Solving Rotational Dynamics Problems with Torques & Acceleration

AI Thread Summary
The discussion revolves around solving a rotational dynamics problem involving a wheel, torque, and acceleration. The user correctly calculates the acceleration (a) as approximately 7.02 m/s² and the velocity (v) at point B as 19.83 m/s. However, the tension (T) in the string is calculated as 294.79 N, which is reported as incorrect. Suggestions include re-evaluating the relationship between torque and tension, and verifying the calculations using the moment of inertia and angular acceleration. Clarification on the correct approach to find the tension is sought to resolve the issue.
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Hello,
I have a problem dealing with torques and acceleration. I am sure I solved it right but when submitting the answers, I get the response "Incorrect" :cry:

The problem:

A wheel of radius 2 m, mass 53 kg, and moment of inertia (3/4) (53 kg) (2m)^2 about the center of mass is mounted on a frictionless horizontal axle.
(g = 9.8). A light cord wrapped around the wheel supports an object of mass 106 kg. The weight is released from rest at the level of A and falls a distance h, past level B (AB=28 m). a) Find the velocity as it passes B b) Determine the tension of the string.

I set up everything.

Torque = I* alpha = T*R since alpha = a/R and we know I, conclusion is T=42*a

Then: T=m(g - a): putting T from above, I got a=7.0189189 m/s^2
To find V as the mass passes point B: Vf^2 = 2*a*28m ---> and v at B = 19.83 m/s. This was OK

For b) I used T=m(g-a), since I know a = 7.0189189m/s^2 , I substituted it at the equation and I got T= 294.79 N but this is not the right answer.

Maybe I can use I*alpha = T*R and from that get T because everything is known, but I am not sure. Any suggestions?
 
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Can anyone help?
 
For part a)
F=mg
Torque=mgr
mgr=I(alpha)
28=r(theta)
Wf^2=Wi^2+2(alpha)(theta)
Vf=r(Wf)

For part b)
a=R(alpha)
T=m(g-a)

Do these things help?
 
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