Dynamic Rotation Total Torque Calculation

[inner08]

Homework Statement

Two blocks of mass m1=3kg and m2=5kg are linked by a cord passing through a pulley of radius R=8cm and of mass M=4kg. We neglect friction and we assimilate the pulley to a disk. We place the origin at the center of the pulley.

a) what is the total torque on the system?
b) what is the kinetic moment (I hope I translated it correctly..its moment cinetique in french) of the system when the blocks have a speed of v?
c) Find the acceleration of the blocs by applying the equation torque(ext)=dL/dt.

Homework Equations

torque(ext)=dL/dt
T1-T2= Ia
a = alpha * r

The Attempt at a Solution

I drew a fbd and came up with this:

m1: T1-m1*g=m1*a
m2: m2*g - T2 = m2*a
pulley: T2 - T1 = I(alpha)

I figured i'd try to isolate alpha and then substitute it in the equation T1-T2 to find the torque.

m2*g - m2*a - (m1*a + m1*g) = I * alpha
5 * 9.8 - 5a - 3a - 3*9.8 = (1/2)MR^2 * alpha
49 - 8a - 29.4 = (1/2)4*0.08^2 * alpha
19.6 - 8a = 0.0128 * alpha
19.6 - 8(alpha*r) = 0.0128 *alpha
19.6 - .64alpha = 0.0128alpha
19.6 = 0,6528alpha
alpha = 30

Substitute alpha in the equation torque = T2 - T1

19.6 - .64 * 30 = 0.4 <-- this is wrong..it should be 1.57

 

[OlderDan]

You are being asked for the torque acting on the system, not the torque acting on the wheel. This problem is a but unusual. It wants you to look at the angular momentum of the whole system relative to the origin and the effect of external torques acting on that system

 

[kyle8921]

I would first commend the student for their attempt at solving the problem and using the correct equations. However, there are a few errors in their approach.

Firstly, in the equation for the pulley, the student has incorrectly multiplied the moment of inertia (I) by alpha. The correct equation is T2-T1=I*alpha*r, where r is the radius of the pulley.

Secondly, in the calculation for alpha, the student has used the wrong units for the moment of inertia. It should be in kg*m^2, not cm^2.

Lastly, in the final calculation for the torque, the student has used the wrong value for alpha. It should be 30 radians/s^2, not 30.

Overall, the student's approach is correct, but they need to pay closer attention to units and use the correct values in their calculations. The correct answer for the torque should be 1.57 Nm.