Tension in Pendulum

[MedPR]

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If you raise a pendulum to some height, then drop it and allow it to oscillate there are three forces acting on it. Tension, mg, and the centripetal force.

I understand that in equilibrium, netforce = 0, so force up + force down = 0. However, In this example there are three forces and the net force is not equal to 0. This is actually from TBR, but I don't remember exactly where and I'm too lazy to get my book to look it up.

The explanation says that T+mg = Fcentripetal. I understand how two of the forces must add up to be the third force, but how do you know the net force is Fcentripetal and not the Tension? What I mean is, how do you know that T+mg=F and not F+mg=T?

 

[Ssina]

because centripetal force is always the NET force... we don't really have a centripetal force directly acting on any object, but we have an actual force of gravity (mg from the earth) and the tension (of the wire).... so their net effect or force on the pendulum's bob creates the net force, which is the centripetal

I personally think it's wrong to say that there are 3 forces acting... I think it's more correct to draw one body diagram and put tension and mg on it, then draw another one with Fnet of both creating this centripetal force... but who's gonna think of 50 diagrams on the test, so we just say 3 forces acting on it

 

[MedPR]

because centripetal force is always the NET force... we don't really have a centripetal force directly acting on any object, but we have an actual force of gravity (mg from the earth) and the tension (of the wire).... so their net effect or force on the pendulum's bob creates the net force, which is the centripetal

I personally think it's wrong to say that there are 3 forces acting... I think it's more correct to draw one body diagram and put tension and mg on it, then draw another one with Fnet of both creating this centripetal force... but who's gonna think of 50 diagrams on the test, so we just say 3 forces acting on it

Oh, I didn't know that Fc was always the net force. That makes more sense 🙂 Thanks

 

[MT Headed]

Remember, Fnet=Fc is only valid for an object in uniform circular motion. A pendulum's motion is not uniform.

When you first drop the pendulum bob, gravity acts downward and tension pulls towards the pendulum's fulcrum. What direction is the net force then? Think about what direction the bob is accelerating from rest.

Now consider the case where the bob is at the bottom of the swing. Gravity pulls down. Tension pulls up. There is no tangential acceleration because there are no sideways forces. Only at this point is the pendulum bob in uniform circular motion, and Fnet=Fc.

 

[MedPR]

Remember, Fnet=Fc is only valid for an object in uniform circular motion. A pendulum's motion is not uniform.

When you first drop the pendulum bob, gravity acts downward and tension pulls towards the pendulum's fulcrum. What direction is the net force then? Think about what direction the bob is accelerating from rest.

Now consider the case where the bob is at the bottom of the swing. Gravity pulls down. Tension pulls up. There is no tangential acceleration because there are no sideways forces. Only at this point is the pendulum bob in uniform circular motion, and Fnet=Fc.

Yes, thank you. I believe the question asked what the net force was at the point of equilibrium if a pendulum bob was dropped from x height. In that problem, Fnet=Fc does apply, correct? So Fc=T+mg?

 

[MT Headed]

👍

Just make sure you get the concept I was describing, too. It isn't usually covered in physics, but it is certainly mcat worthy. It's just the kind of extension of known material that they love to test.

 

[MedPR]

Yea I definitely hadn't thought of that. I actually thought pendulums had constant/uniform acceleration since it was only gravity causing it to accelerate. I'm still not exactly sure why it's not constant though.. Does it have something to do with the fact that mgsintheta is the force (?) tangent to the arc?

 

[milski]

Yea I definitely hadn't thought of that. I actually thought pendulums had constant/uniform acceleration since it was only gravity causing it to accelerate. I'm still not exactly sure why it's not constant though.. Does it have something to do with the fact that mgsintheta is the force (?) tangent to the arc?

Yes, pretty much that's it. The net force on the pendulum changes, so the acceleration changes as well.

Something to consider about the centripetal force is that it's never a force on its own. It's always a result of some force or combination of forces - be it friction, tension, gravity, etc.

 

[Ssina]

Remember, Fnet=Fc is only valid for an object in uniform circular motion. A pendulum's motion is not uniform.

When you first drop the pendulum bob, gravity acts downward and tension pulls towards the pendulum's fulcrum. What direction is the net force then? Think about what direction the bob is accelerating from rest.

Now consider the case where the bob is at the bottom of the swing. Gravity pulls down. Tension pulls up. There is no tangential acceleration because there are no sideways forces. Only at this point is the pendulum bob in uniform circular motion, and Fnet=Fc.

Veryy good point! I sometimes forget this fact

The tension is not the same through out the cycle and the speed is changing, since we go from PE to KE, as oppose to uniform circular motion with constant speed... Also the pendulum is rotating vertically as oppose to a car going in circle where gravity is perpendicular

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