Tension on a simple pendulum

[bocobuff]

Homework Statement

The diagram shows a simple pendulum consisting of a mass M suspended by a thin, massless string. The magnitude of the tension is T. The mass swings back and forth between +/- θ₀. Select all correct answers, e.g. B, AC, BCD.

A) T is largest at the bottom (θ = 0).
B) T is smallest when θ = +/- θ₀.
C) T equals Mg when θ = θ₀.
D) The vertical component of tension is constant.
E) T = Mg at some angle between zero and θ₀.
F) T is greater than Mg when θ = θ₀.

Homework Equations

none

The Attempt at a Solution

A) T would be equal to Mg so that means C is incorrect. But I'm not sure if this is where the T would be the largest. I think so, because anywhere else would have a vertical Tcosθ and a horizontal Tsinθ component.
B) The same issue as A)
D) The vertical component of T would change as θ changed because of the components right? So that's incorrect.
E) I think the only place T=Mg is when θ=0, not at some angle between zero and θ₀
F) Again, similar issue with A and B. Not sure where the max and min T are on a simple pendulum.

Any suggestions would be appreciated. Thanks.

 

[horatio89]

It would help if you draw the free body diagram for the forces acting on the pendulum at the equil. point, and the two maximum points.

It is worth remembering though, that a pendulum is moving is a circular motion, and there must be a net centripetal force (which is a resultant force, and not an actual "force") pointing in the radial direction, when it is in motion. Compare the magnitude of the forces acting in this direction for the three points.

 

[thomate1]

You are correct in your reasoning for A, B, D, and E. The tension would be greatest at the bottom (θ = 0) and smallest at the maximum angle (θ = +/- θ0). The vertical component of tension would vary as θ changes, so D is incorrect. T can only equal Mg when θ = 0, so E is also incorrect. As for F, T would be greater than Mg at θ = θ0, as the pendulum is swinging towards its maximum angle and the tension would need to be greater to keep the mass from falling.