Question

A 1000 kg car moving at 30 m/s westward slams into and sticks to a 100 kg garbage can in the road. How much kinetic energy is lost in this collision?

Answer 1

The Given scenario is an example of an Inelestic Collision. Collisions in which momentum is conserved but has a loss in Kinetic Energy are called as Inelastic Collisions.

Given That :

Mass of Car m1 = 1000kg

Mass of Garbage Can m2= 100 kg

Velocity of Car u1= 30m/s

Garbage Can is at rest u2= 0

Using Conservation of momentum we have final velocity

  $v= \frac{m_1}{m_1+m_2} u_1$

$v= \frac{1000}{1000+100} * 30 = 27.27 m/s$

Kinetic Energy before Collision = $K_i= \frac{1}{2} * m_1 u_1^2$

Kinetic Energy After Collision $K_f= \frac{1}{2} (m_1+m_2)v^2= \frac{1}{2}*1100*27.27^2$

Loss in Kinetic Energy = Ki- Kf

= 4.5 x 10 5 - 4.1 x 105

= 0.4 x 105 J

Fraction of Kinetic Energy lost is Given By

  $\frac{K_i-K_f}{K_i}= \frac{m_2}{m_1+m_2}$  $= \frac {100}{1000+100}$

= 0.091

Hope This Helps!!!