Q59 of 119 Page 159

The friction coefficient between the horizontal surface and each of the blocks shown in figure (9-E20) is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest.
Take g = 10 m/s2.


Given that the velocity of m=2kg block on reaching the 4kg block before collision is 1 m/s,


The velocity of M=4kg block is u2= o.


The friction coefficient between the horizontal surface and each of the blocks is .


Distance between the blocks is s=16 m.


From work energy principle






Since it is a perfectly elastic collision


Let v1 and v2 are the velocities after collision of block 2kg and 4kg respectively.


By law of conservation of momentum




______ (1)


Again,



_______ (2)


Subtracting equation (2) from (1)




Therefore,



Putting work energy principle for 2kg block when comes to rest





Whereare distances travelled by respective blocks.


Putting work energy principle for 4kg block when comes to rest





So, total distance between 2kg and 4kg block is s




Thus, the separation between the two blocks when they come to rest is 5 cm.


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A uniform chain of mass M and length L is held vertically in such a way that its lower endjust touches the horizontal floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor.

 58

The blocks shown in figure (9-E19) have equal masses. The surface of A is smooth but that of B has a friction coefficient of 0.10 with the floor. Block A is moving
at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic. Take g = 10 m/s2.


 60

A block of mass m is placed on triangular block of mass M, which in turn is placed on a horizontal surface as shown in figure (9-E21). Assuming frictionless surfaces find the velocity of the triangular block when the smaller block reaches the bottom end.


 61

Figure (9-E22) shows a small body of mass m placed over a larger mass M whose surface is horizontal near the smaller mass and gradually curves to become vertical. The smaller mass is pushed on the longer one at a speed u and the system is left to itself. Assume that all the surfaces are frictionless. (a) Find the speed of the larger block when the smaller block is sliding on the vertical part. (b) Find the speed of the smaller mass when it breaks off the larger mass at height h. (c) Find the maximum height (from the ground) that the smaller mass ascends. (d) Show that the smaller mass will again land on the bigger one. Find the distance traversed by the bigger block during the time when the smaller block was in its flight under gravity.