Question

You use a horizontal rope to pull a 50 kg box at constant velocity across the floor. If you pull with a force of 200 N, what is the coefficient of kinetic friction between box and floor.

I know the answer is 0.4, but I don't know HOW to do this problem. Thanks.

Answer 1

They tell you that the box is moving with a constant velocity which means that there is no acceleration AND that your forces equal zero. \[F_{pull} - F_{fric}=0\] So start with what you know:
m=50kg
Pulling force=200N

Now you also know that the force of friction is mu times the natural force:\[F_{fric}=\mu F_{nat}\] AND that the natural force is equal to mass times gravity\[F_{nat}=mg\] So your equation of forces looks like this:\[F_{pull} - \mu mg=0\] Now you can solve for the frictional coefficient:\[\mu=\frac{F_{pull}}{mg}\] Plug in the numbers and solve:\[\mu=\frac{200N}{50kg \times 9.8\frac{m}{s^2}} \rightarrow \mu=0.41\]