Question

A bin is given a push across a horizontal surface. The bin has a mass m, the push gives it an initial speed of 3.30 m/s, and the coefficient of kinetic friction between the bin and the surface is 0.110. (a) Use energy considerations to find the distance (in m) the bin moves before it stops (b) What If? Determine the stopping distance (in m) for the bin if its initial speed is doubled to 6.60 m/s.

Answer 1

Answer:

(a) $x=5.05\ m$

(b) $x=20.20\ m$

Explanation:

Energy Conversion

The bin (of mass m) is initially given a push that makes it move at an initial speed vo. Its kinetic energy is

$\displaystyle K=\frac{1}{2}mv_o^2$

(a) Once pushed, there is only one force acting in the direction of movement of the bin: the friction force. We can calculate the friction force with the formula

$F_r=\mu. m.g$

While the bin is traveling in the rough surface, its kinetic energy is transformed into thermal energy until it stops when running out of speed. The work done by the friction force equals the kinetic energy dissipated, thus

$\displaystyle W=F_r.x=\frac{1}{2}mv_o^2$

Replacing the friction force:

$\displaystyle \mu. m.g.x=\frac{1}{2}mv_o^2$

Simplifying by m and solving for x

$\displaystyle x=\frac{1}{2}\frac{v_o^2}{\mu.g}=\frac{1}{2}\frac{3.3^2}{0.11\cdot 9.8}$

$x=5.05\ m$

(b) If the initial speed was doubled to 6.6 m/s

$\displaystyle x=\frac{1}{2}\frac{v_o^2}{\mu.g}=\frac{1}{2}\frac{6.6^2}{0.11\cdot 9.8}$

$x=20.20\ m$