A mass m is released from a height 80 cm from the right - hand side of the track
ID: 2241247 • Letter: A
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.