A mass m is released from a height 80 cm from the right - hand side of the track

Question

A mass m is released from a height 80 cm from the right - hand side of the track shown in the diagram at right. There is only friction acting along the horizontal portion 30 cm either side of the midpoint O with a kinetic coefficient of friction of ? k = 0.4. Determi ne (i) how many times does the mass m pass through the midpoint O, and (ii) how far from the midpoint does it come to rest.  



A mass m is released from a height 80 cm from the right - hand side of the track shown in the diagram at right. There is only friction acting along the horizontal portion 30 cm either side of the midpoint O with a kinetic coefficient of friction of ? k = 0.4. Determi ne (i) how many times does the mass m pass through the midpoint O, and (ii) how far from the midpoint does it come to rest.  



A mass m is released from a height 80 cm from the right - hand side of the track shown in the diagram at right. There is only friction acting along the horizontal portion 30 cm either side of the midpoint O with a kinetic coefficient of friction of ? k = 0.4. Determine how many times does the mass m pass through the midpoint O, and how far from the midpoint does it come to rest.

Explanation / Answer

Total Energy = mgh

Each pass will lose energy in the amount of umgd, thus

mgh = umgd(x) (mass cancels)

(9.8)(.8) = (.4)(9.8)(.6)(x)

x = 3.33 times

That means it goes through the center three times and stops 1/3 of the way into the rough patch on the fourth attempt. That means it stops 20 cm from the midpoint to the left of the midpoint.

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