A mass m = 0.5 kg sits on a track at a height h1 = 0.5 m as shown in the picture

Question

A mass m = 0.5 kg sits on a track at a height h1 = 0.5 m as shown in the picture. A spring with spring constant k lies at the right end of the track. The track is smooth everywhere except for a small horizontal section of length s = 0.6 m where µk= 0.2.
The mass is released from rest. It slides down the track passing the rough patch and compresses the spring on the right where it stops momentarily. The spring eventually pushes the block back, which then travels to the left passing the rough patch again until it finally stops at a height h2.
a) How much work is done by friction during the motion of the mass? (5 pts.)

Explanation / Answer

given the coefficient of kinetic friction is =0.2 the mass m =0.5 kg length of the friction is s= 0.6 m frictional force is F = mg work done W = force * length =mg s as the block is passing the section two times the total work done is = 2W = 2mgs substituting the values we get work done =1.176 J

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