A block of wood of mass 1.9 kg is placed on a horizontal table and attached by a

Question

A block of wood of mass 1.9 kg is placed on a horizontal table and attached by a massless rope of length 31 cm to a vertical axis that passes through the table. The rope is initially swung around the axis, causing the wood to have a tangential velocity of 4.0 m/s. After one revolution the wood is observed to have a speed of only 2.1 m/s.

a) How much work has friction done on the block of wood during the first revolution? (Answer: -11J)

b) What is the coefficient of kinetic friction between the block of wood and the table? (Answer: 0.304)

c) How many revolutions does the block of wood make before stopping? (Answer: 1.38)

Please show all work. Those are the answers.

Explanation / Answer

a) W = 0.5*m*(V2^2-V1^2) = 0.5*1.9*(2.1^2 - 4^2) = -11 J

b ) W = -u*M*g*s = -u*M*g**2*pi*L

u = W/(M*g**2*pi*L) = 11/(1.9*9.8*2*(22/7)*0.31) = 0.304

c) S = (V^ 2- V1^2)/-2*u*g = 4^2/(2*0.304*9.8) = 2.69 m

number of revolutions = S/(2*pi*L) = 1.38 rev

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