Chapter 26, Problem 73GP

(a)

To determine

Period of oscillation according to observers on the ship.

Answer to Problem 73GP

  $1.17s$ .

Explanation of Solution

Given:

Mass is $1.68kg$

Value of constant $k$ is $48.7N/m$

Formula used:

It is known that,

  $T=2\pi {\left(\frac{m}{k}\right)}^{\frac{1}{2}}$

Where,

  $m$ is mass

  $k$ is constant

  $T$ is time period

Calculation:

Because the spring is at rest on the spaceship, its period is

  $T=2\pi {\left(\frac{m}{k}\right)}^{\frac{1}{2}}=2\pi {\left[\frac{\left(1.68kg\right)}{\left(48.7N/m\right)}\right]}^{\frac{1}{2}}=1.17s$

(b)

To determine

Period of oscillation according to observers on Earth.

Answer to Problem 73GP

  $2.68s$

Explanation of Solution

Given:

Speed is $0.900c$

Period of oscillation according to observers on the ship $1.17s$

Formula used:

It is known that,

  $T_{earth}=\frac{T}{{\left[1-\left(\frac{v^2}{c^2}\right)\right]}^{\frac{1}{2}}}$

Where,

  $v$ is velocity

  $c$ is speed of light, $3.00\times {10}^{8}m/s$

  $T$ is time

Calculation:

The oscillating mass is a clock.

According to observers on Earth, clocks on the spacecraft run slow:

  $T=\frac{\left(1.17s\right)}{{\left[1-{\left(0.900\right)}^2\right]}^{\frac{1}{2}}}=2.68s$