Your grandfather clock's pendulum has a length of 0.9930 m. part a if the clock runs slow and loses 19 s per day, how should you adjust the length of the pendulum? note: due to the precise nature of this problem you must treat the constant g as unknown (that is, do not assume it is equal to exactly 9.80 m/s2).

Explanation:  

The period (T) of a simple pendulum depends on the length (l) of the pendulum and acceleration due to gravity (g). The period of a simple pendulum can be calculated as follows:

T= 2

The number of hours in a day is 24 h.

Convert 24 h to second as follows,

24 x 60 x 60 =86400  s

The number of cycle’s clock made per day is,

86400/2 = 43200

If the clock runs, slow of 19 s, then there is 9.5 cycles is reduces per day. So,

( 43200 -9.5) cycles  = 43190.5 cycles

The period would be reduces by.  43190.5/43200 = 0.9998

Then the new time period is,

T new = 0.9998 Told

Substitute

LNEW/LODD =

LNEW/LODD =0.9996

Substitute 0.9930 m for LODD

LNEW = 0.9930 X 0.9996 = 0.9926

The difference in the lengths is,

LNEW- LODD

= 0.9926-  0.9930 = -0.0004

This is the same as 0.4mm

Therefore, the new length of the pendulum is 0.9926m,  the length of the pendulum should be reduced by. 0.4mm

the average speed is 24.57 km/hr

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