10.1 Friction (application)

Questions and their answers are presented here in the module text format as if it were an extension of the treatment of the topic. The idea is to provide a verbose explanation, detailing the application of theory. Solution presented is, therefore, treated as the part of the understanding process – not merely a Q/A session. The emphasis is to enforce ideas and concepts, which can not be completely absorbed unless they are put to real time situation.

Representative problems and their solutions

We discuss problems, which highlight certain aspects of the study leading to friction. The questions are categorized in terms of the characterizing features of the subject matter :

• Conveyor belt
• Blocks
• Stack of blocks

Conveyor belt

Problem 1 : At an airport, a girl of 50 kg is standing on a conveyor strip, which transports her horizontally from one point to another. If the conveyor strip has the acceleration of 0.2 $m/s^2$ and the girl is standing still on with respect to the strip, then what is friction between her shoe and the strip?

Solution : The girl is standing on an accelerating strip. It is given that she is stand still in the reference of conveyor belt. In the ground reference, however, she is accelerating with the same acceleration as that of conveyor belt.

As seen from the ground reference, the forces in horizontal directions should form an unbalanced force system for her to accelerate with the conveyor strip. In the horizontal direction,

Friction is the only force in the horizontal direction. Hence, it should be in the direction of acceleration. Note that friction on the girl may be less than or equal to the limiting friction, depending on the coefficient of friction between shoe and the strip of the conveyor belt.

$$F_x=F_F=ma=50X0.2=10N$$

Problem 2 : At an airport, a girl of 50 kg is standing on a conveyor strip, which transports her horizontally from one point to another. If the coefficient of static friction between her shoe and the strip is 0.2, then find the maximum acceleration of the belt for which the girl can remain stand still with respect to the conveyor strip.

Solution : The girl is standing on an accelerating strip. It is given that she is stand still in the reference of conveyor. In the ground reference, she is accelerating with the same acceleration as that of conveyor strip.

The girl can hold on her position on the conveyor till the friction becomes limiting friction. We, therefore, analyze the forces in horizontal directions with limiting friction,

$$F_x=F_s=ma$$

$$\mu N=ma$$

$$a=\frac{\mu N}{m}$$

The forces on the girl in the vertical direction form a balanced force system as there is no motion in that direction,

$$F_y=N=mg=50X10=500\mathrm{Newton}$$

Putting this value in the equation of acceleration, we have :

$$a=0.2X\frac{500}{50}=0.2X10=2m/s^2$$

Problem 3 : A box is dropped gently on a conveyor belt moving at a speed “v”. The kinetic coefficient of friction between box and conveyor belt is “μ”. Find the time after which, the box becomes stationary on the belt.