Other Potential Energy - AP Physics 1
Card 1 of 36
A 
block is sliding on a horizontal frictionless floor at a speed of 
and runs into a horizontal spring. The spring has a spring constant of 
. What is the maximum compression of the spring after the collision?
A
Tap to reveal answer
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
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A bungie jumper is attached to a bungie with a constant of 
. The unstretched length of the bungie is 
. If the bungie stretches a maximum of 
passed its unstretched length, what is the mass of the jumper?
A bungie jumper is attached to a bungie with a constant of
Tap to reveal answer
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
is the length of the unstretched bungie, and 
is the distance the bungie stretches. Plugging this into the original expression, we get:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
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A roller coaster car is at the top of the first hill, 100 m above the ground. It starts from rest and goes down the hill due to the force of gravity. What is the speed of the car at the bottom of the hill along the ground? (No energy is lost in this system.)
A roller coaster car is at the top of the first hill, 100 m above the ground. It starts from rest and goes down the hill due to the force of gravity. What is the speed of the car at the bottom of the hill along the ground? (No energy is lost in this system.)
Tap to reveal answer
This is a conservation of energy problem. First, we can set initial energy equal to final energy due to the law of conservation of energy. Therefore, 
can be broken into its components:
Because the initial velocity is 
and the final height is 0 m, the equation can then be simplified:
From here, we can rearrange the equation to solve for the final velocity:
From here, we can plug in the known values and calculate the final velocity of the roller coaster car:
This is a conservation of energy problem. First, we can set initial energy equal to final energy due to the law of conservation of energy. Therefore,
Because the initial velocity is
From here, we can rearrange the equation to solve for the final velocity:
From here, we can plug in the known values and calculate the final velocity of the roller coaster car:
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In a baseball game, a baseball of mass 0.145 kg is thrown at 
towards the batter. The batter then hits the ball, and it flies over the pitcher's head at 
. What was the impulse of the ball?
In a baseball game, a baseball of mass 0.145 kg is thrown at
Tap to reveal answer
First, let's set up an axis for this problem. Have the positive direction be towards the outfield and the pitcher and the negative direction be towards home plate and the batter. Next, identify the given information: 
(This value is negative because the ball is moving towards home plate.)
(This value is positive because the ball is moving towards the outfield.)
The impulse of the baseball is equal to its change in momentum:
Momentum is equal to mass times velocity, so this equation can be simplified further:
By plugging in the given information, we can solve for the impulse:
First, let's set up an axis for this problem. Have the positive direction be towards the outfield and the pitcher and the negative direction be towards home plate and the batter. Next, identify the given information:
The impulse of the baseball is equal to its change in momentum:
Momentum is equal to mass times velocity, so this equation can be simplified further:
By plugging in the given information, we can solve for the impulse:
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A block of mass 
is oscillating on a spring with spring constant 
. The block-spring system is on a level, frictionless desk. If the block passes through the equilibrium position with velocity 
, how far will the spring stretch (in meters)?
A block of mass
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At the equilibrium position, all of the energy in the system is in the form of kinetic energy. When the spring is fully stretched, all of the system's energy is in spring potential energy. Since no energy is leaving the system, we can just set the kinetic energy equal to the potential to find the distance the spring will stretch. Kinetic energy is 
and spring potential energy is 
Setting these equal we get:
Plugging in our values we get:
At the equilibrium position, all of the energy in the system is in the form of kinetic energy. When the spring is fully stretched, all of the system's energy is in spring potential energy. Since no energy is leaving the system, we can just set the kinetic energy equal to the potential to find the distance the spring will stretch. Kinetic energy is
Setting these equal we get:
Plugging in our values we get:
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A spring of rest length 
is compressed to 
. A block of mass 
is placed on top. When the spring is released, the block flies to a maximum height of 
above the ground. Determine the spring constant.
A spring of rest length
Tap to reveal answer
Use conservation of energy:
Initially there is no gravitational energy, and in the final state there is no longer spring potential energy.
Solve for the spring constant:
Plugging in values:
Use conservation of energy:
Initially there is no gravitational energy, and in the final state there is no longer spring potential energy.
