Find the final velocity of each mass if the 19.5 kg object has a velocity of 3.0

ID: 1418045 • Letter: F

Question

Find the final velocity of each mass if the 19.5 kg object has a velocity of 3.0 m/s in the x direction after the collision.

A 19.5 kg object moving in the +x direction at 5.5 m/s collides head-on with a 12.5 kg object moving in the x direction at 3.0 m/s .

Find the final velocity of each mass if the objects stick together.

Find the final velocity of each mass if the collision is elastic.

Find the final velocity of each mass if the 19.5 kg object is at rest after the collision.

Find the final velocity of each mass if the 12.5 kg object is at rest after the collision.

m1 = 19.5 kg

m2 = 12.5 kg

v1i = 5.5 m/s

v2i = - 3 m/s

v = combined velocity after collision

using conservation of momentum

m1 v1i + m2 v2i = (m1 + m2) v

19.5 (5.5) + 12.5 (-3) = (19.5 + 12.5) v

v = 2.2 m/s

For the collision to be elastic

using conservation of momentum

m1 v1i + m2 v2i = m1 v1f + m2 v2f

19.5 (5.5) + 12.5 (-3) = 19.5 v1f + 12.5 v2f

19.5 v1f + 12.5 v2f = 69.75

v1f = (69.75 - 12.5 v2f )/19.5 eq-1

Using conservation of kinetic energy

m1 v21i + m2 v22i = m1 v21f + m2 v22f

19.5 (5.5)2 + 12.5 (-3)2 = 19.5 ((69.75 - 12.5 v2f )/19.5)2 + 12.5 v22f

v2f = 7.4 m/s

v1f = (69.75 - 12.5 v2f )/19.5 = (69.75 - 12.5 (7.4) )/19.5 = - 1.2 m/s

if the 19.5 kg object is at rest after the collision : v1f = 0

using conservation of momentum

m1 v1i + m2 v2i = m1 v1f + m2 v2f

19.5 (5.5) + 12.5 (-3) = 19.5 (0) + 12.5 v2f

v2f = 5.6 m/s

if the 12.5 kg object is at rest after the collision : v2f = 0

using conservation of momentum

m1 v1i + m2 v2i = m1 v1f + m2 v2f

19.5 (5.5) + 12.5 (-3) = 19.5 v1f + 12.5 (0)

v1f = 3.6 m/s

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