Gravitational Potential Energy Calculations

A brick with a mass of \(\text{1}\) \(\text{kg}\) is lifted to the top of a \(\text{4}\) \(\text{m}\) high roof. It slips off the roof and falls to the ground. Calculate the gravitational potential energy of the brick at the top of the roof and on the ground once it has fallen.

Step 1: Analyse the question to determine what information is provided

• The mass of the brick is \(m = \text{1}\text{ kg}\)

• The height lifted is \(h = \text{4}\text{ m}\)

All quantities are in SI units.

Step 2: Analyse the question to determine what is being asked

• We are asked to find the gain in potential energy of the brick as it is lifted onto the roof.

• We also need to calculate the potential energy once the brick is on the ground again.

Step 3: Use the definition of gravitational potential energy to calculate the answer

\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{1}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{4}\text{ m}\right) = \text{39.2}\text{ J} \end{align*}

A netball player, who is \(\text{1.7}\) \(\text{m}\) tall, holds a \(\text{0.5}\) \(\text{kg}\) netball \(\text{0.5}\) \(\text{m}\) above her head and shoots for the goal net which is \(\text{2.5}\) \(\text{m}\) above the ground. What is the gravitational potential energy of the ball:

1. when she is about to shoot it into the net?

2. when it gets right into the net?

3. when it lands on the ground after the goal is scored?

Step 1: Analyse the question to determine what information is provided

• the netball net is \(\text{2.5}\) \(\text{m}\) above the ground

• the girl has a height of \(\text{1.7}\) \(\text{m}\)

• the ball is \(\text{0.5}\) \(\text{m}\) above the girl's head when she shoots for goal

• the mass of the ball is \(\text{0.5}\) \(\text{kg}\)

Step 2: Analyse the question to determine what is being asked

We need to find the gravitational potential energy of the netball at three different positions:

• when it is above the girl's head as she starts to throw it into the net

• when it reaches the net

• when it reaches the ground

Step 3: Use the definition of gravitational potential energy to calculate the value for the ball when the girl shoots for goal

\[{E}_{P}=mgh\]

First we need to calculate h. The height of the ball above the ground when the girl shoots for goal is h = (\(\text{1.7}\) + \(\text{0.5}\)) = \(\text{2.2}\) \(\text{m}\).

Now we can use this information in the equation for gravitational potential energy:

\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{0.5}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{2.2}\text{ m}\right) \\ & = \text{10.78}\text{ J} \end{align*}

Step 4: Calculate the potential energy of the ball at the height of the net

Again we use the definition of gravitational potential energy to solve this:

\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{0.5}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{2.5}\text{ m}\right) \\ & = \text{12.25}\text{ J} \end{align*}

Step 5: Calculate the potential energy of the ball on the ground

\begin{align*} {E}_{P} & = mgh \\ & = \left(\text{0.5}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{0}\text{ m}\right) \\ & = \text{0}\text{ J} \end{align*}