Momentum and Newton's laws of motion

AS Level Physics · Dynamics. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

Test this topic freeAll AS Level Physics topics

The idea

Mass is the property of an object that resists change in its motion. It is the same everywhere. Weight is the gravitational force on the object, so it changes when g changes.

Momentum is mass × velocity and is a vector. Newton's second law says that the resultant force on an object equals its rate of change of momentum. When the mass is constant this becomes F = ma. The acceleration is always in the direction of the resultant force, not always in the direction of motion.

No resultant force means constant velocity (first law). Forces come in pairs that act on two different objects (third law).

Rules to remember

Common mistake

Putting a single force into F = ma instead of the resultant force. In vertical problems, find the resultant of the weight and the other force first.

Worked example

A student of mass 60 kg stands on a scale in a lift. The lift accelerates downwards at 1.5 m s−2. What is the contact force from the scale on the student? (g = 9.81 m s−2)

  1. Weight = mg = 60 × 9.81 = 588.6 N downwards.
  2. Taking downwards as positive, resultant force = weight − contact force = ma = 60 × 1.5 = 90 N.
  3. Contact force = 588.6 − 90 = 498.6 N.

Answer: About 500 N upwards, which is less than the student's weight.

Practice questions

Try each one, then open the answer.

1. An object of mass 5.0 kg is taken to a planet where the acceleration of free fall is 3.7 m/s2. What are its mass and weight there?

  1. A
    5.0 kg and 18.5 N
  2. B
    5.0 kg and 49 N
  3. C
    1.9 kg and 18.5 N
  4. D
    18.5 kg and 49 N
Show answer

Answer: A. Mass is unchanged; weight = mg = 5.0 × 3.7 = 18.5 N.

2. A book rests on a table. Which pair of forces is a Newton's third law pair?

  1. A
    the weight of the book and the normal contact force from the table
  2. B
    the gravitational pull of the Earth on the book and the gravitational pull of the book on the Earth
  3. C
    the weight of the book and the weight of the table
  4. D
    the normal force on the book and friction
Show answer

Answer: B. Third-law pairs are equal, opposite, of the same type and act on different bodies. Weight and the normal force both act on the book, so they are not a pair.

3. Water leaves a hose at 12 m s−1 at a rate of 0.50 kg s−1. It hits a wall horizontally and does not rebound. What force does the water exert on the wall?

  1. A
    3.0 N
  2. B
    6.0 N
  3. C
    24 N
  4. D
    72 N
Show answer

Answer: B. Force = rate of change of momentum = (mass per second) × change in velocity = 0.50 × 12 = 6.0 N.

More questions on this topic

Read the full notes

Keep going

← Equations of motionNon-uniform motion →All rules on one pageStuck? Ask a question