Chapter 36: Q. 18 (page 1059)

At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.

Short Answer

Expert verified

The speed of a moving clock is $46 m / s .$

Step by step solution

Given Information

We have to find the speed in $m / s$ for a moving clock lose $1.0 ns$ in $1.0$ day according to experimenters on the ground using binomial approximation.

Simplify

The ground's frame is $S$ .

The moving clock frame is $S' .$

$∆ t = 1.0 d + 1.0 n s ∆ t' = 1.0 d = 86400 s$

We have: $∆ t = y ∆ t' .$

When calculating powers of sums of 1 and a small number x, the binomial approximation comes in handy.

Now, we use binomial approximation for $y :$

localid="1649844482103" $\frac{∆ t}{∆ t'} = 1 + \frac{v^{2}}{2 c^{2}} \frac{∆ t}{∆ t'} - 1 = \frac{v^{2}}{2 c^{2}} 2 c^{2} (\frac{∆ t}{∆ t'} - 1) = v^{2} v = c \sqrt{2 (\frac{∆ t}{∆ t'} - 1)} v = c \sqrt{2 (\frac{1.0 n s}{1.0 d})} v = (3 \times 10^{8} m / s) \sqrt{(\frac{2 (1.0 \times 10^{- 9} s)}{86400 s})} v = 46 m / s$

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At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.

Short Answer

Step by step solution

Given Information

Simplify

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At what speed, in m/s,would a moving clock lose role="math" localid="1649531760117" 1.0nsin 1.0day according to experimenters on the ground?Hint: Use the binomial approximation.

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

Solid State Physics

Radiation

Engineering Physics

Electricity

Fluids

Energy Physics

Study anywhere. Anytime. Across all devices.

At what speed, in $m / s,$ would a moving clock lose role="math" localid="1649531760117" $1.0 ns$ in $1.0$ day according to experimenters on the ground?
Hint: Use the binomial approximation.