# Tough physics problem. Conical pendulum.

1. Oct 27, 2013

### dlreynolds562

1. The problem statement, all variables and given/known data

Hey, thanks for taking a look at this.

"The figure below shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass m, the string has a length L and negligible mass, and the bob follows a circular path of the circumference C. What are the tension in the string and the period of the motion? (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.)"

The figure is just the conical pendulum as described.

2. Relevant equations

3. The attempt at a solution

I start by breaking tension into x and y components.

Tx = Tsinθ & Ty = Tcosθ

Force balance in the y direction

ƩFy = Ty - mg = 0
=> Tcosθ = mg

Force balance in the x direction

ƩFx = Tsinθ

I guess this is just equal to the centripetal force?

Tsinθ = mv^2/r

... so I guess to answer the first question T = mg/cosθ, but it says not to leave it in terms of theta

cosθ = h/L

using Pythagorean theorem

h^2 = L^2 - R^2

and also C = 2∏r, -> r = C/(2∏)

h = sqrt(L^2 - (C/(2∏)^2)

Now plugging all that into the equation from above

Tcosθ = mg

gives

T = mgL/sqrt(L^2-(C/2∏)^2)

This is what I have so far and I really don't think it is right.

2. Oct 27, 2013

### voko

Why do you think that is not right?

3. Oct 27, 2013

### Staff: Mentor

Your tension expression looks okay to me