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mezya [45]
4 years ago
15

If the clock runs slow and loses 15 s per day, how should you adjust the length of the pendulum?

Physics
1 answer:
Shkiper50 [21]4 years ago
8 0

Answer:

L= 1 m,   ΔL = 0.0074 m

Explanation:

A clock is a simple pendulum with angular velocity

         w = √ g / L

Angular velocity is related to frequency and period.

         w = 2π f = 2π / T

We replace

        2π / T = √ g / L

        T = 2π √L / g

We will use the value of g = 9.8 m / s², the initial length of the pendulum, in general it is 1 m (L = 1m)

With this length the average time period is

           T = 2π √1 / 9.8

           T = 2.0 s

They indicate that the error accumulated in a day is 15 s, let's use a rule of proportions to find the error is a swing

           t = 1 day (24h / 1day) (3600s / 1h) = 86400 s

         e= Δt = 15 (2/86400) = 3.5 104 s

The time the clock measures is

           T ’= To - e

           T’= 2.0 -0.00035

           T’= 1.99965 s

Let's look for the length of the pendulum to challenge time (t ’)

           L’= T’² g / 4π²

           L’= 1.99965 2 9.8 / 4π²

           L ’= 0.9926 m

Therefore the amount that should adjust the length is

           ΔL = L - L’

           ΔL = 1.00 - 0.9926

           ΔL = 0.0074 m

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