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# A plank of mss M is placed on a rough horizontal surface and a constant horizontal force is applied to it. A man of mass m runs on the plank. Find the acceleration of the man so that the plank does not move on the surface. Coefficient of friction between the plank and the surface is µ . Assume sufficient friction between man and the plank to avoid slipping of man on the plank.

68 Points
11 years ago

Dear Kaushik ,

Two cases can arise :

1) the man runs in the direction of application of the force F on the plank

Then the friction acts on him in the direction of F and so he applies the friction in opposite direction of  F on the plank . His accelecration be a. As he increases a , the force in backward direction increases and eventually the limit reaches when the Friction below on the plank reaches its maximim value = µ (m+M) g

in this case ,  mamax - F =  µ (m+M) g , so

amax =  µ (m+M) g + F /m

so  a <= (µ (m+M) g + F )/m

2) the man runs opposite to the direction of application of the force F on the plank

Then the friction acts on him in the opposite  direction of F and so he applies the friction in the direction of F on the plank . His accelecration be a. As he increases a , the force in forward  direction increases and eventually the limit reaches when the Friction below on the plank reaches its maximim value = µ (m+M) g.

in this case ,  mamax + F =  µ (m+M) g , so

amax =  µ (m+M) g - F /m

so  a <= (µ (m+M) g -F )/m

All the best.

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