COLLEGE PHYICS
COLLEGE PHYICS
5th Edition
ISBN: 9781266793394
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 7, Problem 87P
To determine

The location of the rod in x and y coordinates of the center of mass from the origin.

Expert Solution & Answer
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Answer to Problem 87P

The location of the rod in x and y coordinates of the center of mass from the origin is (5cm, 6.7cm).

Explanation of Solution

Write the expression for location of the center of mass of the rod in x direction.

  xCM=m3x1+m3x2+m3x3m3+m3+m3        (I)

Here, xCM is the location of the center of mass of the rod in x direction, m is the mass of the rod, and x1,x2, and x3 is the position of the rod along x axis.

Rewrite the above expression.

  xCM=m(13x1+13x2+13x3)m(13+13+13)=(13x1+13x2+13x3)(13+13+13)        (II)

Write the expression for location of the center of mass of the rod in y direction.

  yCM=m3y1+m3y2+m3y3m3+m3+m3        (III)

Here, yCM is the location of the center of mass of the rod in y direction, m is the mass of the rod, and y1,y2, and y3 is the position of the rod along y axis.

Rewrite the above expression.

  yCM=m(13y1+13y2+13y3)m(13+13+13)=(13y1+13y2+13y3)(13+13+13)        (IV)

Conclusion:

Substitute 0cm+0cm/2 for x1, 0cm+10.0cm/2 for x2, and 10.0cm+10.0cm/2 for x3 in the equation (II) to find xCM.

  xCM=(13(0cm+0cm2)+13(0cm+10cm2)+13(10cm+10cm2))(13+13+13)=03+5cm3+10cm31=5cm

Substitute 0cm+10cm/2 for y1, 10.0cm+10.0cm/2 for y2, and 0cm+10.0cm/2 for y3 in the equation (IV) to find yCM.

  xCM=(13(0cm+10cm2)+13(10cm+10cm2)+13(0cm+10cm2))(13+13+13)=5cm3+10cm3+5cm31=6.7cm

Thus, the location of the rod in x and y coordinates of the center of mass from the origin is (5cm, 6.7cm).

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Chapter 7 Solutions

COLLEGE PHYICS

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