Masses connected by string/rod

• dinmore
In summary, the author is looking for help with simulating two point masses connected by a massless string or rod. He is having difficulty calculating the force exerted on each mass. He plans to use the rod version for simplicity.
dinmore
Hi,

I'm making a game and could do with a hand working out how to simulate the main element of it. I'm sure I should be able to work this out, it seems relativly simple, but I'm so out of practice the solutions eluding me.

I need to simulate two point masses connected by a massless string or rod (it doesn't matter which; so whichever's easiest). I'm fine with the basics of moving them about but can't figure out how to calculate the force exerted on each mass by the string/rod. I guess it'd be derived from the velocities of the opposite mass but further than that I'm stuck.

Can anyone help?

actually the force acting on the mass can be calculated from a movement of the attached mass. That is not exactly useless because you can define the movement. In the case of the rod the situation is fairly simple- the 3D translation plus rotation with respect to the center of mass; The interobject distance is fixed.

For a string the situation is slightly mor complicated, because the interobject distance is not fixed. The force should, however, act along the string, so we can use the second Newton's law.

Let's consider , for example, a case when two masses are at rest and one mass gets an impuls in an arbitrary direction. It will move freely until the distance between the masses wil be equal to the string length. Then the impulse perpendicular to the string will remain unchanged (no force is acting in that direction). As to the implulse along the string, we can consider this as an impact along the string, so we can find the impulses after the impact. It will be also a good idea to use the inertial system where the total impulse is zero, because it should remain zero unless an external force is acting on our objects.

Ah, of course. I was forgetting all about the system having a centre of mass, silly me. Think I'll use the rod version for simplicity (not just calculations - drawing a slack string right would be nasty), maybe I'll do it with string in the next version.

Now all I've got to do is dig out the angular motion equations.

Thanks for that.

Heh. Actually I think it's easier to work out what's going on with string. Think I'll go with that instead.

1. What is the difference between masses connected by string and masses connected by rod?

Masses connected by string are connected by a thin, flexible material, while masses connected by rod are connected by a solid, rigid material. This affects how the masses move and interact with each other.

2. How does the length of the string or rod affect the movement of the masses?

The length of the string or rod can affect the frequency and amplitude of the motion of the masses. A longer string or rod may result in slower and larger movements, while a shorter string or rod may result in faster and smaller movements.

3. How does the mass of the string or rod itself impact the system?

The mass of the string or rod can affect the inertia and overall behavior of the system. A heavier string or rod may result in slower movements and a more stable system, while a lighter string or rod may result in faster movements and a less stable system.

4. Can a system of masses connected by string or rod exhibit simple harmonic motion?

Yes, a system of masses connected by string or rod can exhibit simple harmonic motion if certain conditions are met. These conditions include a restoring force that is proportional to the displacement and the masses being equally spaced along the string or rod.

5. How does the angle of the string or rod affect the motion of the masses?

The angle of the string or rod can impact the direction and speed of the motion of the masses. If the string or rod is at an angle other than horizontal, the motion of the masses may be influenced by gravity and the tension in the string or rod.

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