Four particles are in a 2-D plane with masses, x- and y- positions, and x- and y
ID: 1455501 • Letter: F
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
8 kg
-2.6 m
-4.7 m
3.1 m/s
-4.2 m/s
2
7.6 kg
-3.5 m
3.6 m
-5 m/s
5.2 m/s
3
9.3 kg
4.4 m
-5.6 m
-6 m/s
2.1 m/s
4
9 kg
5.4 m
2.5 m
3.9 m/s
-3 m/s
1)What is the x position of the center of mass?
_____________m
2)What is the y position of the center of mass?
_____________m
3)What is the speed of the center of mass?
______________m/s
4)When a fifth mass is placed at the origin, what happens to the horizontal (x) location of the center of mass?
It moves to the right.
It moves to the left.
It does not move.
It can not be determined unless you know the mass.
5)When a fifth mass is placed at the center of mass, what happens to the vertical (y) location of the center of mass?
It moves up.
It moves down.
It does not move.
It can not be determined unless you know the mass.
m
x
y
vx
vy
1
8 kg
-2.6 m
-4.7 m
3.1 m/s
-4.2 m/s
2
7.6 kg
-3.5 m
3.6 m
-5 m/s
5.2 m/s
3
9.3 kg
4.4 m
-5.6 m
-6 m/s
2.1 m/s
4
9 kg
5.4 m
2.5 m
3.9 m/s
-3 m/s
Explanation / Answer
1.We know that the x - position of Centre of mass =( m1* x1 + m2*x2 + m3*x3 + m4*x4 ) /( m1 +m2+m3+m4)
Centre of mass=1.242 m
2. The same way as we found for part 1 we can find, so,
y - position of Centre of mass =( m1* y1 + m2*y2 + m3*y3 + m4*y4 ) /( m1 +m2+m3+m4) =-1.1746 m
3. Vy of the centre of mass = ( m1* Vy1 + m2*Vy2 + m3*Vy3 + m4*Vy4 ) /( m1 +m2+m3+m4) =-0.0457 m/s
. Vx of the centre of mass = ( m1* Vx1 + m2*Vx2 + m3*Vx3 + m4*Vx4 ) /( m1 +m2+m3+m4) =-1 m/s
therefore speed = root over (Vy2 + Vx2)=1.17 m/s
4. when a fifth particle is placed at the origin its x5 = 0, so in the formula m5*x5 = 0, but its mass is not 0 . So the value of the denominator increase and the x position of the centre of mass decreases.
5. when a fifth particle is placed at the origin its x5 = 0, so in the formula m5*y5 = 0, but its mass is not 0 . So the value of the denominator increase and the x position of the centre of mass decreases.
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