Revision summary

Name the body or system, the direction and the interval. Distinguish an individual body's momentum change from conservation of the total.

Signed impulse

Use signed velocities, particularly for a rebound. Add positive and negative graph areas algebraically. Convert ms to s for an impulse in N s. Peak force is not generally average force.

A named contact force supplies the net impulse only if other impulses in that direction are negligible. Newton's-third-law partners act on different bodies and do not cancel in one body's equation.

In a sensor comparison, check force recipient, sign, calibration, zero, sample times and the whole pulse interval. A force measured on the wall has the opposite sign from the corresponding force on the ball. Missing a peak or shifting the baseline biases the area.

Conserve the selected system's total momentum

This requires zero or negligible net external impulse on the system during the interval. Internal impulses cancel in the total, while each body's momentum can change. If external impulse is significant, include it as the change in total momentum.

Use one signed axis. Momentum alone gives one equation for two unknown final velocities. Sticking supplies v_A = v_B; other outcomes need their own additional information.

For cart measurements, include moving attachments in each mass, obtain signed velocities immediately before/after the same collision, and keep any gate interval entirely on one side of contact. A gate measures an interval-average speed; direction must be known separately. Tilt, friction and misplaced measurement intervals can undermine the ideal account.

Choose the energy and relative-speed conditions

For the stated arrangement with A left of B, approach speed is u_A - u_B and separation speed is v_B - v_A. Equality applies to the perfectly elastic separating case. Check the arrangement and signs when using these expressions.

Total momentum can be conserved while kinetic energy decreases or increases in an interaction. Account for the corresponding changes in other stores and transfers. Total energy does not disappear.

A force-time area is an impulse in N s; a force-displacement area is work in N m = J. Momentum and kinetic energy have different units and different conservation conditions.