Answer Ellastic Collision: Momentum, CM velocity & Relative Velocity

[jacy]

hi,
I have solved this problem. I just wanted to know whether i have the correct answer. Also in the problem the object 2 which is moving to the left with the velocity of 2m/s has to be considered negative right. I mean i have to consider the velocity to be (-2m/s). Please help me its urgent.

Two objects moving in opposite direction collide ellastically. Object 1 has a mass of 20 kg moves to the right with velocity 5m/s. Object 2 has a mass of 30 kg moves to the left with velocity 2m/s.
a) Find total momentum.
b) Find velocity of center of mass
c) Find relative velocity before the collision.
d) Find the velocities after the collision.
e) Find relative velocity after the collision.

a) total momentum= Total mass * V(cm)
V(cm)= (20 kg * 5m/s + 30 kg * (-2m/s))/20 kg + 30 kg
= 0.8 m/s

total momentum= (20kg + 30kg)* 0.8 m/s
= 40 kg m/s

b) V(cm) velocity of center of mass = 0.8 m/s

c) Relative velocity before collision V(r)= V(1) - V(2)
= 5m/s - (-2m/s)
= 7m/s

d) m1v1 + m2v2 = m1v1' + m2v2'
v1' and v2' are velocities after the collision
20kg*5m/s + 30kg*(-2m/s) = 20kg*v1' + 30kg*v2'
40 kg m/s = 20 kg ( v1' + (3/2) v2' )
2 m/s = v1' +(3/2) v2'
For one dimensinal ellastic collision we know that
v1 - v2 = -(v1' - v2')
7m/s = -v1' + v2'
On solving 2 m/s = v1' +(3/2) v2'
7m/s = -v1' + v2'
we get v2'= 3.6 m/s and v1' = -3.4 m/s

e) Relative velocity after collision V(r) = v1' - v2'
= -3.4 m/s - 3.6 m/s
= -10 m/s

 

[Doc Al]

All good except for an addition error on the very last line.

 

[jacy]

All good except for an addition error on the very last line.

Thanks, so its true that the object 2 which is moving to the left to have negative velocity. I highly appreciate your effort in checking my work, thanks.

 

[Doc Al]

so its true that the object 2 which is moving to the left to have negative velocity.

Absolutely.

 

[jacy]

Absolutely.

Thanks Al for your help.