Solving Rigid Body Dynamics: Find Tension in Cable A

[pconn5]

Not really sure if this is where this should be but oh well.

1. Homework Statement

It is given that:

b = 200 mm
mass = 6 kg

Find the tension in cable A immediately after cord B is cut.


2. Homework Equations
Moment = I*alpha + m*a*d
F = ma?


3. The Attempt at a Solution
I tried to do
Moment about A = I*alpha (second part is zero?) , so 9.81*6*.1 = 1/6*6*2*.2^2*alpha

I then solved for alpha.

And plugged it into:
Moment about G(center) = I*alpha, but this is wrong and I don't really understand why to be honest with you. It trips me up when the forces are not perpendicular to the center for some reason.

The final answer is T = 23.5 N.

Thanks.

 

[anathema]

Thank you for your post. I understand that you are trying to find the tension in cable A after cord B is cut. Your approach of using moments and the equation F=ma is a good start. However, there are a few things that you can improve on to get the correct answer.

Firstly, when you are taking moments about point A, you need to consider all the forces acting on the object. In this case, you have the weight of the object (6 kg) acting downwards and the tension in cable A acting upwards. So your equation should be:

Moment about A = I*alpha = (6 kg)(9.81 m/s^2)(0.1 m) - T(0.2 m)

where T is the tension in cable A. This is because the moment due to a force is equal to the force multiplied by the perpendicular distance from the point to the line of action of the force.

Next, you correctly solved for alpha using the equation Moment about A = I*alpha. However, when you substitute this value for alpha into the equation Moment about G = I*alpha, you are not considering the forces acting on the object. You need to use the equation F=ma to find the acceleration of the object, and then use that in the equation Moment about G = I*alpha to solve for the tension in cable A.

So your final set of equations should be:

(6 kg)(9.81 m/s^2)(0.1 m) - T(0.2 m) = (1/6)(6 kg)(0.2 m)^2 * alpha

T = (6 kg)(0.1 m)(alpha)

Using the equation F=ma, you can find the acceleration alpha, and then substitute that back into the second equation to solve for T.

I hope this helps. Let me know if you have any further questions. Good luck with your calculations!