Ask what the problem wants
Before choosing an equation, underline the requested quantity. Acceleration at an instant often suggests a force equation. A speed after moving between two positions may be easier through work and energy. A velocity immediately after a brief collision may suggest momentum. These are starting questions, not rules that replace checking assumptions.
Next define the system and the interval. A cart alone and two carts together do not have the same external forces. “During the collision” and “while sliding afterward” may require separate models. Write those boundaries before deciding what is conserved.
Use forces when acceleration is the direct unknown
For a 4 kg cart pulled right by 18 N against 6 N of friction, the signed net force is 12 N right. Dividing by the mass gives 3 m/s² right. Adding the force magnitudes would erase their directions; dividing only the applied force by mass would erase friction.
Keep the free-body diagram tied to the object you selected. A force that exists on a different body does not belong on this diagram. The cited Newton-law section gives the governing relation; your diagram supplies the terms and signs.
Use energy to connect states, with a work check
A 1 kg object released from rest 5 m above a reference level has 50 J of gravitational potential energy if g is approximated as 10 m/s². With no dissipative work, its speed at that level is 10 m/s. If friction converts 18 J into thermal energy along the path, only 32 J remains as kinetic energy, giving 8 m/s.
This original comparison makes the assumption visible. Writing “energy is conserved” is incomplete if you then ignore the thermal energy. Mechanical energy is only one part of total energy. Identify any work or energy transfer that your chosen mechanical-energy equation must include.
Use momentum for the collision, then test energy separately
A 2 kg cart at 3 m/s sticks to a stationary 1 kg cart. With negligible external horizontal impulse, their combined momentum is 6 kg m/s before and after impact, so the final velocity is 2 m/s. Their kinetic energy decreases from 9 J to 6 J. A sticking collision does not justify conserving kinetic energy.
For your next review, write a three-line decision record: chosen system; reason the proposed conservation law applies; independent check on the result. Then change one assumption. An external impulse changes the momentum equation; friction changes the mechanical-energy accounting. Explaining that change is a stronger method check than remembering the numerical answer.
Check the underlying concepts
The sources support these concepts. The numerical examples and suggested routines are original Keiko study guidance, with no promise of a particular score outcome.
- For constant mass, net external force equals mass times acceleration. University Physics Volume 1, Section 5.3: Newton's Second Law (checked 2026-09-13).
- Mechanical energy is conserved when the relevant nonconservative work is zero. University Physics Volume 1, Section 8.3: Conservation of Energy (checked 2026-09-13).
- Negligible net external impulse permits conservation of total momentum. University Physics Volume 1, Section 9.3: Conservation of Linear Momentum (checked 2026-09-13).
Put this into practice
Sources
Every source below was accessed on the listed date. Pages — especially department admissions pages — change without notice; the links go to the live versions.
- University Physics Volume 1, Section 5.3: Newton's Second Law — OpenStax. Accessed 2026-07-06.
- University Physics Volume 1, Section 8.3: Conservation of Energy — OpenStax. Accessed 2026-08-02.
- University Physics Volume 1, Section 9.3: Conservation of Linear Momentum — OpenStax. Accessed 2026-08-02.
Related guides
Sources and corrections
Sources last checked 2026-09-13Every source cited on this page was checked on the date shown, and we update the page when a source changes. If something looks wrong, tell us and we'll recheck it.