A block can slide along the track shown, with a flat bottom and curved, elevated

Question

A block can slide along the track shown, with a flat bottom and curved, elevated ends. The flat part has length L = 40cm. The curved portions of the track are frictionless, but the flat part has a coefficient of kinetic friction of k = 0.20. The block is released from rest at point A, at a height = L/2.

How many times will the block pass completely through the flat part of the track? Justify your answer.

When it comes to a stop, is it traveling to the right or to the left? Justify your answer.

When it stops, how far from the left side of the flat part of the track does it stop?

Explanation / Answer

Here ,

h = 40/2 cm = 0.20 m

uk = 0.20

energy lost in each trip across the frictional surface , W = uk * m* g * L

W = m * 0.20 * 9.8 * 0.40

W = 0.784*m

Now, let the number of trips is N

Using conseravtion of energy

N * 0.784 * m = m * 9.8 * 0.20

m = 2.5

hence , the number of times the block passes the flat part of track is 2.

when it comes to stop ,

the block is moving to the right

----

distance from the left side = 0.5 * 0.40 = 0.20 m

the distance from the left side is 0.20 m

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