Chapter 36: Q. 19 (page 1059)

You fly $5000 k m$ across the United States on an airliner at $250 m / s .$ You return two days later at the same speed.
a. Have you aged more or less than your friends at home?
b. By how much?
Hint: Use the binomial approximation

Short Answer

Expert verified

$a .)$ Because my proper time is smaller than the time in the Earth frame, I have aged less.

$b .)$ In frame $S \to ∆ t = 4 \times 10^{4} s,$

In frame $S' \to ∆ τ = 14 n s$

Step by step solution

Part (a) Step 1: Given Information

We have given that,

Airliner takes of and attains $v = 250 m / s$ .

Airliner returns to original position after $2$ days.

We have to assume you've aged more or less than your family and friends.

Part (a) Step 2: Simplify

Because my proper time is smaller than the time in the Earth frame, I have aged less.

Part (b) Step 1: Given Information

We have given that,

Airliner takes of and attains $v = 250 m / s .$

Airliner returns to original position after $2$ days.

We need to figure out how much is the Earth's frame and the airliner's frame.

Part (b) Step 2: Simplify

The Earth's frame is $S$ .

The Airliner's frame is $S' .$

In the $S$ frame:

$∆ t = \frac{2 \times 5 \times 10^{6} m}{250 m / s} ∆ t = 4 \times 10^{4} s$

In the frame $S' :$

$∆ τ = ∆ t {(1 - \frac{v^{2}}{c^{2}})}^{1 / 2} ∆ τ = ∆ t (1 - \frac{v^{2}}{2 c^{2}}) ∆ τ = ∆ t \cdot \frac{v^{2}}{2 c^{2}} ∆ τ = (4 \times 10^{4} s) \frac{1}{2} (\frac{250 m / s}{3 \times 10^{8} m}) ∆ τ = 1.4 \times 10^{- 8} s ∆ τ = 14 n s$

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You fly $5000 k m$ across the United States on an airliner at $250 m / s .$ You return two days later at the same speed.
a. Have you aged more or less than your friends at home?
b. By how much?
Hint: Use the binomial approximation

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Simplify

Part (b) Step 1: Given Information

Part (b) Step 2: Simplify

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You fly 5000kmacross the United States on an airliner at 250m/s.You return two days later at the same speed.a. Have you aged more or less than your friends at home?b. By how much?Hint: Use the binomial approximation

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Simplify

Part (b) Step 1: Given Information

Part (b) Step 2: Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electrostatics

Force

Engineering Physics

Space Physics

Conservation of Energy and Momentum

Thermodynamics

Study anywhere. Anytime. Across all devices.

You fly $5000 k m$ across the United States on an airliner at $250 m / s .$ You return two days later at the same speed.
a. Have you aged more or less than your friends at home?
b. By how much?
Hint: Use the binomial approximation