11SCI - Mechanics
Finn Le Sueur
2024
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!
\[ \begin{aligned} E_{p} &= mass \times gravity \times height \cr E_{p} &= m \times g \times \Delta h \end{aligned} \]
\[ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} \]
Calculate the gravitational potential energy of a ball with mass, \(0.5kg\) kicked onto a roof which is \(3m\) high.
\[ \begin{aligned} m&=0.5kg, \Delta h = 3m, g=10ms^{-2} && \text{(K)} \cr E_{p} &= ? && \text{(U)}\cr E_{p} &= mg\Delta h && \text{(F)}\cr E_{p} &= 0.5 \times 10 \times 3 && \text{(S)}\cr E_{p} &= 15J && \text{(S)} \end{aligned} \]
Calculate the height of a \(100kg\) barbell that gained \(1800J\) of gravitational potential energy.
\[ \begin{aligned} m&=100kg, E_{p}=1800J && \text{(K)} \cr \Delta h&= ? && \text{(U)} \cr E_{p}&=mg\Delta h && \text{(F)} \cr 1800 &= 100 \times 10 \times \Delta h && \text{(S)} \cr \Delta h &= \frac{1800}{1000} = 1.8 && \text{(S)} \end{aligned} \]
Calculate the mass of a cat that climbed \(5m\) into a tree and gained \(400J\) of gravitational potential energy.
\[ \begin{aligned} \Delta h&=5m, E_{p} = 400J && \text{(K)} \cr m &= ? && \text{(U)}\cr E_{p} &= mg\Delta h && \text{(F)}\cr 400 &= m \times 10 \times 5 && \text{(S)}\cr m &= \frac{400}{50} = 8kg && \text{(S)} \end{aligned} \]