Chapter 8.3, Problem 24E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

# The masses mi are located at the points Pi. Find the moments Mx and My and the center of mass of the system.24. m1 = 5, m2 = 4, m3 = 3, m4 = 6;P1(−4, 2), P2(0, 5), P3(3, 2), P4(1, −2)

To determine

To find: The moments Mx, My and the center of mass of the system.

Explanation

Given:

The mass m1=5 located at the point P1=(âˆ’4,2).

The mass m2=4 located at the point P2=(0,5).

The mass m3=3 located at the point P3=(3,2).

The mass m4=6 located at the point P4=(1,âˆ’2).

Number of count is n=4.

Calculation:

Calculate the moment Mx using the formula:

Mx=âˆ‘i=1nmiyi (1)

Substitute 4 for n in Equation (1).

Mx=âˆ‘i=14miyi=m1y1+m2y2+m3y3+m4y4 (2)

Substitute 5 for m1, 4 for m2, 3 for m3, 6 for m4, 2 for y1, 5 for y2, 2 for y3, and (âˆ’2) for y4 in Equation (2).

Mx=(5Ã—2)+(4Ã—5)+(3Ã—2)+[6Ã—(âˆ’2)]=24

Hence, the moment Mx of the system is 24.

Calculate the moment My using the formula:

My=âˆ‘i=1nmixi (3)

Substitute 4 for n in Equation (2).

My=âˆ‘i=14mixi=m1x1+m2x2+m3x3+m4x4 (4)

Substitute 5 for m1, 4 for m2, 3 for m3, 6 for m4, (âˆ’4) for x1, 0 for x2, 3 for x3, and 1 for x4 in Equation (4)

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