Question

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 

Answer 1

1. Momentum before collision = momentum after collision 
   M₁U₁ +M₂ (−U₂) = (M₁ + 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 (M₁ +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