## Mahi Tuatahi

1. Write the date and “Gravitational Potential Energy” in your books

## Ngā Whāinga Ako

1. Give the symbols and units for potential energy.
2. Use the equation $E_{p} = mgh$

:::instruction Write these in your book :::

## 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

## 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

## 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

## 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

## 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

## 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