Chapter 36: Q. 25 (page 1060)

A human hair is about $50 μ m$ in diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?
Hint: Use the binomial approximation.

Short Answer

Expert verified

At a speed of $3 \times 10^{6} m / s$ , a meter stick shrink by a hair.

Step by step solution

Given Information

We have given that a human hair is about $50 μ m$ in diameter.

We must determine at what pace in m/s a meter stick "shrinks by a hair" using the binomial approximation.

Simplify

$S$ : Grounds reference frame

$S'$ : The meter establishes a frame of reference.

$L' = l (inframe S') .$

On the ground, an experimenter measures the length to be constricted to:

$L = \sqrt{1 - β^{2} l} \approx (1 - \frac{1}{2} β^{2}) l$

$l - L = \frac{1}{2} β^{2} l$

As a result, $β$ has the following value:

$β = \sqrt{\frac{2 (l - L)}{l}} β = \sqrt{\frac{2 (50 \times 10^{- 6} m)}{1.00 m}} β = 0.01$

Now, we must determine the value of $v$ using the following relation:

$v = β \cdot c v = 0.01 \times (3 \times 10^{8} m / s) v = 3 \times 10^{6} m / s$

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A human hair is about $50 μ m$ in diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?
Hint: Use the binomial approximation.

Short Answer

Step by step solution

Given Information

Simplify

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A human hair is about 50μmin diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?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

Physics of Motion

Work Energy and Power

Rotational Dynamics

Circular Motion and Gravitation

Conservation of Energy and Momentum

Medical Physics

Study anywhere. Anytime. Across all devices.

A human hair is about $50 μ m$ in diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?
Hint: Use the binomial approximation.