A block is released from rest at the top of a smooth quarter circle of radius 3m

Question

A block is released from rest at the top of a smooth quarter circle of radius 3m. The block then slide on an 8.0 m long surface that has a Uk=.10 , on the other side of this horizontal surface is another smooth quarter circle track. Find the distance, d, measured from the left edge of the horizontal surface, where the block will eventually stop. 7. A block is released from rest at the top of a smooth quarter circle of radius 3 m. The block then slide on an 8.0 m long horizontal surface that has a ,-0.10. On the other side of this horizontal surface is another smooth quarter circle track. Find the distance, d, measured from the left edge of the horizontal surface, where the block will eventually stop R=3m Hu= 0.1 Smooth

Explanation / Answer

Potential energy of the block at point A :

PEa = mgh

Here h = 3m

Now all this potential energy must be lost to work done by friction

So mgh = u*mg*D

Wher u = 0.1

D = h/u = 3/0.1 = 30m

As the total distance travelled is greater than the length of the flat track,

So it will move up the circular ramp on the right end.

After moving up some distance it will descend down and move back to the left end. Now the total distance moved by the block is 8*2 = 16 m.

Similarly again it moves to the right end to cover a total distance of 3*8=24 m . When total distance moved is 30m ,it will stop.

So, it will happen when it moves the remaining 30- 24 = 6m from the right end to left end .

So it will come to rest at d = 8 -6 = 2 m from the left end.

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