1) A 5.00 kg piece of wood slides on the surface shown in the figure to the righ

Question

1) A 5.00 kg piece of wood slides on the surface shown in the figure to the right. The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.100 with the wood. The piece of wood starts at from rest 10.0 m above the rough bottom and it will move back and forth across the bottom until it finally comes to rest. If the left side of the rough bottom is at x=0 m, where will the wood eventually come to rest? (x=?)

Please explain

A 5.00 kg piece of wood slides on the surface shown in the figure to the right. The curved sides are perfectly smooth, but the rough horizontal bottom is 30 m long and has a kinetic friction coefficient of 0.100 with the wood. The piece of wood starts at from rest 10.0 m above the rough bottom and it will move back and forth across the bottom until it finally comes to rest. If the left side of the rough bottom is at x=0 m, where will the wood eventually come to rest? (x=?)

Explanation / Answer

The block comes to rest when all the potential energy of the block is lost,

Initial potential energy= mgh=5*9.8*10=490 J

Frictional force = mew*m*g=0.1*5*9.8

Let the block move distance x,

Work done by friction= 0.1*5*9.8*x

Work done by friction=Initial potential energy

0.1*5*9.8*x=5*9.8*10

x=100 m

The block moves from x=0 to x=30, comes back and again moves from x=0 to x=30 and then moves 10 m backward.

So the block stops at x=20 m

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