   Chapter 8, Problem 12P

Chapter
Section
Textbook Problem

Find the x- and y-coordinates of the center of gravity for the boomerang in Figure P8.12a. modeling the boomerang as in Figure P8.12b, where each uniform leg of the model has a length of 0.300 m and a mass of0.250 kg. (Note: Treat the legs like thin rods.) Figure P8.12

To determine
The x -and y -coordinates of the center of gravity of the boomerang.

Explanation

Section1:

To determine: The x -coordinate of the center of gravity of the boomerang.

Answer: The x -coordinate of the center of gravity of the boomerang is 0m .

Explanation:

Given info: The angle of legs of the boomerang from the vertical axis is 40.0° and the length of the leg is 0.300m .

By treating the legs of the boomerang as uniform thin rods, the center of the gravity of each rod is positioned at the center of the geometric axis of the boomerang. The x component of the center of gravity of the boomerang is located at x=0m because of symmetry of the legs of the boomerang.

Conclusion:

Therefore, the x -coordinate of the center of gravity of the boomerang is 0m .

Section2:

To determine: The y -coordinate of the center of gravity of the boomerang.

Answer: The y -coordinate of the center of gravity of the boomerang is 9.64×102m .

Explanation:

Given info: The angle of legs of the boomerang from the vertical axis is 40.0° and the length of the leg is 0.300m .

The y component of the center of gravity of the boomerang is located at half of the height of the boomerang by its symmetry.

The formula for the y co-ordinate of the center of gravity of the boomerang is,

ycm=lsinθ2

• l is length of legs of the boomerang

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