College Physics : Gravitational Potential Energy

Study concepts, example questions & explanations for College Physics

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Example Questions

Example Question #21 : College Physics

\(\displaystyle 2kg\) bouncy ball is dropped from \(\displaystyle 10 m\). When it bounces back up is reaches a height of \(\displaystyle 8m\). How much energy was loss?

\(\displaystyle g=10\frac{m}{s^2}\)

Possible Answers:

\(\displaystyle 200N\)

\(\displaystyle 20J\)

\(\displaystyle 100J\)

\(\displaystyle 200J\)

\(\displaystyle 40J\)

Correct answer:

\(\displaystyle 40J\)

Explanation:

The formula for gravitational potential energy is:

\(\displaystyle GPE=mgh\)

To find the potential energy lost, we need to find the potential energy of the ball at two heights, then find the difference. 

\(\displaystyle GPE_{before} = 2kg (10\frac{m}{s^2})(10m)\)

\(\displaystyle GPE_{before} = 200J\)

\(\displaystyle GPE_{after} = 2kg (10\frac{m}{s^2})(8m)\)

\(\displaystyle GPE_{after} = 160J\)

\(\displaystyle GPE_{before} - GPE_{after} = GPE \ lost\)

\(\displaystyle 200J- 160J = 40J\)

Note that the energy was not actually lost; rather, it was converted to kinetic energy. 

Example Question #22 : College Physics

A baseball weighing \(\displaystyle 2kg\) is dropped from a second story window which is \(\displaystyle 20m\) high. What is the gravitational potential energy?

\(\displaystyle g=10\frac{m}{s^2}\)

Possible Answers:

\(\displaystyle 40N\)

\(\displaystyle 40J\)

\(\displaystyle 400N\)

\(\displaystyle 400J\)

\(\displaystyle 100J\)

Correct answer:

\(\displaystyle 400J\)

Explanation:

Gravitational potential energy is given by the equation:

\(\displaystyle GPE= mgh\)

We are given all the information needed to solve for the potential energy.

\(\displaystyle mass=2kg\)

\(\displaystyle g = 10\frac{m}{s^2}\)

\(\displaystyle Height=20m\)

Plug in known values and solve.

\(\displaystyle GPE= 2kg(10\frac{m}{s^2})(20m)\)

\(\displaystyle GPE = 400\frac{kg\cdot m^2}{s^2}\)

\(\displaystyle GPE = 400J\)

Recall that the units for energy are Joules. Newtons is the unit for force.

Example Question #23 : College Physics

\(\displaystyle 15kg\) bowling ball is released from \(\displaystyle 10m\) in the air. What is it's gravitation potential energy upon release?

\(\displaystyle g=10\frac{m}{s^2}\)

Possible Answers:

\(\displaystyle 100J\)

\(\displaystyle 1000J\)

\(\displaystyle 500J\)

\(\displaystyle 1500J\)

\(\displaystyle 1200J\)

Correct answer:

\(\displaystyle 1500J\)

Explanation:

The equation for gravitational potential energy is:

\(\displaystyle GPE = mgh\)

We are given all the information needed to answer the question.

\(\displaystyle mass = 15kg\)

\(\displaystyle gravity=10\frac{m}{s^2}\)

\(\displaystyle height = 10 m\)

Plug in known values and solve.

\(\displaystyle GPE = 15kg (10\frac{m}{s^2})(10m)\)

\(\displaystyle GPE = 1500J\)

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