A mass m=0.5kg sits on a track at a height h1=0.5m. A spring with a spring const

Question

A mass m=0.5kg sits on a track at a height h1=0.5m. A spring with a 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 where mu=0.2. The mass is released from rest, sliding 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? the value of h2?
b)if the spring constant has value k=500 N/m calculate the maximum compression on the spring?

any help would be MUCH appreciated!

Explanation / Answer

a. as the mass passes through the frictional path twice. the total work done by friction=2*mu*m*g*s=1.176 J now previously the mas had energy=mgh1=2.45 J after reaching height h2 the energy will be=1.274 J mgh2=1.274 J h2=.26m b. when the mass reaches to the spring the energy it has=2.45-1.176/2=1.862 J if the spring is compressed by x , then kx^2/2=1.862 x=.o86 m=8.6 cm

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