Question

An object is gently placed on a long conveyer belt moving with a speed of $5 \,m \,s^{-1}$. If the coefficient of friction between the block and the belt is $0.5$ the block will slide on the belt up to a distance (Take $g = 10\, m\, s^{-2}$)

• A. $2.0 \,m$
• B. $2.5 \,m$
• C. $3.0 \,m$
• D. $3.5 \,m$

Answer 1

The Correct Option is B

The force of friction between the block and the belt is $f = \mu mg$ where $m$ is the mass of the object. This force produces an acceleration of the block which is given by $a=\frac{force}{mass}=\frac{\mu mg}{m}=\mu g$ The block will slide on the belt without slipping until its speed $\left(\upsilon\right)$ becomes equal to the speed of the belt. Since $u =0$, we have $\upsilon^{2} = 2as$ or $s=\frac{\upsilon^{2}}{2a}=\frac{\upsilon^{2}}{2\mu g}=\frac{\left(5\,m\,s^{-1}\right)^{2}}{2\times0.5\times10\,m\,s^{-2}}=2.5\,m$