Question

The pendulum in a grandfather clock is made of brass and keeps perfect time at 17 C. How much time is gained or lost in a year if the clock is kept at 25 C? (Assume the frequency dependence on length for a simple pendulum applies.)

Answer 1

Higher temperatures will extend the brass pendulum slightly. Find out what the temperature coefficient for brass is and calculate how long the pendulum has become after being exposed to 25 deg. You don't know the original length L, so determine the relative increase, like L at 17 deg, so k*L at 25 deg. k is the factor you need to find.

Next, look at the formula for the pendulum: T = 2*PI * SQRT(L/g), where T is the period of the pendulum and 'g' is the gravitational acceleration. For a temperature difference between 17 and 25 deg, only L changes in this formula as 'g' and PI remain constant.

Now you have two equations, one for 17 deg and one for 25 deg:

T17 = 2*PI*SQRT(L/g) and T25 = 2*PI*SQRT(k*L/g). This means that both periods relate to each other via T25/T17 = SQRT(k). As you found k earlier, you can calculate the new period, which is the rate at which the clock ticks seconds at 25 deg. Along the same line of reasoning, you can then find out how much extra seconds this clock ticks in a year.

Answer 2

time lost

Answer 3

we knowcequation
T=2π√(L/g)
T=time period
L=length of pendulum
g=gravitational accaleration
L will b greater as temperature increases
T will b greater as L increases
L increases means slower the cloack

Answer 4

@shamim - true, but how much slower then ?

Answer 5

need to know the relationship between length L and temperature

Answer 6

Just found it... http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html. The table on this page shows a linear thermal expansion coefficient of 16.6E-6 meter/meter/deg Kelvin.

Answer 7

Thank you so much i have tried the problem for hours without getting anywhere.