   Chapter 8.3, Problem 24E

Chapter
Section
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=(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=(1,2).

Number of count is n=4.

Calculation:

Calculate the moment Mx using the formula:

Mx=i=1nmiyi (1)

Substitute 4 for n in Equation (1).

Mx=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 (2) for y4 in Equation (2).

Mx=(5×2)+(4×5)+(3×2)+[6×(2)]=24

Hence, the moment Mx of the system is 24.

Calculate the moment My using the formula:

My=i=1nmixi (3)

Substitute 4 for n in Equation (2).

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

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

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