Weight of a block in equilibrium in a system.

[IAmPat]

Homework Statement

The picture below shows a mobile
in equilibrium. Each of the rods is 0.16m long and each hangs from a supporting string that is attached one fourth of the way across it. The mass of each rod is 0.10kg. The mass of the strings connecting the blocks to the rods is negligible. What is the mass of block A.

Homework Equations

Net Torque = 0
Rod length (left side) = 0.12m
Rod length (right side) = 0.04m

Weight of Rod (left side) = 0.075kg
Weight of Rod (right side) = 0.025kg

Weight of block A = 9.8A

The Attempt at a Solution

I've tried two methods, neither worked. I don't know how to get the torque of the rod itself.

(0.30 + 0.075) * 9.8 = 3.675N
3.675 * 0.12 = 0.441 >> Torque of left side

.441 = [[A + 0.025] * 9.8] * 0.04
11.025 = [A + 0.025] * 9.8
1.125 = A + 0.025
1.1 = A >> Mass of A

But this was wrong. I also tried to do the problem by ignoring the mass of the rod, but that was also wrong.

 

[PhanthomJay]

You have incorrectly assumed that the mass of each part of the lower rod acts at the point where the block masses are attached. The resultant mass of the rod acts at its center of mass.

 

[AlexChandler]

You have incorrectly assumed that the mass of each part of the lower rod acts at the point where the block masses are attached. The resultant mass of the rod acts at its center of mass.

It should work out correctly using tension forces on the rod at the points where the block masses are attached. Certainly you would have to agree that this is where the forces are actually exerted.. It is not incorrect to handle the problem this way.

What I would try is to choose two points, call them O and P. Say P is on the lower rod at the point where mass A is hanging from the lower rod. The sum of all torques on the rod calculated with P as the origin must be zero. So this equation allows you to find the tension in the string that the lower rod is hanging from. Now say point O is on the lower rod at the point where the known mass hangs from. Calculated the Sum of all the torques about this point and it must also be equal to zero. You know all of the distances and you know the tension in the string. This should lead you to the correct answer.

 

[PhanthomJay]

It should work out correctly using tension forces on the rod at the points where the block masses are attached. Certainly you would have to agree that this is where the forces are actually exerted.. It is not incorrect to handle the problem this way.

There are forces acting on the lower rod from from three masses, the 0.30 kg mass of the left block, the unknown mass of block A, and the 0.1 kg mass of the rod itself. The weight force of the hanging masses act on the lower rod at the points where their respective masses are attached. The weight of the rod itself does not act at those points. It is simplest to find out where the resultant weight of the rod acts, apply that force at that point, and them sum torques = 0 about the point where the string supporting the lower rod is attached to it. This is what the OP was attempting to do, but incorrectly determined the moment arm of the rod's weight.

 

[rwisz]

I would like to point out that there seems to be some missing information in this problem. In order to accurately determine the mass of block A, we need to know the weight of the entire system, including the weight of the rods and the strings connecting them to the blocks. Without this information, it is impossible to accurately calculate the mass of block A.

Additionally, the equations used in the attempt at a solution are not entirely correct. The net torque equation should also take into account the distance from the pivot point (where the string is attached to the rod) to the center of mass of the rod, which is not given in the problem. This distance is necessary to accurately calculate the torque of the rods.

In order to solve this problem, we would need to know the weight of the entire system and the distance from the pivot point to the center of mass of the rods. With this information, we can use the net torque equation to set up a system of equations and solve for the mass of block A. Without these crucial pieces of information, it is not possible to accurately determine the mass of block A.