Four objects are situated along the y axis as follows: a 2.01-kg object is at +3

Question

Four objects are situated along the y axis as follows: a 2.01-kg object is at +3.08 m, a 2.91-kg object is at +2.40 m, a 2.50-kg object is at the origin, and a 3.91-kg object is at -0.491 m. Where is the center of mass of these objects? Two particulars with masses 6m and 6m are moving toward each other along the x axis with the same initial speeds v .The particles with mass 6m is travelling to the left, and particle 6m is travelling to the right. They undergo a head-on elastic collision and each rebounds along the same line as it approached. Find the final speeds of the particles.

Explanation / Answer

1.

m1 = 2.01 kg

x1 = 3.08 m

m2 = 2.91 kg

x2 = 2.40 m

m3 = 2.58 kg

x3 = 0

m4 = 3.91 kg

x4 = - 0.491 m

center of mass is given as

Xcm = (m1 x1 + m2 x2 + m3 x3 + m4 x4)/ (m1 + m2 + m3 + m4)

Xcm = (2.01 x 3.08 + 2.91 x 2.40 + 2.58 x 0 + 3.91 (-0.491)) / (2.01 + 2.91 + 2.58 + 3.91) = 0.986 m

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