Four objects are situated along the y axis as follows: a 1.93-kg object is at +2.93 m, a 3.06-kg object is at +2.58 m, a 2.41-kg object is at the origin, and a 3.96-kg object is at -0.498 m. Where is the center of mass of these objects?

x, y (0, 1)

Explanation:

the X coordinate of the center mass is

X(c) = Σm(i)*x(i) / Σx(i)

X(c) = (0 + 0 + 0 + 0) / (1.93 + 3.06 + 2.41 + 3.96)

X(c) = 0 / 11.36

X(c) = 0

The y coordinate of the center mass is

Y(c) = Σm(i)y(i) / Σm(i)

Y(c) = [(1.93)(2.93) + (3.06)(2.58) + (2.41)(0) + (3.96)(-0.498)] / (1.93 + 3.06 + 2.41 + 3.96)

Y(c) = (5.6549 + 7.8948 + 0 - 1.97208) / 11.36

Y(c) = 11.57762 / 11.36

Y(c) = 1.02

Therefore, the center of masses is at x, y (0, 1)

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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