Kinetic energy

Kinetic energy is the measure of the objects energy due to movement, $\text{K.E.} = \frac{1}{2}mv^2$. The change in kinetic energy is the transfer in energy, hence the work done by movement.

Example

A mass of 11kg is pulled at an angle of $15^\circ$. The tension in the rope is $65\text{ N}$, the coefficent of friction is $0.19$, find the distance it travels as it acceleates between $2\text{ms}^{-1}$ and $14\text{ms}^{-1}$.

Find $F$

$$\begin{align} R &= 11g - 65\sin(15)\\ &= 90.976\\ \end{align}$$ $$\begin{align} F &= \mu R\\ &= 0.19 \times 90.976\\ &= 17.285\\ &= 17.3 \text{ N}\\ \end{align}$$

Calculate the displacement

$$\begin{align} \text{Change in K.E.} &= \frac{1}{2}m(v^2 - u^2)\\ &= \frac{1}{2} \times 11 \times (14^2 - 2^2)\\ &= 1056 \text{ J} \end{align}$$ $$\begin{align} 1056 &= Fs\\ &= (65\cos(15) - 17.3) \times s\\ s &= 23.216\\ &= 23.2\text{ m} \end{align}$$