Solve for the spring constant:
Plugging in values:
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A spring of rest length 
is used to hold up a 
rocket from the bottom as it is prepared for the launch pad. The spring compresses to 
. Determine the potential energy of the spring.
A spring of rest length
Tap to reveal answer
The spring force is going to add to the gravitational force to equal zero.
Plugging in values:
Solving for 
Using
Plugging in values:
The spring force is going to add to the gravitational force to equal zero.
Plugging in values:
Solving for
Using
Plugging in values:
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A golf ball is dropped from a height of 
, what is the velocity of the golf ball when it is halfway down its descent?
A golf ball is dropped from a height of
Tap to reveal answer
Energy is conserved throughout this entire problem, before the ball is dropped all of the energy is in the form of potential energy represented by 
, halfway down there is potential and kinetic energy
present. Energy at the start must be equal to the energy halfway down which gives rise to the equation:
where 
is the initial height and 
is the height halfway down. Mass can be cancelled out and the heights and gravity constant can be plugged in in order to find velocity. Plugging in the values:
Energy is conserved throughout this entire problem, before the ball is dropped all of the energy is in the form of potential energy represented by
where
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A horizontal spring is oscillating with a mass sliding on a perfectly frictionless surface. If the amplitude of the oscillation is 
and the mass has a value of 
and a velocity at the rest length of 
, determine the spring constant.
A horizontal spring is oscillating with a mass sliding on a perfectly frictionless surface. If the amplitude of the oscillation is
Tap to reveal answer
Using conservation of energy:
Plugging in values:
Solving for 
Using conservation of energy:
Plugging in values:
Solving for
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A block is sliding on a horizontal frictionless floor at a speed of and runs into a horizontal spring. The spring has a spring constant of . What is the maximum compression of the spring after the collision?
A
Tap to reveal answer
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
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A bungie jumper is attached to a bungie with a constant of . The unstretched length of the bungie is . If the bungie stretches a maximum of passed its unstretched length, what is the mass of the jumper?
A bungie jumper is attached to a bungie with a constant of
Tap to reveal answer
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
is the length of the unstretched bungie, and is the distance the bungie stretches. Plugging this into the original expression, we get:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
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A roller coaster car is at the top of the first hill, 100 m above the ground. It starts from rest and goes down the hill due to the force of gravity. What is the speed of the car at the bottom of the hill along the ground? (No energy is lost in this system.)
A roller coaster car is at the top of the first hill, 100 m above the ground. It starts from rest and goes down the hill due to the force of gravity. What is the speed of the car at the bottom of the hill along the ground? (No energy is lost in this system.)
Tap to reveal answer
This is a conservation of energy problem. First, we can set initial energy equal to final energy due to the law of conservation of energy. Therefore, can be broken into its components:
Because the initial velocity is and the final height is 0 m, the equation can then be simplified:
From here, we can rearrange the equation to solve for the final velocity:
From here, we can plug in the known values and calculate the final velocity of the roller coaster car:
This is a conservation of energy problem. First, we can set initial energy equal to final energy due to the law of conservation of energy. Therefore,
Because the initial velocity is
From here, we can rearrange the equation to solve for the final velocity:
From here, we can plug in the known values and calculate the final velocity of the roller coaster car:
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In a baseball game, a baseball of mass 0.145 kg is thrown at towards the batter. The batter then hits the ball, and it flies over the pitcher's head at . What was the impulse of the ball?
In a baseball game, a baseball of mass 0.145 kg is thrown at
Tap to reveal answer
First, let's set up an axis for this problem. Have the positive direction be towards the outfield and the pitcher and the negative direction be towards home plate and the batter. Next, identify the given information:
(This value is negative because the ball is moving towards home plate.)
(This value is positive because the ball is moving towards the outfield.)
The impulse of the baseball is equal to its change in momentum:
Momentum is equal to mass times velocity, so this equation can be simplified further:
By plugging in the given information, we can solve for the impulse:
First, let's set up an axis for this problem. Have the positive direction be towards the outfield and the pitcher and the negative direction be towards home plate and the batter. Next, identify the given information:
The impulse of the baseball is equal to its change in momentum:
Momentum is equal to mass times velocity, so this equation can be simplified further:
By plugging in the given information, we can solve for the impulse:
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A block of mass is oscillating on a spring with spring constant . The block-spring system is on a level, frictionless desk. If the block passes through the equilibrium position with velocity , how far will the spring stretch (in meters)?
