I askeda chegg tutor to help me with this question, and they got a=5.88 and t=.5

Question

I askeda chegg tutor to help me with this question, and they got a=5.88 and t=.588 these both are incorrect

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 Ms = 100 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.

Explanation / Answer

. The object that is hanging from the bottom of the string has two vertical forces. Its weight is the downward force and the tension in the string is the upward force. Since it is accelerating toward the floor, the net force is its weight minus the tension. Let’s use the following equation to determine its acceleration.

T – Weight = mass * acceleration
Weight = 0.15 * 9.8 = 1.47 N
1.47 – T = 0.15 * a
T = 1.47 – 0.15 * a

For the spool, I drew circle with string wrapped around it. The tension is producing a torque that causes the spool to accelerate.

Torque = T * r = T * 0.03

AND

Torque = I *
I = ½ * m * r^2 = ½ * 0.1 * 0.03^2 = 4.5 * 10^-5
Since we need to determine the acceleration, let’s convert to a by dividing by r.
= a ÷ 0.03

Torque = 4.5 * 10^-5 * (a ÷ 0.03) = a * 1.5 * 10^-3
Set the two torque equations equal to each other and solve for T.

T * 0.03 = a * 1.5 * 10^-3
T = a * 0.05
Set the two equation for T equal to each other and solve for a.

1.47 – 0.15 * a = a * 0.05
1.47 = a * 0.2
a = 7.35 m/s^2

To see if this is the correct acceleration, let’s substitute this number into the following equations and solve for T.

T = 1.47 – 0.15 * a = 1.47 – 0.15 * 7.35 = 0.3675 N
T = a * 0.05 = 7.35 * 0.05 = 0.3675 N

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