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Chapter 4: Q.65 (page 109)

A typical laboratory centrifuge rotates at 4000rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.

a. What is the acceleration at the end of a test tube that is 10cmfrom the axis of rotation?

b. For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0mand stopped in a 1.0mslong encounter with a hard floor?

Short Answer

Expert verified

a. 1.75×104m/s2

b.4.4×104m/s2

Step by step solution

01

Given information

The given values are:

ω=4000rpmr=10cm=0.1mt=1ms=1×10-3sh=1m

02

Part a) Step 1: Explanation

Convert rpmin rad/s

ω=4000rpmω=4000×2π60ω=419rad/s

The acceleration at the end of a test tube is:

an=rω2an=0.1×(419)2 an=17556.1an=1.75×104m/s2

03

Part b) Step 1: Explanation

v12-v22=2ghv12-0=2×9.8×1v12=19.6v1=19.6v1=4.427m/s

The magnitude of the acceleration a test tube would experience if dropped from a height of 1.0mand stopped in a 1.0mslong encounter with a hard floor is

v2=v1-at0=4.427-a×1×10-3a=4.4271×10-3a=4427.2a=4.4×103m/s2

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