Forces and momentum

Physics · Space, time and motion. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A free-body diagram shows one object and only the forces acting on it. Newton's first law says the velocity is constant when the resultant force is zero. The second law says the resultant force equals the rate of change of momentum, which becomes F = ma when the mass is constant. The third law says forces come in pairs: equal in size, opposite in direction, of the same type, and acting on two different objects.

Momentum (mass × velocity) is a vector. The total momentum of an isolated system is conserved in every collision and explosion. Kinetic energy is conserved only in an elastic collision.

An object moving in a circle at constant speed is accelerating towards the centre, so a resultant centripetal force must act towards the centre.

Rules to remember

Common mistake

Students pair the weight of an object with the normal force on it as a third-law pair. Both act on the same object, so they are not a pair: the partner of the Earth's pull on the object is the object's gravitational pull on the Earth.

Worked example

A 3.0 kg block is pulled along a rough level floor by a horizontal force of 20 N. The coefficient of dynamic friction is 0.25 and g = 9.8 m s−2. What is the acceleration of the block?

  1. Normal force = weight = 3.0 × 9.8 = 29.4 N.
  2. Friction = μdFN = 0.25 × 29.4 = 7.35 N.
  3. Resultant force = 20 − 7.35 = 12.65 N.
  4. a = F ÷ m = 12.65 ÷ 3.0 = 4.2 m s−2.

Answer: About 4.2 m s−2.

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