Three particles, A, B, and C have the following masses, coordinates, and velocit

Question

Three particles, A, B, and C have the following masses, coordinates, and velocities in the lab:

particle mass (kg) x (m) y (m) vx (m/s) vy(m/s)
A 0.2 0.8 -0.4 24 5
B 1.6 1 1 14 8
C 2.1 0.3 0.7 -5 3


a)What are the x and y coordinates of the center of mass of these three particles?

b)If the three particles are moving with the velocities shown, with what velocity (vx, vy) is the center of mass moving in the lab?

c)Find the velocity components of particle A in the center of mass (cm) frame.

d) Find the momentum components of particle A in the center of mass (cm) frame.

Explanation / Answer

a)x=(0.2*0.8+1.6*1+2.1*.3)/(.2+1.6+2.1) =0.613 m y=(0.2*-0.4+1.6*1+2.1*0.7)/(.2+1.6+2.1) =0.767 b)vx=(0.2*24+1.6*14+2.1*-5)/(3.9) =4.282 vy=(0.2*5+1.6*8+2.1*3)/3.9 =5.153 c)v=va-vcm =(24-4.282)i+(5-5.153)j =19.728i-0.153j d)v=ma*va-mcm*vcm =0.2*24-3.9*4.282 i+0.2*5-3.9*5.153 j =-11.9 i+-19.1 j

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