A block of mass
Tap to reveal answer
At the equilibrium position, all of the energy in the system is in the form of kinetic energy. When the spring is fully stretched, all of the system's energy is in spring potential energy. Since no energy is leaving the system, we can just set the kinetic energy equal to the potential to find the distance the spring will stretch. Kinetic energy is and spring potential energy is
Setting these equal we get:
Plugging in our values we get:
At the equilibrium position, all of the energy in the system is in the form of kinetic energy. When the spring is fully stretched, all of the system's energy is in spring potential energy. Since no energy is leaving the system, we can just set the kinetic energy equal to the potential to find the distance the spring will stretch. Kinetic energy is
Setting these equal we get:
Plugging in our values we get:
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A spring of rest length is compressed to . A block of mass is placed on top. When the spring is released, the block flies to a maximum height of above the ground. Determine the spring constant.
A spring of rest length
Tap to reveal answer
Use conservation of energy:
Initially there is no gravitational energy, and in the final state there is no longer spring potential energy.
Solve for the spring constant:
Plugging in values:
Use conservation of energy:
Initially there is no gravitational energy, and in the final state there is no longer spring potential energy.
Solve for the spring constant:
Plugging in values:
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A spring of rest length is used to hold up a rocket from the bottom as it is prepared for the launch pad. The spring compresses to . Determine the potential energy of the spring.
A spring of rest length
Tap to reveal answer
The spring force is going to add to the gravitational force to equal zero.
Plugging in values:
Solving for
Using
Plugging in values:
The spring force is going to add to the gravitational force to equal zero.
Plugging in values:
Solving for
Using
Plugging in values:
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A golf ball is dropped from a height of , what is the velocity of the golf ball when it is halfway down its descent?
A golf ball is dropped from a height of
Tap to reveal answer
Energy is conserved throughout this entire problem, before the ball is dropped all of the energy is in the form of potential energy represented by , halfway down there is potential and kinetic energy present. Energy at the start must be equal to the energy halfway down which gives rise to the equation:
where is the initial height and is the height halfway down. Mass can be cancelled out and the heights and gravity constant can be plugged in in order to find velocity. Plugging in the values:
Energy is conserved throughout this entire problem, before the ball is dropped all of the energy is in the form of potential energy represented by
where
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A horizontal spring is oscillating with a mass sliding on a perfectly frictionless surface. If the amplitude of the oscillation is and the mass has a value of and a velocity at the rest length of , determine the spring constant.
A horizontal spring is oscillating with a mass sliding on a perfectly frictionless surface. If the amplitude of the oscillation is
Tap to reveal answer
Using conservation of energy:
Plugging in values:
Solving for
Using conservation of energy:
Plugging in values:
Solving for
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A block is sliding on a horizontal frictionless floor at a speed of and runs into a horizontal spring. The spring has a spring constant of . What is the maximum compression of the spring after the collision?
A
Tap to reveal answer
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
First, we calculate the kinetic energy of the block as it slides:
We know that all of the kinetic energy is converted to spring potential energy during the collision. We can use the equation for the potential energy of a spring and set it equal to the kinetic energy. Then, solve for the compression distance:
← Didn't Know|Knew It →
A bungie jumper is attached to a bungie with a constant of . The unstretched length of the bungie is . If the bungie stretches a maximum of passed its unstretched length, what is the mass of the jumper?
A bungie jumper is attached to a bungie with a constant of
Tap to reveal answer
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
is the length of the unstretched bungie, and is the distance the bungie stretches. Plugging this into the original expression, we get:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
Neglecting air resistance, we can say that the energy stored in the bungie when it is at its maximum stretched distance is equal to the initial gravitational potential energy of the jumper:
The initial height is the length of the bungie when it is fully stretched. We can write this out as:
Rearranging for the mass of the jumper, we get:
We have all of our values, allowing us to solve:
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