How tall is the tower in the following case?You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor...
How tall is the tower in the following case?
You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 27 s. The acceleration of gravity is 9.81 m/s^2. How tall is the tower?
1 Answer
justaguide | College Teacher | (Level 2) Distinguished Educator
The time period T of a pendulum to complete one cycle while it swings is given by T = 2*pi*sqrt(L/g) where L is the length of the pendulum and g is the acceleration due to gravity.
In the question it is noticed that a pendulum extending from the ceiling almost touches the floor and that its period is 27 s. The acceleration of gravity is 9.81 m/s^2.
Substituting these values in the formula for time period
27 = 2*pi*sqrt(L/9.81)
=> L/9.81 = (27/2*pi)^2
=> L = (27/2*pi)^2*9.81 m
=> L = 181.14 m
The height of the tower is approximately equal to 181.14 m