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. Figure 3 shows a string is wrapped around a uniform solid pulley of radius R =

ID: 1483761 • Letter: #

Question

. Figure 3 shows a string is wrapped around a uniform solid pulley of radius R = 0.5m. The pulley can rotate freely about its axis. The loose end of the string is attached to a stone. The mass of the pulley mp = 2.5kg and the stone has a mass of ms = 1.5kg (different from the homework, the masses here are NOT the same). The moment of inertia for the pulley is Idisk = 1 2mpR2 . (a) What is the relationship between the magnitude of the angular acceleration ? and the the magnitude of the linear acceleration of the stone a? (b) Find the angular acceleration ? of the pulley as the stone descends. (c) Find the tension in the string.

2.50-kg pulley 1.50-kg stone

Explanation / Answer


a)

angular acceleration alpha = a/R

b)

net torque on pulley = T*R

but net torque = I*alpha ....(1)


along vertical


mg - T = m*a

T = mg - ma.........(2)

(mg - ma)*R = (/12)M*R^2*alpha


(mg - ma) = (1/2)M*a

(1.5*9.8)-(1.5*a) = (1/2)*2.5*a


linear acce;leration a = 5.345 m/s^2

alpha = a/R = 10.69 rad/s^2   <<_--------answer

++++++


c)


T = mg - ma

T = 1.5*(9.8-5.345) = 6.6825 N <<---answer