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
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To determine the height of the tower, we can use the formula for the period of a simple 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.
(a) To find the height of the tower, we need to determine the length of the pendulum. Since the man notes that the pendulum extends from the ceiling almost to the floor, we can assume that the length of the pendulum is equal to the height of the tower.
Given:
T = 28.0 s
g = 9.8 m/s^2 (acceleration due to gravity on Earth)
We can rearrange the formula to solve for L:
L = (g * T^2) / (4π^2)
Substituting the given values:
L = (9.8 m/s^2 * (28.0 s)^2) / (4π^2)
Calculating this expression will provide us with the height of the tower.
(b) To find the period on the Moon, where the free-fall acceleration is 1.67 m/s^2, we can again use the formula for the period of a simple pendulum:
T' = 2π√(L'/g')
Where T' is the period on the Moon, L' is the length of the pendulum on the Moon (which is equal to the height of the tower), and g' is the acceleration due to gravity on the Moon.
Given:
g' = 1.67 m/s^2
We can rearrange the formula to solve for T':
T' = 2π√(L'/g')
Since L' is the same as the height of the tower, the value of T' can be found by substituting the known values into the equation above.