Conservation of Momentum and Energy Transfer

In this educational video, we delve into a classic physics problem involving a spring gun to illustrate key concepts such as conservation of momentum, kinetic energy calculation, and elastic potential energy.

Problem Overview:

A 60 g ball is propelled at 22 m/s into the barrel of a spring gun weighing 240 g, initially at rest on a frictionless surface. The ball becomes lodged in the barrel at maximum spring compression. Assuming negligible thermal energy increase due to friction, we aim to determine:

1. The velocity of the spring gun after the ball comes to rest within the barrel.
2. The proportion of the ball's initial kinetic energy that is stored in the spring.

Methodology:

1. Applying Conservation of Momentum: In an isolated, frictionless system, total momentum remains constant. We calculate the final velocity of the combined ball-gun system by equating it to the initial momentum of the ball.
2. Calculating Kinetic Energy: We assess both the initial kinetic energy of the ball and the final kinetic energy of the combined system.
3. Determining Elastic Potential Energy: The difference between the initial and final kinetic energies represents the energy stored in the spring. We compute this to find the fraction of the initial kinetic energy converted into elastic potential energy.

Learning Outcomes:

• Understanding Conservation Laws: This problem exemplifies the application of conservation of momentum and energy principles in physics problem-solving.
• Energy Transformation Insight: Grasping how kinetic energy transforms into elastic potential energy is crucial for comprehending physics concepts demonstrated in such scenarios.