 × V₁. Therefore the new speed is only ¼ of the original speed. This makes sense because the new mass is also 4 times as large.
Playing in the rain, a little girl tackles a little boy. Just before she tackles him, the boy is running east at 3 m/s and the girl is running south at 4 m/s. After the tackle, the girl holds on and the two slide on the wet grass. Our system consists of just the two children. Immediately after the tackle, what can we say about how the momenta of each child compare?
The momentum of both children will be in the same direction. Because the girl holds on after the tackle the two children will be moving in the same direction at the same speed. Thus we know they will each have momentum in the same direction. Unless the two children happen to have exactly the same mass, they will not have equal momenta. Since the system had a non-zero momentum just before the collision, the system cannot have zero momentum after the collision. That would violate the conservation of momentum.
Two asteroids are flying through space, each with an unknown momentum, p1 and p2. Which of these is a true statement about the x-component of their total momentum, p sub x?
The momentum of the x component must have a magnitude between zero and the sum of the magnitudes of their individual momenta. Meaning 0 ≤ |p of x | ≤ (|p₁| + |p₂|).
Two trucks of equal mass and equal magnitude of velocity are about to collide head on, predict what will happen.
The trucks will stick together after the collision and not move.
Two trucks are about to collide head on. The green truck has a velocity that is smaller than that of the red truck. What will happen.
The trucks will stick together and move in the direction of the red truck because it has greater velocity.
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.
You observe two identical balls of putty headed directly toward each other at the same speed; what can you say about their total momentum?
They have zero total momentum.
Momentum of an isolated system
Total momentum is constant. No momentum in or out; momentum can be neither created nor destroyed
Two cars experience a collision on a city road. Both drivers are using their brakes when the cars hit. Which statement is true?
Using the impulse approximation, conservation of momentum can be applied to the very brief time period of the collision itself (giving approximate results). The collision between the cars involves brief forces that are much stronger than the forces of friction exerted on the cars by the road. Thus if we apply conservation of momentum to a very thin "slice" of time surrounding the collision, the total momentum of the two cars will not change very much and will be approximately conserved.
Single car moving at 10 m/s collides with another car of the same mass, m at rest. What is the final velocity of the system?
V = 5 m/s.
Is it correct to say that, if no net impulse is exerted on a system, then no change in the momentum of the system will occur?
Yes, always.
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 × 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 a cannon exerts on a cannonball is equal and opposite to the force the cannonball exerts on the cannon. Does it follow that the impulse the cannon exerts on the cannonball is equal and opposite to the impulse the cannonball exerts on the cannon?
Yes, because the interaction between both occurs during the same time interval. Since the times are equal and the forces are equal and opposite, the impulses Ft are also equal and opposite. Impulse is a vector quantity and can be canceled.
Does a moving object have momentum?
Yes, but, like velocity, in a relative sense—that is, with respect to a frame of reference, usually Earth's surface. The momentum possessed by a moving object with respect to a stationary point on Earth may be quite different from the momentum it possesses with respect to another moving object.
A fast moving car hitting a haystack or hitting a cement wall produces different results? Do they both experience the same change in momentum? The same impulse? The same force?
Yes, they experience the same change in momentum and impulse. Although stopping the momentum is the same whether done slowly or quickly, the force on impact is vastly different.
If some quantity, let's call it "Z," is conserved for a certain system, during a certain process, that means __________.
Z for that system does not change in any way during that process. This also must mean that any change in Z for parts of the system during the process is offset by an equal but opposite change for the Z of other parts of the system.
When the force that produces an impulse acts for twice as much time, the impulse is
doubled. Impulse = force × time. So same force x 2time = an impulse that is twice as great
When the speed of an object is doubled, its momentum
doubles. Because momentum = mass and velocity. If velocity is doubled so is acceleration.
A cannon fires a cannonball horizontally. Right after the cannonball is fired, the magnitude of the momentum of the cannonball is ________ that of the cannon. Ignore friction between the cannon and the ground.
equal to. Due to conservation of momentum, the momentum of the cannon must be equal and opposite than of the fired cannonball.
The impulse approximation is used in situations where __________.
external forces on the system are present, but they are small compared to the large, brief internal forces between parts of the system
Momentum is conserved in the absence of
external forces. Internal systems that have no outside forces have no change in momentum.
A boxer rides with the punch so as to reduce _______.
force
Freight car A is moving toward identical freight car B that is at rest. When they collide, both freight cars couple together. Compared with the initial speed of car A, the speed of the coupled freight cars is
half. After the collision, the mass of the moving freight car has doubled. Twice the mass = half the velocity.
