A stone is suspended from the free end of a wire that is wrapped around the oute

Question

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in the figure below. The pulley is a uniform disk with mass M= 12.5 kg and radius R = 51.0 cm and turns on frictionless bearings. You measure that the stone travels 20.0 m in the first 3.75 s starting from rest.

A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in the figure below. The pulley is a uniform disk with mass M= 12.5 kg and radius R = 51.0 cm and turns on frictionless bearings. You measure that the stone travels 20.0 m in the first 3.75 s starting from rest. Find the mass of the stone. kg Find the tension in the wire. N

Explanation / Answer

s = 0.5.a.t2

a = 2s/t2.....(1)

mg - T = m.a

T = m(g-a) ......(2)

T.R = I.a/R

m(g-a).R2 = I.a

m = I.a/(g-a).R2

m = 0.5.M.(2s/t2)/[g - (2s/t2)]

m = 0.5.(12.5)(2*20/3.75^2)/[9.8 - (2*20/3.75^2)

m = 2.555 kg

T = m.(g - a) = 2.555*(9.8- 2s/t2) = 17.77 N

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