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Chapter 36: Q. 25 (page 1060)

A human hair is about 50渭min diameter. At what speed, in m/s, would a meter stick 鈥渟hrink by a hair鈥�?

Hint: Use the binomial approximation.

Short Answer

Expert verified

At a speed of 3脳106m/s, a meter stick shrink by a hair.

Step by step solution

01

Given Information

We have given that a human hair is about 50渭min diameter.

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

02

Simplify

S: Grounds reference frame

S': The meter establishes a frame of reference.

L'=l(inframeS').

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

L=1-尾2l鈮�1-12尾2l

l-L=12尾2l

As a result, 尾has the following value:

尾=2(l-L)l尾=2(50脳10-6m)1.00m尾=0.01

Now, we must determine the value of vusing the following relation:

v=尾路cv=0.01脳(3脳108m/s)v=3脳106m/s

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