Question

A box of unknown mass is sliding with an initial speed v = 4.80 m/s across a horizontal frictionless warehouse floor when it encounters a rough section of flooring d = 4.70 m long. Thecoefficient of kinetic friction between the rough section of flooring and the box is 0.100. Using energy considerations, determine the final speed of the box (in m/s) after sliding across the rough section of flooring.m/s

Answer 1

Given data,

Initial speed of the box,

`v=4.80\text{ m/s}`

Length of the floor,

`d=4.70\text{ m}`

Coefficient of friction,

`\mu_k=0.100`

Calculate the acceleration,

`\begin{gathered} a=\text{coefficient of friction}* g \\ a=0.100*9.8 \\ a=0.98m/s^2 \end{gathered}`

Consider the kinematic equation of motion.

`\begin{gathered} v^2=u^2-2ad \\ v^2=(4.80\text{ m/s})^2-2*0.98m/s^2*4.70\text{ m} \\ v^2=23.04-9.212^{} \\ v=3.717^{}\text{ m/s} \end{gathered}`

Therefore, the final speed of the box is

`v=3.717\text{ m/s}`