# A car of mass 2000kg travelling at 5ms−1 collides with a minibus of mass 5000kg travelling in the opposite direction at 7ms−1. The vehicles stick and move together after collision. If the collision lasts for 0.1seconds;

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A car of mass 2000kg travelling at 5ms−1 collides with a minibus of mass 5000kg travelling in the opposite direction at 7ms−1. The vehicles stick and move together after collision. If the collision lasts for 0.1seconds;

1. Determine the velocity of the system after collision of 3 decimal places.
2. Calculate the impulsive force on the minibus
3. Calculate the change in kinetic energy of the system
4. Explain the change in kinetic energy of the system

1. Momentum before collision = momentum after collision
M1U1 +M2 (−U2) = (M+ M2) V
(2000 x 5)2 +5000 x (−7) = 7000V
V = −25000
7000
= −3.571 ms−1
2. Ft = M(V−U)
f = m(V−U)
t
F = 5000 ( −3.571 − (−7)
0.1
F = 171,450 N
3. initial K.E = ½ M1U12 + ½ M2 (−U2)2
= ½ x 2000 X 52 + ½ x 5000 x (−7)2
= 25,000 + 122, 500
= 147,500J
final K.E + ½ (M+M2) V2
= ½ (2000 + 5000) (−3.571)2
= 44,632 J
Change in K.E = K.E lost − final K.E − Initial K.E
= (44,632 − 147,500) J
= −102,868J
4. The change /lost K.E is converted into heat, sound, light and spent in deformation