A ball with a mass of #2 kg# is rolling at #7 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

Answer 1

v1 = -2,33 m/s
v2 = 4,66 m/s

in the elastic collisions remain constant both the total kinetic energy both the momentum. Therefore: #1/2 m1 v1°^2 = 1/2 m1v1^2 + 1/2 m2 v2^2#. #m1 v1° = m1 v1 + m2 v2 #. replacing the values in the equation of conservation of momentum, you find: (1) #v1= 7 -2 v2 # . that you put in the equation of conservation of energy. Resolving the second degree equation, you find: #6v2^2 -28 v2 =0#. then #V2=0# not useful and #v2 = 4,66 m/s#. If You put in the (1), you find: #v1= -2,66 m/s # i.e. the smaller ball comes back.

If you put the values in the equation of conservation of energy, you find that it is verified

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Answer 2

Nathan Ashcroft

The post-collision velocities are 2 m/s for the 2 kg ball and 6 m/s for the 4 kg ball.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.