Answer to Question #189073 in Mechanics | Relativity for prince

Question

1.581 1.575 1.541 1.523 1.554 1.544 1.534

1.595 1.551 1.500 1.569 1.546 1.539 1.579

1.556 1.566 1.548 1.529 1.518 1.586 1.511

1.531 1.511 1.589 1.521 1.555 1.568 1.559

1.553 1.563 1.538 1.561 1.565 1.542 1.533

1.578 1.543 1.552 1.512 1.536 1.525 1.549

(a) Determine the frequency with which each value occurred and tabulate the data accordingly.

(b) Plot a histogram of the measurements.

(c) Calculate the mean value of the period and the standard deviation from the mean. (d) If the length of the pendulum is 60.0 cm, use the mean value of the period to calculate the gravitational acceleration g.

Answer 1

Solution.

$c) T=1.549s;$

$\sigma=0.022s;$

$d) l=0.6m; T=1.549s;$

$T=2\pi\sqrt\dfrac{l}{g}\implies g=\dfrac{4\pi^2l}{T^2};$

$g=\dfrac{4\sdot3.14^2\sdot0.6m}{(1.549s)^2}=9.862m/s^2;$

Answer: $c) T=1.549s;\sigma=0.022s;$

$d)g=9.862m/s^2.$