Question

You wish to determine the height of the smokestack of a local coal burning power plant. You convince a member of the maintenance crew to mount the support for a simple pendulum at the top of the stack and you suspend a 1.00 kg mass that just misses the ground at its lowest point from the pendulum cord. If the period of the pendulum is 38.3 s, determine the height of the smokestack in m.

If you had the ability to take this pendulum to the moon, where the acceleration due to gravity is 1.67 m/s2, what would you expect the period of the pendulum to be in seconds.

Answer 1

Step-by-step explanation:

To determine the height of the smokestack using a simple pendulum, we can use the formula:

T = 2π √(L/g)

where T is the period of the pendulum in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity in m/s^2.

Given that the period of the pendulum is 38.3 s and the acceleration due to gravity on Earth is 9.8 m/s^2, we can solve for L:

38.3 = 2π √(L/9.8)

L = (38.3^2) * 9.8 / (4π^2)

L = (1461.69) / (39.4784)

L = 37.03 m

So the height of the smokestack is 37.03 m.

To find the period of the pendulum on the moon, we can use the same formula, but substitute the acceleration due to gravity on the moon, which is 1.67 m/s^2, for the value of g.

T = 2π √(L/1.67)

Given that L=37.03m, we can calculate the period of the pendulum on the moon:

T = 2π √(37.03/1.67)

T = 2π √22.24

T ≈ 45.5 seconds