- #1
spacediver
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This isn't a real homework problem (i.e. I made this problem up myself for my own purposes), but I figured this is the correct forum to post. 1. Homework Statement
In the following figure we have two rods connected to each other, and the bottom rod is connected to the blue structure (G), and G is connected to a large immovable object. The rods can rotate around point H, and the bottom rod can rotate around the joint it creates with G.
Assume that the rods are of equal length, and are uniformly weighted.
Suppose gravity doesn't exist for the purposes of this question.
There is a muscle fiber that connects the rods. My question is this:
When the muscle fiber contracts, and exerts tension at the attached points on both rods, what happens to the system? In particular, what happens to point H? Assume F1 and F2 are directed perpendicular to each rod, and are of equal magnitude.
Force = mass * acceleration
Torque = perpendicular force component * distance between fulcrum and force application
Moment of inertia of rods = 1/3 Mass*length^2
Angular acceleration due to torque = Moment of inertia/Torque
[/B]
I understand that if these two segments weren't connected to G, then one could calculate the position of point H by taking advantage of the fact that the centre of mass does not change, since all the forces are internal. In that case, you would first calculate the centre of mass. Then you could calculate the torque, due to each force around point H, calculate the angular acceleration of each rod around point H, and then using geometry, one could figure out where point H is as the rods rotate around point H, since the centre of mass does not change.
But in the illustrated example, I don't think things are as straightforward.
F1 creates a clockwise torque in the top rod around H.
F2 creates a counterclockwise torque in the bottom rod around point H
F2 also creates a clockwise torque in the bottom rod around G.
And this is where my mind gets stuck. I'm not as interested in the precise answer, as I am in understanding how to approach such a problem. I'd like to be able to learn how to think about this sort of problem, and would appreciate and guidance.
In the following figure we have two rods connected to each other, and the bottom rod is connected to the blue structure (G), and G is connected to a large immovable object. The rods can rotate around point H, and the bottom rod can rotate around the joint it creates with G.
Assume that the rods are of equal length, and are uniformly weighted.
Suppose gravity doesn't exist for the purposes of this question.
There is a muscle fiber that connects the rods. My question is this:
When the muscle fiber contracts, and exerts tension at the attached points on both rods, what happens to the system? In particular, what happens to point H? Assume F1 and F2 are directed perpendicular to each rod, and are of equal magnitude.
Homework Equations
Force = mass * acceleration
Torque = perpendicular force component * distance between fulcrum and force application
Moment of inertia of rods = 1/3 Mass*length^2
Angular acceleration due to torque = Moment of inertia/Torque
The Attempt at a Solution
[/B]
I understand that if these two segments weren't connected to G, then one could calculate the position of point H by taking advantage of the fact that the centre of mass does not change, since all the forces are internal. In that case, you would first calculate the centre of mass. Then you could calculate the torque, due to each force around point H, calculate the angular acceleration of each rod around point H, and then using geometry, one could figure out where point H is as the rods rotate around point H, since the centre of mass does not change.
But in the illustrated example, I don't think things are as straightforward.
F1 creates a clockwise torque in the top rod around H.
F2 creates a counterclockwise torque in the bottom rod around point H
F2 also creates a clockwise torque in the bottom rod around G.
And this is where my mind gets stuck. I'm not as interested in the precise answer, as I am in understanding how to approach such a problem. I'd like to be able to learn how to think about this sort of problem, and would appreciate and guidance.
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