# AP Physics 1 : Other Potential Energy

## Example Questions

### Example Question #1 : Other Potential Energy

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?

Explanation:

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:

### Example Question #21 : Motion

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?

Explanation:

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:

### Example Question #2 : Other Potential Energy

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.)

Explanation:

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:

### Example Question #1 : Other Potential Energy

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?

Explanation:

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:

### Example Question #1 : Other Potential Energy

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.

Explanation:

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:

### Example Question #2 : Other Potential Energy

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.

None of these

Explanation:

The spring force is going to add to the gravitational force to equal zero.

Plugging in values:

Solving for

Using

Plugging in values:

### Example Question #132 : Work, Energy, And Power

A golf ball is dropped from a height of , what is the velocity of the golf ball when it is halfway down its descent?

Explanation:

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:

### Example Question #141 : Work, Energy, And Power

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)?

Not enough information

Explanation:

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:

### Example Question #142 : Work, Energy, And Power

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.