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O-Level Physics · Secondary 3 and 4

Dynamics and Newton's Laws

Dynamics explains why objects move the way they do. Kinematics describes motion, and dynamics links that motion to the forces acting. In this upper secondary topic you learn to draw free-body diagrams, find resultant forces, apply Newton's three laws and use F = ma, and to tell mass apart from weight. These ideas run through the rest of the course, from pressure and moments to energy and the force on a current-carrying wire in electromagnetism.

What the syllabus expects

  • Identify the forces acting on an object and draw a labelled free-body diagram
  • Find the resultant of forces acting along a straight line
  • Describe the effect of balanced and unbalanced forces on a body at rest or in motion
  • Recall and use F = ma, where F is the resultant force
  • Identify action and reaction force pairs using Newton's third law
  • Distinguish between mass and weight and use W = mg, with g = 10 N/kg near the Earth
  • Describe the effects of friction and how it can be increased or reduced

Forces and resultant force

A force is a push or a pull, measured in newtons (N). Force is a vector, so its direction matters as much as its size. The resultant force is the single force that has the same effect as all the forces acting together. For forces along a straight line, add those in the same direction and subtract those in opposite directions. If a trolley is pushed forward with 30 N while friction of 12 N acts backwards, the resultant force is 30 − 12 = 18 N forwards. A free-body diagram shows the object on its own, with an arrow for every force acting on it, each starting from the object and labelled with its name and size. Typical forces are weight, normal reaction, friction, air resistance, tension and thrust.

Newton's first and second laws

Newton's first law says that an object stays at rest, or keeps moving at constant velocity in a straight line, unless a resultant force acts on it. So a moving object does not need a resultant force to keep moving, it needs one only to speed up, slow down or change direction. The tendency of an object to resist changes to its state of motion is called inertia, and mass is a measure of inertia. Newton's second law links the resultant force to the acceleration it produces: F = ma, with F in N, m in kg and a in m/s². The acceleration is always in the direction of the resultant force. One newton is the resultant force that gives a mass of 1 kg an acceleration of 1 m/s². A resultant force of 3000 N on a 1200 kg car gives an acceleration of 3000 ÷ 1200 = 2.5 m/s².

Newton's third law

Newton's third law says that if body A exerts a force on body B, then body B exerts a force on body A that is equal in size and opposite in direction. The two forces in a pair are always the same type of force and they act on different bodies, which is why they never cancel each other out. When you push against a wall, the wall pushes back on you with an equal force. A book resting on a table is a classic test. The Earth pulls the book down (its weight), and the book pulls the Earth up with an equal gravitational force. That is one pair. The table pushes the book up (normal reaction), and the book pushes down on the table. That is a second pair. The weight and the normal reaction both act on the book, so they are not a third-law pair, even though they happen to be equal here.

Mass, weight and friction

Mass is the amount of matter in a body, measured in kilograms, and it is the same wherever the body is. Weight is the gravitational force on the body, measured in newtons, given by W = mg, where g is the gravitational field strength. Near the Earth's surface g is about 10 N/kg, and on the Moon it is about 1.6 N/kg. A 5.0 kg bag weighs 50 N on Earth but only 8.0 N on the Moon, while its mass stays 5.0 kg. Friction is a force that opposes the relative motion of two surfaces in contact. It causes heating and wear, for example in machine parts, but it is also useful, giving grip to tyres and shoes and making brakes work. Friction can be reduced with lubricants, ball bearings and smoother surfaces. Air resistance is a similar opposing force that increases with speed.

Worked example

A box of mass 20 kg is pulled along a horizontal floor by a horizontal rope with a tension of 90 N. A friction force of 30 N acts on the box. Take g = 10 N/kg. (a) Calculate the weight of the box. (b) Calculate the acceleration of the box. (c) The tension is then reduced so that the box moves at constant velocity. State the new tension and explain your answer.

  1. Weight: W = mg = 20 × 10 = 200 N, acting vertically downwards and balanced by the normal reaction from the floor.
  2. Horizontally, the tension and friction act in opposite directions, so the resultant force = 90 − 30 = 60 N in the direction of the pull.
  3. Apply F = ma with the resultant force: a = F ÷ m = 60 ÷ 20 = 3.0 m/s².
  4. Constant velocity means zero acceleration, so by Newton's first law the resultant force must be zero.
  5. For a zero resultant, the tension must equal the friction, so the new tension is 30 N.

Answer: (a) 200 N (b) 3.0 m/s² in the direction of the pull (c) 30 N, because at constant velocity the resultant force is zero, so the pull must exactly balance the 30 N friction.

Common mistakes

  • Putting the applied force into F = ma instead of the resultant force. Subtract friction and any other opposing forces first.
  • Thinking an object needs a resultant force to keep moving at a steady speed. A resultant force changes velocity. Constant velocity means the forces are balanced.
  • Naming weight and normal reaction as a Newton's third law pair. They act on the same object. A third-law pair always acts on two different objects and is the same type of force.
  • Giving weight in kilograms or mass in newtons. Mass is in kg, weight is a force in N, and W = mg links them.
  • Assuming a decelerating object must have a resultant force forwards because it is still moving forwards. The resultant force points the same way as the acceleration, so for a car slowing down it points backwards.

Exam tips

  • Draw a quick free-body diagram and write the resultant force as a separate line before you use F = ma. It prevents the most common error in this topic.
  • In third-law answers, name both bodies and state that the forces are equal in size, opposite in direction, of the same type and act on different bodies.
  • Whenever a question says constant velocity or at rest, write resultant force = 0 straight away. It usually leads straight to the unknown force.

Practice questions

1. Easy: An astronaut has a mass of 70 kg. Find his weight on Earth, where g = 10 N/kg, and on the Moon, where g = 1.6 N/kg. What is his mass on the Moon?

Show answer

On Earth W = 70 × 10 = 700 N. On the Moon W = 70 × 1.6 = 112 N. His mass is still 70 kg, because mass does not depend on location.

2. Medium: A car of mass 1500 kg accelerates uniformly from 10 m/s to 22 m/s in 6.0 s. Calculate the resultant force on the car.

Show answer

3000 N. First find the acceleration: a = (22 − 10) ÷ 6.0 = 2.0 m/s². Then F = ma = 1500 × 2.0 = 3000 N in the direction of motion.

3. Harder: A ball of mass 0.50 kg falls vertically. At one instant the air resistance on it is 2.0 N. Take g = 10 N/kg. (a) Find its acceleration at that instant. (b) The ball later reaches terminal velocity. What is the air resistance then?

Show answer

(a) Weight = 0.50 × 10 = 5.0 N downwards. Resultant force = 5.0 − 2.0 = 3.0 N downwards, so a = 3.0 ÷ 0.50 = 6.0 m/s² downwards. (b) At terminal velocity the resultant force is zero, so the air resistance equals the weight, 5.0 N.

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