Question

How far the conveyor belt moves while the object is slipping?

• A. $\frac{v_o^2}{{\mu }_{k}g}$
• B. $\frac{v_o^2}{2{\mu }_{k}g}$
• C. $\frac{v_o^2}{{\mu }_{s}g}$
• D. $\frac{v_o^2}{2{\mu }_{s}g}$

Answer 1

Answer: (A)

$\frac{v_o^2}{{\mu }_{k}g}$

Block will slip on conveyor belt until it would not get velocity equal to conveyor belt

As only friction is acting on it so friction would increase its speed

$a=f/m={\mu }_{k}mg/m={\mu }_{k}g$

apply third equation of motion

$v=v_{0}u=0$

$v^2=u^2+2as$

$v_0^2=0+2{\mu }_{k}gs$

$s=\frac{v_0^2}{2{\mu }_{k}g}$