Gravitational Potential Energy

11SCI - Mechanics

Finn LeSueur

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

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