Question

A simple pendulum consists of a ball connected to one end of a thin brass wire. the period of the pendulum is 1.11s. the temperature rises by 149 degrees celsius and the length of the wire increases. determine the change in the period of the heated pendulum.

Answer 1

The period of a simple pendulum increases when the temperature rises due to the expansion of the brass wire, proportional to the coefficient of linear expansion and the change in temperature.

Step-by-step explanation:

The period of a simple pendulum is directly related to the square root of its length. An increase in temperature will cause the length of the brass wire to expand due to thermal expansion. The formula for the period T of a pendulum is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If the temperature rises, the length increases by L = L₀(1 + αΔT), with α being the coefficient of linear expansion and ΔT the change in temperature. The change in period ΔT is then approximately αΔT/2 times the original period, since the period depends on the square root of the length.