Question

A suitcase is gently dropped on a conveyor belt moving at $3m/s$. If the coefficient of friction between the belt and the suitcase is $0.5$. Find the displacement of suitcase relative to conveyor belt before the slipping between the two is stopped ($g = 10m/{s^2}$)
a. $2.7m$
b. $1.8m$
c. $0.9m$
d. $1.2m$

Answer 1

Hint: The resistance faced by a body in static condition while it tends to move under the action of external force. This resistance is called static frictional force. Apply the coefficient of friction to apply the acceleration. Then apply the acceleration to find the displacement of the suitcase.

Formula used:
$Ma = \mu N$
Where $\mu $ is the coefficient of friction, $N$ is the normal reaction, $a$ is the acceleration.

Complete step by step answer:
Friction is the opposing force which comes between two surfaces so as to impede the relative motion between them. Friction is regarded as an electromagnetic force. Friction can also be due to the cohesive or adhesive force among molecules at close proximities.
The resistance faced by a body in static condition while it tends to move under the action of external force. This resistance is called static frictional force. The ratio of limiting friction (maximum static friction) to normal reaction is called coefficient of static friction. It is a unit less quantity.

Here the suitcase is slipping, then the retardation due to friction
$Ma = - \mu N$
$a = - \dfrac{{\mu Mg}}{M} = - \mu g$
Then apply the kinematic equation
${v^2} - {u^2} = 2as$
Here $v = 0$, a=- \mu g and $u = 3m/s$
${3^2} = - 2{\mu}gs$
$s = 0.9m$

Hence, the correct answer is option (C).

Note: The surfaces in contact will slip on each other without opposition in the absence of friction. This may be producing a dangerous motion. Polishing, using lubricants, using ball bearing, streamlining can reduce friction. Another effective way to reduce friction is to place a thin cushion of air maintained between the solid surfaces in relative motion.