Physics / Unit 5: Work, Energy and Power
5.2 Kinetic Energy and the Work-Energy Theorem
Notes
Energy is the ability to do work. Kinetic energy is energy of motion: $\displaystyle KE = \frac{1}{2}mv^2$.
- Doubling the speed makes $KE$ four times larger; doubling the mass doubles it.
- Work-energy theorem: the net work on an object equals its change in kinetic energy, $W_{\text{net}} = \Delta KE$.
- Example: a 2 kg ball at $3 \text{ m/s}$ has $\displaystyle KE = \frac{1}{2}(2)(3^2) = 9 \text{ J}$.
Practice
What is the kinetic energy of a 1,000 kg car moving at $20 \text{ m/s}$?
$\displaystyle KE = \frac{1}{2}(1000)(20^2) = 500 \times 400 = 200000 \text{ J}$.
A cyclist doubles her speed. Her kinetic energy:
$KE \propto v^2$, and $2^2 = 4$.
A 4 kg cart at rest has 72 J of net work done on it. What is its final speed?
$\displaystyle 72 = \frac{1}{2}(4)v^2 \Rightarrow v^2 = 36 \Rightarrow v = 6 \text{ m/s}$.
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