Question

For the system of particles described in the Part B, find the x coordinate xcm of the center of mass. Assume that the particle of mass M is at the origin and the positive x axis is directed to the right. Express your answer in terms of L.

Answer 1

Answer:

for mass M, x_cm = 1.33 L

for mass 2M, x_cm = 0.33 L

for mass 3M, x_cm = 0.67 L

Explanation:

The system of mass image in the attachment

The x-coordinate of the mass center from the mass M

             x_{cm} = [ M(0) + (2M)L + (3M)(2L) ]÷(M + 2M + 3M)

                    = [ 2LM + 6LM ] / (6M)

                    = 1.33 L

The x-coordinate of mass center from the mass 2M is

             x_{cm} = [ M(-L) + (2M)(0) + (3M)(L) ] ÷ (M + 2M + 3M)

                    = [ - LM + 3LM ] / (6M)

                    = 0.33 L

The x-coordinate of mass center from the mass 3M is

             xcm = [ M(-2L) + (2M)(-L) + (3M)(0) ]÷(M + 2M + 3M)

                    = [ - 2LM - 2LM ] / (6M)

                    = 0.67 L