Find kinetic friction given mass speed and time.

Question

You kick a $12\text{kg}$ box across the floor. The box initially slides at $2.0 \text{m/s}$, but comes to a stop within $1.2 \text{s}$.

What is the magnitude of the force of kinetic friction on the box?

Answer 1

First find the deceleration on the box.

$v=u+at$

$0 = 2+a(1.2)$

$a=-\frac 53 \mathrm{ms^{-2}} $

Then find the force.

$F=ma =(12) (-\frac 53)=-20\mathrm{N} $

Note that it is negative because it is decelerative. As they asked only for the magnitude, you can quote the final answer without the negative sign as $20\mathrm{N}$.

Answer 2

$\Delta K=F.d$ or $\dfrac12mv^2-\dfrac12mv_0^2=F\cdot d$. Here $v=0$ and $$d=\dfrac{v+v_0}{2}t=\dfrac{0+2}{2}1.2=1.2\text{m}$$ so $$F=\dfrac{-\frac12(12)2^2}{1.2}\text{N}=-20\text{N}$$