Conservation of Energy, pendulum problem

[Litcyb]

Homework Statement

To form a pendulum, a 0.092 kg ball is attached to one
end of a rod of length 0.62 m and negligible mass, and the other
end of the rod is mounted on a pivot. The rod is rotated until it is
straight up, and then it is released from rest so that it swings down
around the pivot.When the ball reaches its lowest point, what are
(a) its speed and (b) the tension in the rod? Next, the rod is rotated
until it is horizontal, and then it is again released from rest. (c) At
what angle from the vertical does the tension in the rod equal the
weight of the ball? (d) If the mass of the ball is increased, does the
answer to (c) increase, decrease, or remain the same?

Homework Equations

ƩFy=> t-mgcosθ = ma
a= (v^2/r) ---> t-mgcosθ = m*(v^2/r)

Ki+Ui= Kf+Uf

The Attempt at a Solution

I have done part A and B already. But I am struggling trying to figure out part C.

I know, that they are asking at what angle, would t=mg(weight of the bob)

so if we substitute t= mg in t-mgcosθ = ma, we get => mg-mgcosθ=m(v^2/r)

in this step, the book calculated for velocity and then calculated the height.

I sincerely don't know how to go about this problem.

Im having trouble trying to find the height in order to apply it to the equation for conservation of energy.

In the book solution, they solved it by first using Newtons second law to find V^2f . They didnt show how to solve for height.

Please, can someone give an insight of possible ways i can approach this problem?

Thank you in advance.

 

[mfb]

The height above the pivot is just r*cosθ (or maybe -r*cosθ depending on your sign definition). As you know the initial height, you can calculate the height difference, which allows to get v as function of θ.

 

[Litcyb]

Im sorry, I don't understand, I am bit more confused than i was before. Would you please elaborate a bit more? how do you the height above is that?

 

[mfb]

Did you draw a sketch? You get the height via simple trigonometry, the expression depends on your definition of the angle θ.

 

[Litcyb]

but isn't height= r(1-cosθ).
where r=length of the cord?

 

[haruspex]

but isn't height= r(1-cosθ).
where r=length of the cord?

It depends where you choose to measure the height from. Simplest is to measure it from the axis of rotation.