How Do You Calculate the Angle Theta for a Pendulum Near Mt. Everest?

[evan b]

Homework Statement

Estimate the angle theta of the pendulum bob if it is 4.80km from the center of Mt. Everest.

The Attempt at a Solution

Tan(theta) = (GMeverest/r^2)/g

I have been trying to use this formula, but i don't think its the right one?

 

[Kurdt]

I think that formula should be ok for an estimate.

 

[baba89]

I would first clarify the question and gather more information. What is the specific setup of the pendulum in relation to Mt. Everest? Is the pendulum bob at rest or in motion? What is the mass of the pendulum bob? Without this information, it is difficult to provide an accurate response.

Assuming the pendulum bob is at rest and the setup is a simple pendulum, we can use the formula for the period of a pendulum: T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. Since we are given the distance from the center of Mt. Everest (4.80km), we can use this as the length of the pendulum (L). To find the value of g, we can use the universal law of gravitation: F = GmM/r^2, where F is the force of gravity, G is the universal gravitational constant, m is the mass of the Earth, M is the mass of the pendulum bob, and r is the distance between the center of the Earth and the pendulum bob. By rearranging this equation, we can solve for g: g = GM/r^2. Now, we can substitute the values we have into the formula for the period of a pendulum and solve for theta:

T = 2π√(L/g)

= 2π√(4.80km/((GM/r^2)))

= 2π√(4.80km/((6.67x10^-11 Nm^2/kg^2)(5.98x10^24 kg)/(4.80km)^2))

= 2.36 seconds

Therefore, the angle theta of the pendulum bob is approximately 2.36 seconds. However, please note that this is an estimation and may not be accurate without more information about the setup and conditions of the pendulum.