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elixir [45]
3 years ago
8

A student uses a stopwatch to measure the period of the pendulum of the Beverly clock in the corridor. His measurements are: (a)

13.54is (b) 13.44 s (c) 13.89 s (d) 13.41 s (e) 13.17s (f) 13.22 s . Calculate his best estimate of the period Calculate the associated error .Explain the assumptions behind your estimation of the error
Physics
1 answer:
Westkost [7]3 years ago
6 0

Answer:

Reading is close to (b) 13.44 which is the best estimate of the period

Associated error, \Delta E =0.178 s

Given:

t_{a} = 13.54 s

t_{b} = 13.44 s

t_{c} = 13.89 s

t_{d} = 13.41 s

t_{e} = 13.17 s

t_{f} = 13.22 s

Solution:

1.The best estimate of the period can be calculated by the mean of the measurements and the one closest to the mean is the best estimate of the measurement:

Mean, \bar {x} = \fra{sum of all observations}{No. of observation}

Mean, \bar {x} = \frac{t_{a} + t_{b} + t_{c} +t_{d} + t_{e} + t_{f}}{6}

Mean, \bar {x} = \frac{13.54 + 13.44 + 13.89 + 13.41 + 13.17 + 13.22}{6}

Mean, \bar {x} = 13.445 s

It is close to 13.44 s

2. Associated error is given by:

\Delta E_{n} = |measured value - actual value|

\Delta E_{n} = |t_{n} - \bar {x}|

where

n = a, b,......, e

Now,

\Delta E_{a} = |t_{a} - \bar {x}| = |13.54 - 13.44| = 0.01

\Delta E_{b} = |t_{b} - \bar {x}| = |13.44 - 13.44| = 0.00

\Delta E_{c} = |t_{c} - \bar {x}| = |13.89 - 13.44| = 0.45

\Delta E_{d} = |t_{d} - \bar {x}| = |13.41 - 13.44| = 0.03

\Delta E_{e} = |t_{e} - \bar {x}| = |13.17 - 13.44| = 0.027

\Delta E_{f} = |t_{f} - \bar {x}| = |13.54 - 13.44| = 0.10

Mean Absolute Error, \Delta E = \frac{\Sigma E_{n}}{6}

\Delta E = \frac{0.01 + 0.00 + 0.45 + 0.03 +0.027 + 1.10}{6}

\Delta E =0.178 s

3. The assumption behind the estimation is population is considered to distributed normally.

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