Question

A spiral staircase winds up to the top of a tower in an old castle. To measure the height of the tower, a rope is attached to the top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measured to be 7.48 s. What is the height of the tower

Answer 1

To measure the height of the tower, the period of the pendulum is measured. By using the given period, we can calculate the length of the pendulum, which is equal to the vertical height of the tower. Then, we can find the height of the tower by doubling the length of the pendulum.

Step-by-step explanation:

To measure the height of the tower, the period of the pendulum is measured. The period of a simple pendulum depends on its length and the acceleration due to gravity. By using the given period, we can calculate the length of the pendulum, which is equal to the vertical height of the tower. Then, we can find the height of the tower by doubling the length of the pendulum.

Answer 2

Tower height: 13.9027m

Step-by-step explanation:

To determine the height we first remember that the period of the simple pendulum, for oscillations of small amplitude, is determined by its length and gravity. It does not influence the mass of the body that oscillates nor the amplitude of the oscillation.

The period of the simple pendulum is the time it takes for the pendulum to pass through a point in the same direction. It is also defined as the time it takes to get a complete swing. Its value is determined by:

T=2π×√(L/g)

T: pendulum period

L: pendulum length

g: acceleration of gravity

From which we clear the length of the pendulum which is in our problem the height of the tower:

L/g = (7.48s / (2π)) ^ 2

L= (1.4172s²) × (9.81m/s²) = 13.9027m