A 5.5 kg object moving in the + x direction at 5.5 m/s collides head-on with a 3

Question

A 5.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 3.1 kg object moving in the -x direction at 4.0 m/s. Find the final velocity of each mass for each of the following situations. (Take the positive direction to be +x.)

B) The collision is elastic.

_______m/s (5.5 kg mass)

_______ m/s (3.1 kg mass)

C) The 5.5 kg body is at rest after the collision.

_______ m/s (5.5 kg mass)

_______ m/s (3.1 kg mass)

D) The 3.1 kg body is at rest after the collision.

_______m/s (5.5 kg mass)

_______ m/s (3.1 kg mass)

E) The 5.5 kg body has a velocity of 4.0 m/s in the -x direction after the collision.

_______m/s (5.5 kg mass)

_______m/s(3.1 kg mass)

Explanation / Answer

b)Let the final velocities be v1 and v2( in same direction) .Conserving momentum,

5.5*5.5-3.1*4=5.5v1+3.1 v2

Also, since the collision is elastic, velocity of approach=velocity of separation

5.5+4=v2-v1

Solving,

v1=-1.35m/s (meaning it moves in the -x direction)

v2=8.15m/s

c)Conserving momentum,

5.5*5.5-3.1*4=5.5*0+3.1 v2

v(5.5kg)=0

v2=v(3.1)=5.76m/s

d)5.5*5.5-3.1*4=5.5*v1+3.1*0

v(5.5)=3.25m/s

v(3.1)=0

e)5.5*5.5-3.1*4=5.5*-4+3.1*v2

v(5.5)=-4m/s

v(3.1)=12.85m/s

However, this is impossible since the total energy after collision cannot be greater than the initial energy.

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