Q35 of 40 Page 109

A block of mass 15 kg is placed on a long trolley. The coefficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 m s-2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, (b) an observer moving with the trolley.

Given:

Mass of block, M = 15 Kg


Coefficient of static friction, � = 0.18


Acceleration of the trolley, a = 0.5 ms-2


Time for which the trolley accelerates, t = 20 s


To check whether the block will slide or not, let us compare the force due to trolley and


trolley and Block.


Using the Newton’s second law of motion,


Force, F on the block due to accelerating trolley is given by,


F = M× a


F = 15 Kg× 0.5 ms-2


F = 7.5 N


Frictional force, fs


fs = �× M× g


fs = 0.18× 15Kg × 10 ms-2


fs = 27 N


F<fs


The force of friction between the block and the trolley is greater than the applied force by trolley. Hence for an observer on ground the block will seem to be moving at the same velocity as that of trolley.


b) For an observer moving with the trolley, the trolley and the box will seem to be at rest.


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A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

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C. climbs up with a uniform speed of 5 m s-1


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(Ignore the mass of the rope).



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The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s-2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

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