Question

Using the equation for the final velocity in terms of masses and initial velocity of the gliders for a perfectly inelastic collision, work out the final kinetic energy, assuming one of the glider is at rest initially. Compare this to the initial kinetic energy and show that kinetic energy is not conserved in the collision. Do this only with variables; none of your data should be included

Answer 1

In a perfectly inelastic collision, conservation of momentum is used to find the final common velocity. Comparing initial and final kinetic energy reveals that kinetic energy is not conserved and some is lost during the collision.

Step-by-step explanation:

To investigate the changes in kinetic energy during a perfectly inelastic collision, where one glider is initially at rest while the other moves with an initial velocity, we use the conservation of momentum principle. Suppose mass m1 moves with an initial velocity u and mass m2 is at rest. After the collision, they stick together and move with a common velocity v, which is determined by the equation m₁ * u = (m₁ + m₂) * v. Solving for v yields v = m₁ * u / (m₁ + m₂).

The initial kinetic energy of the system is KEinitial = 0.5 * m₁ * u₂ since only mass m1 is in motion. The final kinetic energy is given by KEfinal = 0.5 * (m₁ + m2) * v₂.

Substituting v, we get KEfinal = 0.5 * (m₁ + m₂) * (m₁ * u / (m₁ + m₂))² = 0.5 * m₁² * u₂ / (m₁ + m₂). Comparing the expressions for initial and final kinetic energies, it is evident that KEfinal < KEinitial, confirming the loss of kinetic energy in the collision, which signifies that kinetic energy is not conserved in a perfectly inelastic collision.

Answer 2

Comparison has been made.

Step-by-step explanation:

Consider perfectly inelastic collision.Two masses of m1 and m2 with initial velocities u1 and u2 before colliding, stick together after collision and move with common speed v. then according to the rule of momentum preservation

m1u1+m2u2= (m1+m2)v

`v= (m1u1+m2u2)/(m1+m2)`

If u1 and u2 are known the final common velocity can be determined

Initial kinetic energy is

`(1)/(2)m1u1^(2)+(1)/(2)m2u2^(2)`

The collion here is perfectly inelastic this means kinectic energy is not conserved. Therefore, initial kinectic energy is not equal to final kinectic.

`(1)/(2)m1v^(2)+(1)/(2)m2v^(2)`