Forces, Motion, and Energy
This domain tests Newton's laws, kinematics, momentum, and energy conservation, usually through short calculations on a single object or a simple collision. Items ask you to draw or interpret a free-body diagram, find an acceleration or final speed, compare work and kinetic energy, or decide whether momentum is conserved.
Core rules
- Newton's first law: with zero net force, an object at rest stays at rest and a moving object continues at constant velocity. Constant velocity does not mean zero force; it means balanced forces.
- Newton's second law: F_net = ma. Weight is W = mg, with g ≈ 9.8 m/s², and weight is a force while mass is not.
- Newton's third law: forces come in equal, opposite pairs acting on different objects.
- Kinematics: v = u + at; s = ut + ½at²; v² = u² + 2as, valid for constant acceleration only.
- Momentum: p = mv, conserved in a closed system; impulse = FΔt = Δp.
- Energy: W = Fd cos θ; KE = ½mv²; PE = mgh; P = W/t; efficiency = useful output ÷ total input × 100%.
Worked example
A 2.0 kg cart starts from rest and is pushed by a net force of 6.0 N over 3.0 m on a frictionless track. Find its final speed and kinetic energy.
Reasoning: a = F/m = 6.0 ÷ 2.0 = 3.0 m/s². Using v² = u² + 2as with u = 0: v² = 2 × 3.0 × 3.0 = 18, so v = 4.2 m/s. Work done = Fd = 6.0 × 3.0 = 18 J. KE = ½ × 2.0 × 18 = 18 J, matching the work input - the work–energy check confirms the answer. Time to travel 3.0 m is t = v/a = 1.4 s.
Traps that cost marks
- Reporting weight in kilograms or mass in newtons.
- Believing that zero net force requires the object to be stationary.
- Pairing action–reaction forces on the same object so they "cancel."
- Using kinematics equations when acceleration is not constant.
- Forgetting that friction does negative work and reduces mechanical energy.
- Confusing momentum (mv) with kinetic energy (½mv²); doubling speed doubles momentum but quadruples KE.
- Dropping the sign that encodes direction.