Question

(d) The students are now asked to consider the kinetic energy changes in an inelastic collision, specifically whether the initial values of one of the physical quantities affect the fraction of mechanical energy dissipated in the collision. How could you modify the experiment to investigate this question? Be sure to explicitly describe the calculations you would make, specifying all equations you would use (but do not actually do any algebra or arithmetic)

Answer 1

Kinetic energy is not conserved during Inelastic collision but momentum is conserved.

Relation between velocity before collision and velocity after collision can be determined using conservation of momentum.

Subtract the value of kinetic energy after collision from the kinetic energy before collision, the outcome will be energy dissipated during collision.

Let velocity of object A of mass m before collision is u

It collides with object B of mass M and velocity of both objects stuck together is v

Now,

Applying Conservation of momentum,

=> m*u = (M + m)*v

=> v = (m*u) / (M + m)

Now,

Kinetic energy before collision, K_i = 1/2*m*u²

Final Kinetic energy, K _f = 1/2*(M + m)*v² = 1/2*(M + m)*((m*u) / (M + m))²

                                       = 1/2*(m*u)² / (M + m)

Energy lost in collision, E' = K _f - K_i = [ 1/2*(m*u)² / (M + m) - 1/2*m*u² ]