Momentum - AP Physics C Electricity & Magnetism
Card 0 of 20
A 5000kg pickup truck with a 500kg load is traveling at a velocity of 
. It crashes with a 3000kg car traveling in the opposite direction with a velocity of 
. The truck (together with its load) and the car stick together after they crash. What is their velocity after the collision?
A 5000kg pickup truck with a 500kg load is traveling at a velocity of
We need to use conservation of momentum to solve this problem.
Initially, the pickup truck moves at 
. The load moves together with the truck so the load is also moving at 
.
We can calculate the truck-load momentum as follows:
Note that this is the sum of the truck's momentum AND the load's momentum. We are looking at is as a whole since they are moving together.
The car moves at 
. Be careful with signs here! The problem says it moves in the opposite direction. We used a positive velocity for the truck/load, so the velocity of the car should be negative if it is moving in the opposite direction. We can also see from the diagram that the car is moving to the left.
Therefore, we have that the momentum for the car as:
We can find the initial momentum of the system (truck, load, and car) via simple addition:
After the collision, we know that all three objects move together, so they all move with the same velocity. Therefore we can express the momentum of the system after the collision as follows:
is the velocity of the objects after the collision. This is the sum of the momentum of all three objects; we were able to simplify the equation because they all move with the same velocity.
By conservation of momentum we know that the momentum of the system before the collision is equal to the momentum of the system after the collision.
Use this to solve for the final velocity.
We need to use conservation of momentum to solve this problem.
Initially, the pickup truck moves at
We can calculate the truck-load momentum as follows:
Note that this is the sum of the truck's momentum AND the load's momentum. We are looking at is as a whole since they are moving together.
The car moves at
Therefore, we have that the momentum for the car as:
We can find the initial momentum of the system (truck, load, and car) via simple addition:
After the collision, we know that all three objects move together, so they all move with the same velocity. Therefore we can express the momentum of the system after the collision as follows:
By conservation of momentum we know that the momentum of the system before the collision is equal to the momentum of the system after the collision.
Use this to solve for the final velocity.
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Two identical atoms, A and B, are at rest some distance apart in a vacuum.
If atom A moves at a constant velocity, 
, toward atom B, which of the following is most likely to be true?
Two identical atoms, A and B, are at rest some distance apart in a vacuum.
If atom A moves at a constant velocity,
Assuming the atoms have the same mass, a collision between atoms in a vacuum is most nearly an elastic collision. This means the kinetic energy of the system is conserved and when they collide, all of the kinetic energy in atom A will be transferred perfectly to atom B. So just after collision, atom A will have velocity 
and atom B will have velocity 
. Note that momentum is always conserved.
Assuming the atoms have the same mass, a collision between atoms in a vacuum is most nearly an elastic collision. This means the kinetic energy of the system is conserved and when they collide, all of the kinetic energy in atom A will be transferred perfectly to atom B. So just after collision, atom A will have velocity
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A pickup truck with a mass of 
is travelling along a highway at a velocity of 
when the brakes suddenly give out. In order to slow the vehicle, a mass of sand will be dumped into the back of the pickup truck by another vehicle.
Assuming no outside forces are acting on the system, how many 
of sand would need to be dumped in the rear of the pickup truck to reduce its speed to 
?
A pickup truck with a mass of
Assuming no outside forces are acting on the system, how many
Because of conservation of momentum, the product of the initial mass and velocity should equal the final mass and velocity. The equation for conservation of momentum is:
The initial mass of the truck is 
The initial velocty is 
The final velocity is 
Plug in known values to the conservation of momentum equation.
Simplify.
Note that while necessary, the final mass is not our final answer. The final mass, 
, is the mass of the truck, 
, and the mass of the sand added to the truck, 
.
The mass of the truck is known so set up an equation and solve for the mass of sand added to the truck.
Because of conservation of momentum, the product of the initial mass and velocity should equal the final mass and velocity. The equation for conservation of momentum is:
The initial mass of the truck is
The initial velocty is
The final velocity is
Plug in known values to the conservation of momentum equation.
Simplify.
Note that while necessary, the final mass is not our final answer. The final mass,
The mass of the truck is known so set up an equation and solve for the mass of sand added to the truck.
Compare your answer with the correct one above
A pickup truck with a mass of 
is travelling along a highway at a velocity of 
when the brakes suddenly give out. In order to slow the vehicle, a mass of sand will be dumped into the back of the pickup truck by another vehicle.
It turns out the truck can only take on an additional 
payload without risking structural damage. By how much will the speed of the truck be reduced after 
of sand is dumped in the truck bed?
A pickup truck with a mass of
It turns out the truck can only take on an additional
The equation for conservation of momentum is:
Given:
Plug in given values into the conservation of momentum equation.
Simplify.
![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/383221/gif.latex "120000kg\cdot 1\frac{km}{hr}=4800kg\cdot v_{f}\")
Subtract the final velocity from the initial velocity to find change in speed (since these velocities are in the same direction).
.
The equation for conservation of momentum is:
Given:
Plug in given values into the conservation of momentum equation.
Simplify.
Subtract the final velocity from the initial velocity to find change in speed (since these velocities are in the same direction).
