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Chapter 15: Q. 49 (page 417)

Scientists are measuring the properties of a newly discovered elastic material. They create a 1.5-m-long, 1.6-mm-diameter cord, attach an850g mass to the lower end, then pull the mass down2.5mm and release it. Their high-speed video camera records 36 oscillations in 2.0s. What is Young's modulus of the material?

Short Answer

Expert verified

Young modulus is8.1脳109N/m2.

Step by step solution

01

Expression for young modulus

Young's modulus of the material is ,

Y=FL础螖尝

Substitute all values

Y=kLA

where kis the spring constant of the material.

The length of the cord is l.

The cross-sectional area isA.

Y=kL蟺顿2/4

=4kL蟺顿2

02

Expression for k

The frequency of oscillation of the material is ,

f=12蟺km

Rearrange it,

f2=14蟺2km

f24蟺2m=k

03

Calculation of young modulus

young modulus is,

=16蟺尘蹿2LD2

Wherem=0.850kg,f=18Hz,L=1.5m,D=1.6脳10-3m

Y=16蟺(0.850kg)(18Hz)2(1.5m)1.6脳10-3m2

=8.1脳109N/m2

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