Kinetic Energy Conservation in Inelastic Collision on Frictionless Ice

Kinetic Energy Conservation: Dave and Paula's Ice Collision

To determine the percentage of initial kinetic energy remaining after Dave and Paula's collision, we'll use the principles of conservation of momentum and kinetic energy.

Before Collision:

• Dave (mass 2m) slides with velocity 'v'.* Paula (mass m) is stationary (velocity 0).

Initial momentum = (2m * v) + (m * 0) = 2mv

After Collision:

• Dave and Paula move together with a common velocity 'V'.

Final momentum = (2m + m) * V = 3mV

Conservation of Momentum:

Initial momentum = Final momentum 2mv = 3mV V = (2/3) * v

Kinetic Energy Analysis:

Initial kinetic energy = (1/2) * (2m) * v^2 = mv^2

Final kinetic energy = (1/2) * (2m + m) * V^2 = (3/2) * m * [(2/3) * v]^2 = (1/2) * mv^2

Conclusion:

The final kinetic energy is equal to the initial kinetic energy. Therefore, 100% of the initial kinetic energy in the system remains after the collision. This is because while kinetic energy is not always conserved in collisions (due to factors like heat generation), in this simplified scenario with no friction, it remains constant.