Could you answer these two questions ? PRACTICE IT Use the worked example above

Question

Could you answer these two questions ?

PRACTICE IT Use the worked example above to help you solve this problem. Consider the figure below, where m = 5.78 kg, m2 = 2.37 kg, m3-4.41 kg, d-0.400 m, and d2 = 1.35 m. Treat the objects as point particles. 1.00 m 0.500 m (a) Three particles are located In a coordinate system shown In Figure (a). Flnd the center of gravity (b) How does the answer change If the object on the left Is displaced upward by 1.00 m and the object on the right is displaced downward by 0.500 m (Figure (b))? Cg EXERCISE HINTS: GETTING STARTED I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. If a fourth particle of mass 1.70 kg is placed at (0 m, 0.100 m) in Figure (a), find the x- and y-coordinates of the center of gravity for this system of four particles Cg Need Help? L-Read it

Explanation / Answer

We know that

Xcom = (m1x1 + m2x2 + m3x3)/(m1 + m2 + m3)

Ycom = (m1y1 + m2y2 + m3y3)/(m1 + m2 + m3)

a)for arrangement shown in a,

Xcg = (5.78 x 0.4 + 2.37 x 0 + 4.41 x 1.35)/(5.78 + 2.37 + 4.41) = 0.658 m

Hence, Xcg = 0.658 m

b)Xcom = (5.78 x 0.4 + 2.37 x 0 + 4.41 x 1.35)/(5.78 + 2.37 + 4.41) = 0.658 m

Ycom = (5.78 x 1 + 2.37 x 0 + 4.41 x -0.5)/(5.78 + 2.37 + 4.41) = 0.285 m

Hence, Xcg = 0.658 m ; Ycg = 0.285 m

excercise

1.7 (0,0.1)

Xcg = (5.78 x 0.4 + 2.37 x 0 + 4.41 x 1.35 + 1.7 x 0)/(5.78 + 2.37 + 4.41 + 1.7) = 0.579 m

Ycg = (5.78 x 0 + 2.37 x 0 + 4.41 x 0 + 1.7 x 0.1)/(5.78 + 2.37 + 4.41 + 1.7) = 0.012 m

Xcg = 0.579 m ; Ycg = 0.012 m

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