A man enters a tall tower, needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor and that its period is 28.0 s.
(a) How tall is the tower?
m
(b) If this pendulum is taken to the Moon, where the free-fall acceleration is 1.67 m/s2 what is the period there?
s
To calculate the height of the tower, you can use the formula for the period of a simple pendulum:
T = 2π√(L/g)
Where:
T is the period of the pendulum,
L is the length of the pendulum,
and g is the acceleration due to gravity.
(a) To find the height of the tower, you need to rearrange the formula to solve for L:
L = (T/2π)² * g
Given that the period T is 28.0 s and assuming the acceleration due to gravity g is approximately 9.8 m/s² on Earth, you can calculate the length L:
L = (28.0/2π)² * 9.8 m
Solving this equation will give you the height of the tower in meters.
(b) To find the period of the pendulum on the Moon, where the acceleration due to gravity is 1.67 m/s², you can use the same formula for the period of a pendulum and substitute the new gravity value:
T' = 2π√(L/g')
Where T' is the period on the Moon, L is the length of the pendulum (which remains the same), and g' is the acceleration due to gravity on the Moon.
To find T', you can rearrange the formula:
T' = T * √(g'/g)
Substituting the given values T = 28.0 s, g = 9.8 m/s², and g' = 1.67 m/s², you can calculate the period on the Moon.