Storing Your Energy: Potential Energy

Objects can have energy at rest simply by having a force act on them. For example, an object at the end of a stretched spring has energy because when you let the object go and it accelerates because of the spring, it can convert that stored energy into kinetic energy.

The energy that an object has by virtue of a force acting on it is called potential energy. For example, an object at height h in the gravitational field at Earth’s surface has this potential energy:

PE = mgh

For example, say you have a basketball at height h. When it drops, its potential energy gets converted into kinetic energy. To figure out how fast the basketball (or any object) is going when it hits the ground, you use this equation:

Sample question

1. During a basketball game, a 1.0-kg ball gets thrown vertically in the air. It’s momentarily stationary at a height of 5.0 m above the floor and then falls back down. What is the ball’s speed when it hits the floor?

   The correct answer is 9.9 m/s.

   1. Find out how much potential energy the ball has when it starts to fall. Use this equation for potential energy:

      PE = mgh

   2. This potential energy will be converted into kinetic energy, so you expand the equation like so:

      

   3. Solve for v²:

      v² = 2gh

   4. Solve for v:

      

   5. Plug in the numbers:

      

Practice questions

1. 1.A 40-kg box of books falls off a shelf that’s 4.0 m above the ground. How fast is the box traveling when it hits the ground?

2. 2.You jump out of an airplane at 2,000 ft and fall 1,000 ft before opening your parachute. What is your speed in ft/s (neglecting air resistance) when you open your chute?

3. 3.The flagpole on top of a 300.0-m skyscraper falls off. How fast is it falling in m/s when it strikes the ground? (Assume that you can neglect air resistance.)

4. 4.If you’re in an airplane at 30,000 ft, what is your potential energy if you have a mass of 70.0 kg?

Following are answers to the practice questions:

1. 8.9 m/s

   1. 1.Figure out how much potential energy the box has when it starts to fall. That potential energy is

      PE = mgh

   2. This potential energy will be converted into kinetic energy, so you have

      

   3. Solve for v²:

      v² = 2gh

   4. 4.Solve for v:

      

2. 254 ft/s

   1. Figure out how much potential energy you have when you start to fall. That potential energy is

      PE = mgh_o

   2. 2.Find out how much potential energy is converted into kinetic energy when you open your parachute. The change in potential energy is

      

   3. This potential energy will be converted into kinetic energy, so you have

      

   4. Note that in the FPI system of units, g = 32.2 ft/s². Solve:

      

3. 77 m/s

   1. Figure out how much potential energy the pole has when it starts to fall. That potential energy is

      PE = mgh

   2. This potential energy will be converted into kinetic energy, so you have

      

   3. Solve for v²:

      v² = 2gh

   4. Plug in the numbers:

      

4. 6.3 x 10⁶ J

   1. The equation for potential energy is

      PE = mgh

   2. Convert 30,000 ft into m using the fact that 1 ft = 0.305 m:

      

   3. Plug in the numbers:

      PE = mgh = (70.0)(9.8)(9,150) = 6.3 x 10⁶ J