Chapter 36: Q. 14 (page 1059)

At what speed, as a fraction of $c,$ does a moving clock tick at half the rate of an identical clock at rest?

Short Answer

Expert verified

At $0.866 c$ , a moving clock tick at half the rate of an identical clock at rest.

Step by step solution

Given Information

We have to find the speed of the moving clock as a fraction of $c .$

Simplify

The ticks that are being counted are those of a ticking clock. In $S^{'} -$ the time interval between two ticks is measured by the same clock, namely the ticking clock. As a result, $∆ t' = ∆ τ$ is the correct time. Between two ticks of the running clock, the rest clock measures a longer interval $∆ t$ . These are linked by the following:

$∆ τ = \sqrt{1 - β^{2}} ∆ t$

Now $∆ τ = \frac{1}{2} ∆ t,$ Thus,

$\sqrt{1 - β^{2}} = \sqrt{1 - \frac{v^{2}}{c^{2}}} = \frac{1}{2}$

$v = c \sqrt{\frac{3}{4}} v = 0.866 c$

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At what speed, as a fraction of $c,$ does a moving clock tick at half the rate of an identical clock at rest?

Short Answer

Step by step solution

Given Information

Simplify

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At what speed, as a fraction of c,does a moving clock tick at half the rate of an identical clock at rest?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Circular Motion and Gravitation

Nuclear Physics

Measurements

Magnetism and Electromagnetic Induction

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

At what speed, as a fraction of $c,$ does a moving clock tick at half the rate of an identical clock at rest?