A 150-g weight is tied to a piece of thread wrapped around a spool, which is sus

Question

A 150-g weight is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R 3 cm and mass M 300 g. Find the tension in the thread and the magnitude of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. R 3 cm Number M 300 g acceleration Number tension 150 g

Explanation / Answer

for the weight

Fnet = m*a

mw*g - T = mw*a

T = mw*g - mw*a...............(1)

for the spool

net torque = I*alfa

I = moment of inertia = (1/2)*Ms*R^2

alfa = a/R

alfa = angular accelration

a = linear acceleration

R = radius = 0.03 m

torque = T*R

thererfore

T*R = I*a/R

T*R = (1/2)*Ms*R^2*a/R

T = (1/2)*Ms*a..............(2)

from 1 & 2

mw*g - mw*a = (1/2)*Ms*a

mw*g = mw*a + (1/2)*Ms*a

a = mw*g/(mw+0.5*Ms)

a = (0.15*9.8)/(0.15+(0.5*0.3)) = 4.9 m/s^2 <-------answer

tension T = 0.5*Ms*a = 0.5*0.3*4.9 = 0.735 N <-------answer

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