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In Figure P10.43 the sliding block has a mass of 0.850 kg, the counterweight has a mass of 0.420 kg, and the pulley is a hollow cylinder with a mass of 0.350 kg, an inner radius of XXXXXXXXXXm, and an...

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In Figure P10.43 the sliding block has a mass of 0.850 kg, the counterweight has a mass of 0.420 kg, and the pulley is a hollow cylinder with a mass of 0.350 kg, an inner radius of XXXXXXXXXXm, and an outer radius of XXXXXXXXXXm. The coefficient of kinetic friction between the block and the horizontal surface is XXXXXXXXXXThe pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of 0.820 m/s toward the pulley when it passes through a photogate.
(a) Use energy methods to predict its speed after it has moved to a second photogate, 0.700 m away.
(b) Find the angular speed of the pulley at the same moment.

Answered Same Day Dec 24, 2021

Solution

Robert answered on Dec 24 2021
138 Votes
a)
By law of conservation of energy,
MEf = MEi
(KEf + PEf)m1 + (KEf + PEf)m2 + KEfpulley + Wfric = (KEi + PEi)m1 + (KEi + PEi)m2 + KEipulley
(1/2m1v1f
2 + m1gh1f) + (1/2m2v2f
2 + m2gh2f) + (1/2Iwf
2) + μkm1gd = (1/2m1v1i
2 + m1gh1i) + (1/2m2v2i
2 +
m2gh2i) + (1/2Iwi
2)
(1/2m1v1f
2 - 1/2m1v1i
2) + (m1gh1f - m1gh1i) + (1/2m2v2f
2 - 1/2m2v2i
2) + (m2gh2f - m2gh2i ) + (1/2Iwf
2 - 1/2Iwi
2 )...
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