Forces and Newton’s laws: study guide

Key ideas

Newton’s laws link force to motion. The net force on an object equals its mass times its acceleration, and every force has an equal and opposite partner force acting on a different object.

• Draw a free-body diagram with every force on the object, then add them as vectors: ΣF = ma, separately along each axis.
• Weight is mg and points down. The normal force is perpendicular to the surface and is not always equal to the weight.
• Kinetic friction is μ_k N and opposes sliding. Static friction adjusts itself up to a maximum of μ_s N.
• On an incline, split the weight into mg sin θ along the slope and mg cos θ into the surface.

Key equations

• ΣF = ma
• W = mg
• f = μN
• a = g sin θ (frictionless incline)
• F = kx (Hooke’s law)

Worked example

A 10 kg box slides down a 30° incline with μ_k = 0.20 (g = 9.8 m/s²). Along the slope: mg sin θ = 10 × 9.8 × 0.5 = 49 N. Friction: μ_k mg cos θ = 0.20 × 10 × 9.8 × 0.866 = 17 N. The net force is 32 N, so a = 32 ÷ 10 = 3.2 m/s².

Common mistakes

• Treating the normal force as always equal to mg. On an incline, or with extra vertical forces, it is different.
• Treating an action–reaction pair as two forces on the same object. They act on different objects, so they never cancel.
• Using the weight instead of the normal force in the friction formula.

Practice

Test yourself with practice questions on this topic: Forces and Newton’s laws