dlreynolds562
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Homework Statement
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.
Homework Equations
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.
