Gravity, energy, heat, work and momentum
Track forces and transfers without confusing energy, temperature, momentum or mass.
What you will tackle
- Use weight and a supplied gravitational relationship
- Calculate kinetic/potential energy and mechanical work
- Apply a one-dimensional momentum model
- Distinguish heat-transfer mechanisms
Forces and conserved quantities
Weight mg is gravitational force; mass does not change merely because local gravitational field strength changes. A supplied inverse-square gravitational model predicts one-quarter force at twice the separation for unchanged masses. Momentum is p = mv with direction. Total momentum is conserved for a system with negligible external impulse; kinetic energy need not be conserved in a collision.
Energy and work
Kinetic energy is mv²/2; near Earth's surface, gravitational potential-energy change is mgΔh when g is approximately constant. A force in the same direction as displacement does work +Fd; an oppositely directed force does −Fd. Energy transfers between stores and to the environment; mechanical energy can become internal energy without total energy disappearing.
Heat is a transfer
Heat is energy transferred because of a temperature difference. Conduction transfers through microscopic interactions, convection through bulk fluid movement, and radiation through electromagnetic waves. Temperature relates to particle motion in a model; it is not the total internal energy of an object. Comparing equal-temperature objects does not establish equal energy content.
Build your notes, then practise
Work on paper before opening an explanation. Guided tasks provide a starting point; independent tasks remove the scaffolding; application tasks ask you to justify a method or interpretation in context.
Guided practice
Guided 1
Use g = 10 m/s². Find the weight of a 2 kg object and the potential-energy increase when raised 3 m. Find work by a 5 N force in the same direction as a 4 m displacement. What is its kinetic energy at 3 m/s?
Show a starting hint
Keep force units N separate from energy units J.
Compare with the explained answer
- Weight is 2·10 = 20 N; potential-energy increase is 2·10·3 = 60 J.
- Work is 5·4 = 20 J under the stated same-direction assumption.
- Kinetic energy is (1/2)·2·3² = 9 J.
Answer / response criteria: 20 N; 60 J; 20 J; 9 J.
Independent practice
Independent 1
A 2 kg cart at +3 m/s joins a stationary 1 kg cart, with negligible external impulse. Find their shared velocity. If their gravitational separation from a source doubled under an inverse-square model, what happens to force? Identify the transfer in a metal spoon warming in hot soup, circulating soup, and sunlight.
Compare with the explained answer
- Initial momentum is 6 kg·m/s; final mass 3 kg gives velocity +2 m/s.
- An unchanged-mass inverse-square force becomes one-quarter as large.
- The dominant examples are conduction in the spoon, convection in circulating soup and radiation from sunlight.
Answer / response criteria: +2 m/s; one-quarter force; conduction, convection, radiation.
Application practice
Application 1
A falling object's potential energy decreases by 100 J, its kinetic energy increases by 80 J and 20 J is transferred to surroundings. Assess conservation. Explain why a collision that conserves momentum need not conserve kinetic energy, and why equal temperatures do not imply equal stored energy.
Compare with the explained answer
- 100 J lost from one store equals 80 + 20 J gained elsewhere, consistent with energy conservation.
- Momentum conservation depends on external impulse; kinetic energy can transfer to deformation, sound and internal energy.
- Stored energy also depends on amount and material, so temperature alone is insufficient.
Answer / response criteria: Energy balances; momentum and kinetic-energy conservation are distinct; temperature alone does not determine stored energy.
What can you explain now?
A falling object's potential energy decreases by 100 J, its kinetic energy increases by 80 J and 20 J is transferred to surroundings. Assess conservation. Explain why a collision that conserves momentum need not conserve kinetic energy, and why equal temperatures do not imply equal stored energy.
Compare with the explanation
Energy balances; momentum and kinetic-energy conservation are distinct; temperature alone does not determine stored energy.
Explain the reasoning before comparing. This review records your self-assessment rather than an official score or mastery decision.
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Source and review status
Coverage follows the named requirements and examples in the 2026–2027 ACT test guide and subject descriptions. That guide explicitly does not list every possible topic. The broader coded College and Career Readiness Standards are also mapped to conceptual teaching and practice; this does not calibrate a learner to a score band. The separate scientific-background context list and reading-complexity rubric have their own stated limits.
Original teaching and explained self-check practice are available. Specialist review and difficulty calibration remain pending. Essays require self-check or teacher review and are not automatically marked or awarded official scores.
Official source specification / guide