# Gravitational Potential Energy

11SCI - Mechanics

2020

## Mahi Tuatahi

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

## Ngā Whāinga Ako

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

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
• 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}