Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y

Question

Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y- velocities as given in the table below:

m

x

y

vx

vy

  1  

9.4 kg

-2.7 m

-4.7 m

2.9 m/s

3.9 m/s

  2  

9.4 kg

-3.7 m

3.7 m

-4.9 m/s

4.9 m/s

  3  

9.4 kg

4.7 m

-5.7 m

-5.9 m/s

1.9 m/s

  4  

7.5 kg

5.7 m

2.7 m

-3.9 m/s

-2.9 m/s

1) What is the distance the center of mass is from the origin?

2) What is the x-component of the velocity of the center of mass?

3) What is the y-component of the velocity of the center of mass?

m

x

y

vx

vy

  1  

9.4 kg

-2.7 m

-4.7 m

2.9 m/s

3.9 m/s

  2  

9.4 kg

-3.7 m

3.7 m

-4.9 m/s

4.9 m/s

  3  

9.4 kg

4.7 m

-5.7 m

-5.9 m/s

1.9 m/s

  4  

7.5 kg

5.7 m

2.7 m

-3.9 m/s

-2.9 m/s

Explanation / Answer

1) x component of COM =(9.4*-2.7 + 9.4*-3.7 + 9.4*4.7 + 7.5*5.7)/(9.4+9.4+9.4+7.5)= 26.77/35.7 = 0.75 m

Y component of COM =(9.4*-4.7 + 9.4*3.7 + 9.4*-5.7 + 7.5*2.7)/(9.4+9.4+9.4+7.5) = -42.73/35.7 = -1.2 m

Distance= sqrt(0.75^2+1.2^2) = 1.4 m

2) x component of velocity of com

= (9.4*2.9+ 9.4*-4.9 + 9.4*-5.9 + 7.5*-3.9)/(35.7)

= - 103.51/35.7 = -2.9 m/s

3) y component of velocity of com

= (78.83)//35.7 = 2.2 m/s

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