Compare your answer with the correct one above
A 5000kg pickup truck with a 500kg load is traveling at a velocity of . It crashes with a 3000kg car traveling in the opposite direction with a velocity of . The truck (together with its load) and the car stick together after they crash. What is their velocity after the collision?
A 5000kg pickup truck with a 500kg load is traveling at a velocity of
We need to use conservation of momentum to solve this problem.
Initially, the pickup truck moves at . The load moves together with the truck so the load is also moving at .
We can calculate the truck-load momentum as follows:
Note that this is the sum of the truck's momentum AND the load's momentum. We are looking at is as a whole since they are moving together.
The car moves at . Be careful with signs here! The problem says it moves in the opposite direction. We used a positive velocity for the truck/load, so the velocity of the car should be negative if it is moving in the opposite direction. We can also see from the diagram that the car is moving to the left.
Therefore, we have that the momentum for the car as:
We can find the initial momentum of the system (truck, load, and car) via simple addition:
After the collision, we know that all three objects move together, so they all move with the same velocity. Therefore we can express the momentum of the system after the collision as follows:
is the velocity of the objects after the collision. This is the sum of the momentum of all three objects; we were able to simplify the equation because they all move with the same velocity.
By conservation of momentum we know that the momentum of the system before the collision is equal to the momentum of the system after the collision.
Use this to solve for the final velocity.
We need to use conservation of momentum to solve this problem.
Initially, the pickup truck moves at
We can calculate the truck-load momentum as follows:
Note that this is the sum of the truck's momentum AND the load's momentum. We are looking at is as a whole since they are moving together.
The car moves at
Therefore, we have that the momentum for the car as:
We can find the initial momentum of the system (truck, load, and car) via simple addition:
After the collision, we know that all three objects move together, so they all move with the same velocity. Therefore we can express the momentum of the system after the collision as follows:
By conservation of momentum we know that the momentum of the system before the collision is equal to the momentum of the system after the collision.
Use this to solve for the final velocity.
Compare your answer with the correct one above
Two identical atoms, A and B, are at rest some distance apart in a vacuum.
If atom A moves at a constant velocity, , toward atom B, which of the following is most likely to be true?
Two identical atoms, A and B, are at rest some distance apart in a vacuum.
If atom A moves at a constant velocity,
Assuming the atoms have the same mass, a collision between atoms in a vacuum is most nearly an elastic collision. This means the kinetic energy of the system is conserved and when they collide, all of the kinetic energy in atom A will be transferred perfectly to atom B. So just after collision, atom A will have velocity and atom B will have velocity . Note that momentum is always conserved.
Assuming the atoms have the same mass, a collision between atoms in a vacuum is most nearly an elastic collision. This means the kinetic energy of the system is conserved and when they collide, all of the kinetic energy in atom A will be transferred perfectly to atom B. So just after collision, atom A will have velocity
Compare your answer with the correct one above
A pickup truck with a mass of is travelling along a highway at a velocity of when the brakes suddenly give out. In order to slow the vehicle, a mass of sand will be dumped into the back of the pickup truck by another vehicle.
Assuming no outside forces are acting on the system, how many of sand would need to be dumped in the rear of the pickup truck to reduce its speed to ?
A pickup truck with a mass of
Assuming no outside forces are acting on the system, how many
Because of conservation of momentum, the product of the initial mass and velocity should equal the final mass and velocity. The equation for conservation of momentum is:
The initial mass of the truck is
The initial velocty is
The final velocity is
Plug in known values to the conservation of momentum equation.
Simplify.
Note that while necessary, the final mass is not our final answer. The final mass, , is the mass of the truck, , and the mass of the sand added to the truck, .
The mass of the truck is known so set up an equation and solve for the mass of sand added to the truck.
Because of conservation of momentum, the product of the initial mass and velocity should equal the final mass and velocity. The equation for conservation of momentum is:
The initial mass of the truck is
The initial velocty is
The final velocity is
Plug in known values to the conservation of momentum equation.
Simplify.
Note that while necessary, the final mass is not our final answer. The final mass,
The mass of the truck is known so set up an equation and solve for the mass of sand added to the truck.
Compare your answer with the correct one above
A pickup truck with a mass of is travelling along a highway at a velocity of when the brakes suddenly give out. In order to slow the vehicle, a mass of sand will be dumped into the back of the pickup truck by another vehicle.
It turns out the truck can only take on an additional payload without risking structural damage. By how much will the speed of the truck be reduced after of sand is dumped in the truck bed?
A pickup truck with a mass of
It turns out the truck can only take on an additional
The equation for conservation of momentum is:
Given:
Plug in given values into the conservation of momentum equation.
Simplify.
Subtract the final velocity from the initial velocity to find change in speed (since these velocities are in the same direction).
.
The equation for conservation of momentum is:
Given:
Plug in given values into the conservation of momentum equation.
Simplify.
Subtract the final velocity from the initial velocity to find change in speed (since these velocities are in the same direction).
Compare your answer with the correct one above
A pitcher throws a 0.15kg baseball at 
towards the batter and the batter hits the ball with his bat. The ball leaves the bat in the opposite direction at a speed of 
. Calculate the impulse experienced by the baseball.
