To determine the new period of the clock's pendulum, 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.
Since the length of the pendulum remains constant, we can assume that L is the same at both temperatures.
However, the acceleration due to gravity can vary due to the change in temperature. The acceleration due to gravity, g, can be approximated as:
g = g₀(1 + αΔT)
where g₀ is the acceleration due to gravity at a reference temperature, α is the linear coefficient of expansion for the material, and ΔT is the change in temperature.
In this case, the pendulum is made of copper, which has a linear coefficient of expansion of α = 0.000016/°C, and the reference temperature is 17.3°C.
To find the new period, we need to calculate the change in temperature, ΔT, and the new acceleration due to gravity, g.
ΔT = 33.9°C - 17.3°C = 16.6°C
g = 9.81 m/s² * (1 + (0.000016/°C * 16.6°C))
Now, we can plug the value of g into the formula for the period of the pendulum to find the new period, T_new.
T_new = 2π√(L/g)
(T_new = 2π√(L/ (9.81 m/s² * (1 + (0.000016/°C * 16.6°C)) ))
After evaluating this equation, we will find the new period of the clock's pendulum.