Finding mass of Moon with Pendulum Bob

[Carterr]

Homework Statement

It is possible to determine the mass of a planet or large moon by using a ‘pendulum bob’ horizontal circular motion experiment. A cosmonaut on the moon finds that a 25 cm long ‘pendulum bob’ moving in uniform horizontal circular motion makes an angle of 22° to the vertical and moves with a period of 2.3 s. What is the mass of the moon? (The radiusof the moon is 1.5 х 105 m)

Homework Equations

??

The Attempt at a Solution

0.25sin(22) = 0.094 (radius)

v = (2∏r) / 2.3 = 0.257 ms^-1

 

[voko]

Start with forces acting on the bob.

 

[Carterr]

so I tried a_c = 0.257² / 0.094 = 0.7 ms^-2

tan(90-22) = g / 0.7
g = 1.12

1.12 = (6.67 x 10^-11)M / (1.5 x 10⁵)²

and I got M = 3.78 x 10²⁰ which is wrong.


I'm not sure how to go with this one

 

[dimension10]

You could use the pendulum equation.

Since 22.3 degree is small enough, use the small angle approx, sin θ ≈ θ so you could derive from the pendulum equation T ≈ 2π√(l/g). So measure the period of the pendulum and find g of the moon. Since g = Gm/r², calculate m since you know r.

 

[voko]

Where does tan(90 - 22) = g / 0.7 come from?

 

[Carterr]

you have 22 degrees as the top angle and the Ac in a right angled triangle. 90-22 = 58. Is that right, I'm not sure.

tan(58) = g / 0.7

 

[voko]

First of all, 90 - 22 = 68, not 58. Even then, I do not understand where your equation comes from. What equations do you get from the free body diagram?