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Home Multiple Integrals Application to Physics Examples Example 2: Center of Mass
 
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Example 2: Center of Mass

A triangular plate bounded by the lines x = 0, x = y, y = 1 has density ρ(x, y) = x + y. Find the moments and center of mass.

Step 1

Sketch the region Z), as in Figure 12.4.4.

12_multiple_integrals-217.gif

Figure 12.4.4

Step 2

We see from the figure that D is the region

0 ≤ x ≤ 1, x ≤ y ≤ 1.

Step 3

Set up and evaluate the iterated integrals for the mass m and moments Mx and My.

12_multiple_integrals-218.gif

12_multiple_integrals-219.gif

12_multiple_integrals-220.gif

12_multiple_integrals-221.gif

12_multiple_integrals-222.gif

The answers are

12_multiple_integrals-223.gif

12_multiple_integrals-224.gif

12_multiple_integrals-225.gif

The point 12_multiple_integrals-226.gif is shown in Figure 12.4.5.

12_multiple_integrals-228.gif

Figure 12.4.5
Home Multiple Integrals Application to Physics Examples Example 2: Center of Mass

Last Update: 2006-11-15