M3 vertical circle rod: thrust vs tension Watch

Heirio
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Report Thread starter 10 months ago
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I've looked it up and the internet tells me that when a rod with a particle at the end is vertically straight above the centre point in a vertical circle, the force acting down is mg and instead of tension, there is thrust acting up in the rod.

my maths teacher agrees with me on this.

however, there is a question in my M3 book that states, in the solutions, that at the highest point, both tension and mg are acting down, which doesn't make sense.

please help
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ghostwalker
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#2
Report 10 months ago
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(Original post by Heirio)
I've looked it up and the internet tells me that when a rod with a particle at the end is vertically straight above the centre point in a vertical circle, the force acting down is mg and instead of tension, there is thrust acting up in the rod.

my maths teacher agrees with me on this.

however, there is a question in my M3 book that states, in the solutions, that at the highest point, both tension and mg are acting down, which doesn't make sense.

please help
If the rod is stationary, then there must be a force acting up (mg) to support the weight of the particle.

For motion in a circle at the point directly above the centre, with the particle moving with speed v, we have:

\dfrac{mv^2}{r}= T+mg where T is the tension.

Considering different values of the speed v.

IF v is zero or "small", then the tension must be negative, i.e. we have thrust in the rod.

As v increases, you come to a point where v^2=rg, and T will be zero, i.e. neither tension or thrust.

For greater values v, where v^2>rg, then T will be positive, and you have tension.
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