Two marbles (m = 0.050 kg each) moving on a table towards each other with the speed of 0.3 m/s collide, and start moving away from each other.

a.) what is the total momentum of this system before the collision?
v1 = m/s, v2 = m/s,

p1 = kg m/s, p2 = kg m/s,

ptotal = kg m/s

b.) determine the magnitude and direction of the velocity of each marble and the total linear momentum after the head-on collision:

v1 = m/s, v2 = m/s,

p1 = kg m/s, p2 = kg m/s,

ptotal = kg m/s

A.)

V1 = 0.3 m/s m/s, V2 = -0.3 m/s,

p1 =  0.015 kg m/s, p2 = -0.015 kg m/s,

ptotal = 0 kg m/s

B.)

V1 = -0.3  m/s, V2 = 0.3 m/s,

p1 = -0.015 kg m/s, p2 = 0.015kg m/s,

ptotal = 0 kg m/s

Explanation:

In the given system let initially V1 be in positive direction and v2 vice versa.

So for a given velocity v and mass m ,momentum is given by

a)

So its already given that bodies are moving with 0.3 m/s in opposite directions so they would have opposite signs.

V1 = 0.3 m/s m/s, V2 = -0.3 m/s,

p1 =  0.015 kg m/s, p2 = -0.015 kg m/s,

So the sign of the momentum would also be opposite for the other mass.

Hence the total momentum before collision would be zero.

b)

Now  they will be having an head on elastic collision .(If not mentioned anything it is taken as head on collision)

So the direction of velocities would reverse and to the intial values so

V1 = -0.3  m/s, V2 = 0.3 m/s,

And hence the momentums are,

p1 = -0.015 kg m/s, p2 = 0.015kg m/s,

Hence after the collision also the total momentum is zero.