Problem 1
A mass moving at speed undergoes a one-dimensional elastic collision with a stationary mass . Find both final velocities. Use an idealized laboratory-frame model: stated parameters remain constant during the process unless the motion itself makes a quantity vary. State a clear sign convention and use the defined symbols consistently. (a) Write the governing laws or constraints. (b) Derive the requested quantities symbolically and state their physical direction or meaning. (c) Check dimensions and examine a simple physical limit to validate the result. Finally, verify that every equation is dimensionally consistent and that the results satisfy the initial conditions. Since no numerical data are specified, the exact answers are expressions in the defined symbols.
problems.proof.stepOf
problems.proof.analysis
First identify the system, sign convention, and idealizations to choose the governing law. This prevents mixing quantities from different directions or reference frames.
problems.proof.pitfall. Do not drop a sign or the component along the chosen axis.