11SCI - Mechanics
Finn Le Sueur
2024
Kinetic energy is the energy that an object possesses due to its velocity!
Kinetic energy depends on the mass and velocity of an object.
\[ \begin{aligned} E_{k} &= \frac{1}{2} \times mass \times \text{velocity squared} \cr E_{k} &= \frac{1}{2} \times m \times v^{2} \end{aligned} \]
\[ \begin{aligned} E_{k} &= \frac{1}{2} \times m \times v \times v \end{aligned} \]
\[ \begin{aligned} K:& \cr U:& \cr F:& \cr S+S:& \end{aligned} \]
Mr LeSueur rides his bike to work at \(32km/h\) (\(8.89ms^{-1}\)). Both he and his bike have a combined mass of \(78kg\). Calculate his kinetic energy.
\[ \begin{aligned} m&=78kg, v=8.89ms^{-1} && \text{(K)} \cr E_{k} &= ? && \text{(U)} \cr E_{k} &=\frac{1}{2}mv^{2} && \text{(F)} \cr E_{k} &= \frac{1}{2} \times 78 \times 8.89^{2} && \text{(S)} \cr &= 3082.3J && \text{(S)} \end{aligned} \]
A ball is bowled with energy \(39.2J\) and velocity \(28ms^{-1}\). Calculate its mass.
\[ \begin{aligned} E_{k}&=39.2J, v=28ms^{-2} && \text{(K)} \cr m &= ? && \text{(U)} \cr E_{k} &=\frac{1}{2}mv^{2} && \text{(F)} \cr 39.2 &= \frac{1}{2} \times m \times 28^{2} && \text{(S)} \cr \sqrt{\frac{39.2 \times 2}{784}} &= m = 0.1kg && \text{(S)} \end{aligned} \]
A dog with mass \(22kg\) sprints across a field with a kinetic energy of \(1100J\). Calculate it’s velocity.
\[ \begin{aligned} m&=22kg, E_{k}=1100J && \text{(K)} \cr v &= ? && \text{(U)} \cr E_{k} &=\frac{1}{2}mv^{2} && \text{(F)} \cr 1100 &= \frac{1}{2} \times 22 \times v^{2} && \text{(S)} \cr \sqrt{\frac{1100 \times 2}{22}} &= v = 10ms^{-1} && \text{(S)} \end{aligned} \]
Alternatively, you can rearrange the formula first, and then substitute in the numbers.
\[ \begin{aligned} m&=22kg, E_{k}=1100J, v=? \cr E_{k} &= \frac{1}{2}mv^{2} \cr 2E_{k} &= mv^{2} \cr \frac{2E_{k}}{m} &= v^{2} \cr \sqrt{\frac{2E_{k}}{m}} &= v = \sqrt{\frac{2 \times 1100}{22}} = 10ms^{-1} \end{aligned} \]
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