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Gravitational Potential Energy

Ngā Whāinga Ako 🔗

  1. Give the symbols and units for potential energy.
  2. Use the equation $E_{p} = m\times g \times \Delta h$

Gravitational Potential Energy / Pūngao Tō Ā-Papa 🔗

The potential an object has due to being at a particular position in a gravitational field.

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

$$ \begin{aligned} E_{p} &= mass \times gravity \times height \cr E_{p} &= m \times g \times \Delta h \end{aligned} $$

Ngā Pātai 🔗

  1. Calculate the gravitational potential energy of a ball with mass, $0.5kg$ kicked onto a roof which is $3m$ high.
  2. Calculate the height of a $100kg$ barbell that gained $1800J$ of gravitational potential energy.
  3. Calculate the mass of a cat that climbed $5m$ into a tree and gained $400J$ of gravitational potential energy.

$$ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} $$

Whakatika Tahi 🔗

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

$$ \begin{aligned} m&=0.5kg, \Delta h = 3m, g=10ms^{-2} && \text{(K)} \cr E_{p} &= ? && \text{(U)}\cr E_{p} &= mg\Delta h && \text{(F)}\cr E_{p} &= 0.5 \times 10 \times 3 && \text{(S)}\cr E_{p} &= 15J && \text{(S)} \end{aligned} $$

Whakatika Rua 🔗

Calculate the height of a $100kg$ barbell that gained $1800J$ of gravitational potential energy.

$$ \begin{aligned} m&=100kg, E_{p}=1800J && \text{(K)} \cr \Delta h&= ? && \text{(U)} \cr E_{p}&=mg\Delta h && \text{(F)} \cr 1800 &= 100 \times 10 \times \Delta h && \text{(S)} \cr \Delta h &= \frac{1800}{1000} = 1.8 && \text{(S)} \end{aligned} $$

Whakatika Toru 🔗

Calculate the mass of a cat that climbed $5m$ into a tree and gained $400J$ of gravitational potential energy.

$$ \begin{aligned} \Delta h&=5m, E_{p} = 400J && \text{(K)} \cr m &= ? && \text{(U)}\cr E_{p} &= mg\Delta h && \text{(F)}\cr 400 &= m \times 10 \times 5 && \text{(S)}\cr m &= \frac{400}{50} = 8kg && \text{(S)} \end{aligned} $$

Whakawai / Practice 🔗