Two toy cars are used to test both inelastic and elastic collisions. One car has

Question

Two toy cars are used to test both inelastic and elastic collisions. One car has a mass m_1 = 1.0 kg, whereas the other car has a mass m_2 = 2.0 kg. The heavier car is initially at rest whereas the lighter car has an initial velocity v = 3.2 m/s as indicated in the sketch below a) Determine the final velocity of the system of both cars assuming they stick together after the collision with the help of a little magnet. b) Imagine another case that the mass mi bounces off elastically of mass m_2. Determine the velocity of each car after the collision. References: p = mv, K = 1/2 mv^2

Explanation / Answer

(A)Applying momentum conservation,

1 x 3.2 = (2 + 1) vf

vf =1.07 m/s (both cars will move with this same velocity)

(B) for elastic collision,

velocity of approach = velocity of separation

3.2 = v1 + v2

v2 = 3.2 - v1

now Applying momentum conservation,

3.2 x 1 = 1(-v1) + 2v2

3.2 = - v1 + 2(3.2 - v1) = - v1 + 6.4 - 2v1

3.2 = - 3 v1 + 6.4

v1 = 1.07 m/s .....velociy of lighter car

v2 = 3.2 - 1.07 = 2.13 m/s ..........velccity of heavier car

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