Question

If you use a horizontal force of 50.0 N to slide a 12.0 kg wooden crate across a floor at a constant velocity, what is the coefficient of kinetic friction between the crate and the floor?

Answer 1

\[F_{fric}=\mu \times F_{nat} \rightarrow F_{nat}=mg\] \[F_{weight}=mass \times gravity \rightarrow F_{weight}=12.0kg \times 9.8\frac{m}{s^2}=117.6N\] Since you are moving at a constant velocity then there is no acceleration in the direction of motion. With no acceleration your forces equal zero. \[\sum F=F_x - F_{fric} \rightarrow 0=50N - \mu(mg) \rightarrow -50N=-\mu (117.6N) \rightarrow \mu=-(\frac{-50N}{117.6N})\] \[\mu=0.425\]