# Gravitational Potential Energy

11SCI - Mechanics

Finn LeSueur

2020

## Mahi Tuatahi

- Write the date and “
**Gravitational Potential Energy**” in your books
- Complete the crossword on page 47 of your sciPAD!

## Ngā Whāinga Ako

- Give the symbols and units for potential energy.
- Use the equation \(E_{p} = mgh\)

## Gravitational Potential Energy / *Pūngao Tō Ā-Papa*

The potential an object has to transfer energy (do work), due to being at a particular position in a gravitational field.

**AKA**: The potential a mass has to fall due to being lifted up!

- Energy is
**always** measured in Joules
- Joules are given the shorthand unit:
**J**

\[\begin{aligned}
E_{p} &= mass \times gravity \times height \\
E_{p} &= m \times g \times h
\end{aligned}\]
## Pātai Tahi

**Calculate the gravitational potential energy** of a ball with mass, \(0.5kg\) kicked onto a roof which is \(3m\) high.

- Formula
- Substitution
- Answer

## Whakatika Tahi

\[\begin{aligned}
E_{p} &= m \times g \times h \\
&= 0.5 \times 10 \times 3 \\
&= 15J
\end{aligned}\]
## Pātai Rua

**Calculate the gravitational potential energy** of a weightlifter who lifts a \(100kg\) barbell from the floor to a height of \(2m\).

- Formula
- Substitution
- Answer

## Whakatika Rua

\[\begin{aligned}
E_{p} &= m \times g \times h \\
&= 100 \times 10 \times 2 \\
&= 2000J
\end{aligned}\]
## Pātai Toru

**Calculate the gravitational potential energy** of a cat with mass \(4kg\) who has climbed a tree to a height of \(5m\).

- Formula
- Substitution
- Answer

## Whakatika Toru

\[\begin{aligned}
E_{p} &= m \times g \times h \\
&= 4 \times 10 \times 5 \\
&= 200J
\end{aligned}\]
## Pātai Wha

**Calculate the gravitational potential energy** of a bird with mass \(300g\) that flies up to a power line at \(4m\) higher than its current position.

- Formula
- Substitution
- Answer

## Whakatika Wha

\[\begin{aligned}
E_{p} &= m \times g \times h \\
&= 0.3 \times 10 \times 4 \\
&= 12J
\end{aligned}\]
## Pātai Rimu

**Calculate the height** of Mr Le Sueur, mass \(71kg\), who ran up a hill and gained \(142,000J\) of energy!

- Formula
- Substitution
- Answer

## Whakatika Rimu

\[\begin{aligned}
E_{p} &= m \times g \times h \\
142,000 &= 71 \times 10 \times h \\
142,000 &= 710 \times h \\
\frac{142,000}{710} &= h \\
200m = h
\end{aligned}\]
## Pātai Ono

**Calculate the mass** a dog who climbed a \(2.5m\) obstacle at the dog park and gained \(625J\) of energy.

- Formula
- Substitution
- Answer

## Whakatika Ono

\[\begin{aligned}
E_{p} &= m \times g \times h \\
625 &= m \times 10 \times 2.5 \\
625 &= m \times 25 \\
\frac{625}{25} &= m \\
25kg = m
\end{aligned}\]