Cassy can get more force on the bricks she breaks with a blow of her bare hand when _______.
her hand is made to bounce from the bricks.
A cannonball shot from a cannon with a long barrel will emerge with greater speed because the cannonball receives a greater: average force. impulse. both. none
impulse. The average force on the cannonball will be the same for a short or long barreled cannon. The longer barrel provides a longer time for the force to act and therefore a greater impulse.
What are the two ways to increase impulse?
increase the force or increase the time the force is applied
Momentum __________.
is a vector, with a magnitude and a direction
A slowly moving ship can have a greater momentum than a fast-moving racing car when _______.
its mass times velocity is greater than that of the car.
The units for momentum are
kg * m/s
Momentum units are
kg × m/s
momentum forumla
mass x velocity
momentum formula
mass × velocity
If two cars have the same mass and speed they __________.
might have the same momentum but might not because direction is not specified.
If the equally massive cars of the preceding question stick together after colliding inelastically, how does their speed after the collision compare with the initial speed of car A?
momentum = mass x velocity. After collison, the two cars become one unit and stick together. Since mass is doubled, velocity is only at ½.
An orange car is moving eastward with a speed of 10 m/s. A purple car is moving northward with the same speed. The two cars undergo an inelastic collision. The orange car has a mass of 3000 kg and the purple car has a mass of 1000 kg. After the collision, the two cars?
move off in a direction nearly eastward, but they also have a small northward component (east, northeast). Since the magnitude of momentum in the east direction is three times greater than that in the north direction, the final velocity needs a higher component in the eastward direction.
The momentum of a system is conserved during a certain process only if __________.
no net external force is exerted on the system during that process
What is the momentum of an 8.8-kg bowling ball rolling at 1.8 m/s ? Round to two significant figures.
p = 16 kg×m / s
What impulse occurs when an average force of 10 N is exerted on a cart for 2.5 s ?
p = 25 kg ×m / s
The quantity that is called impulse can be measured by the _______.
product of force and time.
When a big fish swims into an oncoming smaller fish and swallows it, the momentum of the two-fish system _______.
remains the same.
An orange car is moving eastward with a speed of 10 m/s. A purple car is moving northward with the same speed. The two cars undergo an inelastic collision. If the cars have the same mass, how fast are the two cars moving (together) after the collision?
roughly 7 m/s. The momentum is conserved in each direction, so the final speed in the northward direction is 5 m/s (since the combined mass is twice as high as either car) and the final speed in the eastward direction is 5 m/s. So the final speed is equal to the hypotenuse of a triangle with the two other sides being 5 m/s.
A green ball is moving to the right with an initial speed of 5 m/s. It collides head-on with a yellow ball, initially at rest. Both balls have the same mass. After the collision,
the green ball is stationary and the yellow ball moves to the right with a speed of 5 m/s. Both momentum and energy is conserved.
The change in an object's momentum during a certain time interval is equal to __________.
the net force exerted on the object times the duration of the time interval
During a large, multi-object collision that involves object C, the change in the momentum of object C is equal to __________.
the net impulse exerted on object C The impulse momentum theorem says that any change in an object's momentum always occurs due to a net impulse exerted on that object.
Which has a greater momentum: a heavy truck at rest or a moving skateboard?
the skateboard
Ball 1 has a mass of 2m and speed v, while ball 2 has mass m and speed 2v. Both balls are moving at 45º angles with respect to the vertical. Our system consists of just the two balls and is isolated from external forces. Just before the collision __________.
the total horizontal component of the momentum of the system is zero. The magnitude of each ball's momentum is the same and since they have symmetric angles relative to the vertical direction, they will both have the same magnitude x-component, given by |p sub x| = p x cosine of 45°. Since their horizontal components of momentum are oppositely directed, they will cancel out and the total horizontal component of the momentum of the system is zero.
Two balls are about have a head-on collision. Ball A has a mass m and speed of 2v, whereas ball B has mass 2m and speed v. Our system consists of just the two balls and is isolated from external forces. Just after the collision ______.
the total momentum of the system must be zero. Because of their initial masses, speeds, and directions, the two balls end up having initial momenta that have equal magnitudes but opposite directions. Thus the total momentum of the system before the collision is zero.
To impart the greatest momentum to an object, should you exert the largest force possible, extend that force for as long a time as possible, or both? Explain.
use the largest force for as long a time as possible Ft=mV
When two vehicles collide, momentum is conserved _______.
whether the collision is elastic or inelastic.