How Can a Collision Conserve Momentum, But Not Kinetic Energy?

<p>When two objects interact in a collision, momentum is conserved where momentum (p) is defined as the product of mass (m) and velocity (v). However, if the kinetic energy also depends on mass and velocity (1/2 mv&sup2;) then shouldn&rsquo;t it also be conserved? Nope. Let&rsquo;s work through the whole thing.</p> <h1>Simple Collision Between Two Point Particles</h1> <p>Let&rsquo;s start with the simplest example possible (maybe). Imagine that there is a particle with mass m moving in the x-direction with a velocity v (called particle A). It collides with another particle with mass m, but that&rsquo;s stationary (particle B). Oh, it&rsquo;s a head on collision so that every stays in 1 dimension (the x-direction).</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:700/1*UlBT1EIi690vvy3tcG7B1w.png" style="height:352px; width:700px" /></p> <p>The key thing idea is that during the collision object A pushes on B and B pushes back on A. But these are the SAME interaction such that the magnitude of A on B is equal to B on A. Now let&rsquo;s consider the momentum principle. It says the following:</p> <p><img alt="" src="https://miro.medium.com/v2/resize:fit:638/1*[email protected]" style="height:222px; width:638px" /></p> <p>We can do the same thing for particle B, but remember the two forces are equal and opposite. This means that the change in momentum for A must be the opposite of mass B (assuming the time intervals are the same &mdash; but why wouldn&rsquo;t they be).</p> <p><a href="https://rjallain.medium.com/how-can-a-collision-conserve-momentum-but-not-kinetic-energy-6cd544297200">Visit Now</a></p>