Physic Labs

Problem 1

Two masses m₁,m₂ with collinear velocities u₁,u₂ collide perfectly inelastically. Find their common velocity and kinetic energy lost. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.
v=m1u1+m2u2m1+m2,Klost=m1m2(u1−u2)22(m1+m2)v=\frac{m_1u_1+m_2u_2}{m_1+m_2},\quad K_{\rm lost}=\frac{m_1m_2(u_1-u_2)^2}{2(m_1+m_2)}
problems.proof.analysis

The boxed expressions answer the parts in order. Signs, conditions of validity, and constants follow the conventions in the statement.