Centripetal Force Problem with Tension on an Unknown Planet

[Jimmy5764]

Homework Statement

An experiment is conducted on a "strange" planet to determine the acceleration due to the force of gravity there. A 2 meter length pendulum is suspended and put into horizontal circular path. Data collected: the pendulum makes 10 revolutions in 25 seconds while sweeping out a circle of radius R=.209 meters.
Find "g" for this planet.

Homework Equations

F = MA
Centripetal acceleration = V^2/R

The Attempt at a Solution

V = 10(2πR)/25 = .53m/s
R = .209
X eq: TCos60 = m(V^2)/R
Y eq: TSin60 = mg (no acceleration in the y direction)

 

[kuruman]

So far so good. Can you find g from what you already have?
BTW, the units of V are not m/s^2, but that's a minor point.

 

[Jimmy5764]

So far so good. Can you find g from what you already have?
BTW, the units of V are not m/s^2, but that's a minor point.

I am having trouble solving this because there are three unknowns T, m, and g. I guess my algebra is rusty, or am I missing something? In other words, should I be able to solve this by system of equations at this point?

 

[haruspex]

I am having trouble solving this because there are three unknowns T, m, and g. I guess my algebra is rusty, or am I missing something? In other words, should I be able to solve this by system of equations at this point?

Sometimes it turns out that one of the unknowns is irrelevant. Just work the equations and see if one of them disappears, or the ratio between two of them is all that matters.