A pitcher throws a 0.15kg baseball at
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is 
and its final velocity is 
, where the negative sign indicates that the ball is traveling in the opposite direction. Also, m = 0.15kg. The impulse on the ball can be calculated below.
The negative sign tells that the force on the baseball is opposed to the original momentum.
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is
The negative sign tells that the force on the baseball is opposed to the original momentum.
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Which of the following could be used as units of impulse?
Which of the following could be used as units of impulse?
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Compare your answer with the correct one above
A baseball player hits a 
baseball initially moving at 
, returning it at a speed of 
along the same path. If the ball was in contact with the bat for 
, what magnitude of force did the ball experience during the moment of contact?
A baseball player hits a
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Compare your answer with the correct one above
A pitcher throws a 0.15kg baseball at towards the batter and the batter hits the ball with his bat. The ball leaves the bat in the opposite direction at a speed of . Calculate the impulse experienced by the baseball.
A pitcher throws a 0.15kg baseball at
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is and its final velocity is , where the negative sign indicates that the ball is traveling in the opposite direction. Also, m = 0.15kg. The impulse on the ball can be calculated below.
The negative sign tells that the force on the baseball is opposed to the original momentum.
To calculate the impulse, know that it is equal to the change in momentum.
Write the impulse equation in terms of mass and velocity.
In our case, the initial velocity of the baseball is
The negative sign tells that the force on the baseball is opposed to the original momentum.
Compare your answer with the correct one above
Which of the following could be used as units of impulse?
Which of the following could be used as units of impulse?
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Relevant equations:
Impulse is defined as change in momentum, so has the same units as momentum. These units can easily be found using the given equations.
Compare your answer with the correct one above
A baseball player hits a baseball initially moving at , returning it at a speed of along the same path. If the ball was in contact with the bat for , what magnitude of force did the ball experience during the moment of contact?
A baseball player hits a
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Relevant equations:
Evaluate the impulse based on the mass and change of velocity.
Use the total impulse and time in the second equation.
Solve for the average force.
Compare your answer with the correct one above
In an inelastic collision, which combination of quantities is conserved?
In an inelastic collision, which combination of quantities is conserved?
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
Compare your answer with the correct one above
In an elastic collision, what combination of quantities is conserved?
In an elastic collision, what combination of quantities is conserved?
The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
The primary difference between elastic and inelastic collisions is the conservation of kinetic energy. Kinetic energy is conserved in elastic collisions, but is not conserved in inelastic collisions. Momentum is always conserved, regardless of collision type. Mass is conserved regardless of collision type as well, but the mass may be deformed by an inelastic collision, resulting in the two original masses being stuck together.
There is no description in the problem reagrding position, so we cannot comment on potential energy.
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A 200kg car is traveling west at 
. It collides with a 150kg car that was at rest. Following the collision, the second car moves with a velocity of 
west. Assuming that the collision is elastic, what is the velocity of the first car after the collision?
A 200kg car is traveling west at
The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for 
:
Since the final velocity is positive, we know that the car is still traveling toward the west.
The collision is assumed to be elastic, so both momentum and kinetic energy are conserved. Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we know that the car is still traveling toward the west.
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Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of 
east, while the other travels with a velocity of 
west. The two cars collide and stick together as one mass. What is the magnitude and direction of the resulting velocity?
Two train cars, each with a mass of 2400 kg, are traveling along the same track. One car is traveling with a velocity of
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for 
. Keep in mind that we must designate a positive direction and a negative direction. We will use east as positive and west as negative.
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
Use the law of conservation of momentum:
Momentum is the product of velocity and mass:
We can expand the summation for the initial and final conditions:
Note that we are working with an inelastic collision, meaning that the two masses stick together after the collision. Because of this, they will have the same final velocity:
Use the given values to fill in the equation and solve for
Since the final velocity is positive, we can determine that they train cars are traveling toward the east.
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A 
bullet is fired at 
at a block of wood that is moving in the opposite direction at a speed of 
. The bullet passes through the block and emerges with the speed of 
, while the block ends up at rest.
What is the mass of the block?
A
What is the mass of the block?
This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that 
is 
or 
, 
is 
, 
is unknown, 
is 
.
is 
and 
is 
.
With all this information given, the only unknown is 
.
Plugging everything in, we get:
This problem is a conservation of momentum problem. When doing these types of problems, the equation to jump to is:
It is given to us that
With all this information given, the only unknown is
Plugging everything in, we get:
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In an inelastic collision, which combination of quantities is conserved?
In an inelastic collision, which combination of quantities is conserved?
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
In a perfectly inelastic collision, the two colliding objects stick together; the two colliding objects deform, but mass is still conserved. Momentum is conserved during collisions of any sort, including inelastic collisions.
Kinetic energy is reduced during an inelastic collision, and is only conserved in elastic collisions. During inelastic collisions, some kinetic energy is lost to the environment in the form of heat or sound.
The problem does not give any information regarding position, and thus we cannot comment on any changes or lack of changes in potential energy.
Compare your answer with the correct one above