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Chapter 26: Problem 25

Kurt is measuring the speed of light in an evacuated chamber aboard a spaceship traveling with a constant velocity of \(0.60 c\) with respect to Earth. The light is moving in the direction of motion of the spaceship. Siu- Ling is on Earth watching the experiment. With what speed does the light in the vacuum chamber travel, according to Siu-Ling's observations?

Short Answer

Expert verified
Answer: The observed speed of light according to Siu-Ling's observations is c (the speed of light in a vacuum).

Step by step solution

01

Principle of relativistic velocity addition

The principle of relativistic addition of velocities states that if object A is moving at velocity \(v_A\) relative to object B, and object B is moving at velocity \(v_B\) relative to object C, then the velocity of object A relative to object C, \(v_{AC}\), can be calculated using the formula: \(v_{AC} = \frac{v_A + v_B}{1 + \frac{v_A v_B}{c^2}}\) In our case, the spaceship (object B) is moving with a velocity of \(0.60c\) with respect to Earth (object C), and the light (object A) is moving with a velocity \(c\) with respect to the spaceship. We want to find the velocity of the light (object A) with respect to Earth (object C), which is \(v_{AC}\).
02

Substitute the given values into the formula

Now, we will substitute the given values into the formula for relativistic addition of velocities: \(v_A = c\), \(v_B = 0.60c\), and \(c\) is the speed of light in a vacuum. \(v_{AC} = \frac{c + 0.60c}{1 + \frac{c(0.60c)}{c^2}}\)
03

Simplify the expression for \(v_{AC}\)

Let's simplify the expression: \(v_{AC} = \frac{1.60c}{1 + 0.60} = \frac{1.60c}{1.60}\)
04

Calculate the final result for the speed of light according to Siu-Ling's observations

Now we can find \(v_{AC}\): \(v_{AC} = \frac{1.60c}{1.60} = c\) The speed of light according to Siu-Ling's observations is \(c\), the same as the speed of light in a vacuum. This is expected because, according to the principles of special relativity, the speed of light is the same for all observers, regardless of their relative motion.

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Most popular questions from this chapter

Two lumps of putty are moving in opposite directions, each one having a speed of \(30.0 \mathrm{m} / \mathrm{s} .\) They collide and stick together. After the collision the combined lumps are at rest. If the mass of each lump was $1.00 \mathrm{kg}$ before the collision, and no energy is lost to the environment, what is the change in mass of the system due to the collision? (tutorial: colliding bullets)
A spaceship travels at constant velocity from Earth to a point 710 ly away as measured in Earth's rest frame. The ship's speed relative to Earth is $0.9999 c .$ A passenger is 20 yr old when departing from Earth. (a) How old is the passenger when the ship reaches its destination, as measured by the ship's clock? (b) If the spaceship sends a radio signal back to Earth as soon as it reaches its destination, in what year, by Earth's calendar, does the signal reach Earth? The spaceship left Earth in the year 2000.
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The solar energy arriving at the outer edge of Earth's atmosphere from the Sun has intensity \(1.4 \mathrm{kW} / \mathrm{m}^{2}\) (a) How much mass does the Sun lose per day? (b) What percent of the Sun's mass is this?
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