Ch 5 · 1.5.1 Balanced and Unbalanced Forces · O Level Physics 5054

Topic 5 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 79 lessons.

Introduction

A football flies when you kick it, slows down on the grass, and curves when it hits a post. Every change in motion comes from a force. This lesson names the forces you must know, shows how to draw them on a free-body diagram, and introduces Newton's first and third laws and F = ma. (Syllabus section 1.5.1.)

Key ideas — Types of force

A force is a push or a pull, measured in newtons (N).

🧑‍🏫 Teacher's explanation

Imagine you are playing tug-of-war. If both sides pull with the exact same strength, the rope doesn't move; the forces are 'balanced'. If one side pulls harder, the rope moves toward them; the forces are 'unbalanced'. A force is simply a push or a pull that can change how an object moves or how its shape changes.

📖 Definitions

🔍 Worked example — Easy

A wooden block is pushed across a horizontal table with a force of 15 N to the right. The friction force acting against the motion is 5 N to the left. Calculate the resultant force acting on the block.

🔍 Worked example — Standard

A car of mass 1200 kg is accelerating at 2.5 m/s^2. Calculate the resultant force acting on the car.

🔍 Worked example — Exam-style

A rocket of mass 500 kg is launched upwards. The upward thrust from the engines is 7000 N. Calculate the acceleration of the rocket. (Use g = 9.81 m/s^2)

⚠️ Common errors

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🎯 Exam question

Key ideas — Free-body diagrams

A free-body diagram shows one object and all the forces acting on it, each drawn as an arrow starting on the object, pointing in the force's direction and labelled. Longer arrows show larger forces.

🧑‍🏫 Teacher's explanation

Imagine you are playing tug-of-war. If both teams pull with the exact same strength, the rope doesn't move; the forces are 'balanced'. If one team pulls harder, the rope accelerates toward them; the forces are 'unbalanced'. A free-body diagram is just a simplified map of these 'tugs' acting on a single object.

📖 Definitions

🔍 Worked example — Easy

A wooden block is being pulled across a horizontal floor. A horizontal force of 15 N is applied to the right, and a friction force of 5 N acts to the left. Calculate the resultant force.

🔍 Worked example — Standard

A car of mass 1200 kg is moving at a constant velocity. The driving force (thrust) is 3000 N. Calculate the total resistive force (drag and friction) acting on the car.

🔍 Worked example — Exam-style

A rocket of mass 500 kg is accelerating upwards. The thrust produced by the engine is 7000 N. Calculate the upward acceleration of the rocket. (Use g = 9.81 m/s^2)

⚠️ Common errors

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🎯 Exam question

Key ideas — Resultant force

The resultant is the single force with the same effect as all the forces together. For forces along one straight line, add those in one direction and subtract those in the opposite direction. In the diagram the resultant is 3000 - 1200 = 1800\ N forwards, and the vertical forces cancel.

🧑‍🏫 Teacher's explanation

Imagine you are playing tug-of-war. If both teams pull with exactly the same strength, the rope doesn't move; the forces are 'balanced'. If one team pulls harder, there is a 'resultant' force that makes the rope move in their direction. The resultant force is simply the 'winner' of the tug-of-war—it is the single force that represents the net effect of all forces acting on the object.

📖 Definitions

🔍 Worked example — Easy

A wooden block is being pulled to the right with a force of 15 N. The friction force acting against the motion is 5 N. Calculate the resultant force acting on the block.

🔍 Worked example — Standard

A car of mass 1200 kg is accelerating at 2.5 m/s^2. Calculate the resultant force acting on the car.

🔍 Worked example — Exam-style

An object is subject to two forces: a thrust of 50 N acting downwards and a weight of 45 N acting downwards. The object has a mass of 5 kg. Calculate the acceleration of the object.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Newton's first law

*An object either remains at rest or continues to move in a straight line at constant speed unless acted on by a resultant force.* When the forces are balanced (resultant = 0), nothing about the motion changes. A resultant force is needed to change motion, not to keep it going.

🧑‍🏫 Teacher's explanation

Imagine you are playing tug-of-war. If both teams pull with exactly the same strength, the rope doesn't move; it is in equilibrium. This is what happens when forces are 'balanced'. The net or resultant force is zero, so the object's state of motion stays exactly as it was.

📖 Definitions

🔍 Worked example — Easy

A wooden block is being pulled across a horizontal floor by a constant force of 15 N to the right. The friction force acting against the motion is 15 N to the left. Calculate the acceleration of the block.

🔍 Worked example — Standard

A car of mass 1200 kg is traveling at a constant velocity of 25 m/s along a straight road. The engine provides a forward thrust of 3000 N. Calculate the total resistive force (drag and friction) acting on the car.

🔍 Worked example — Exam-style

A rocket of mass 500 kg is accelerating upwards. The upward thrust is 7000 N and the weight of the rocket is W = mg (use g = 10 m/s^2). Calculate the upward acceleration of the rocket.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — What a resultant force does

A force may change the velocity of an object by changing its speed (speeding up or slowing down) or its direction of motion, or both.

🧑‍🏫 Teacher's explanation

Imagine you are playing tug-of-war. If both teams pull with the exact same strength, the rope doesn't move; this is a 'balanced' state. If one team pulls harder, the rope accelerates toward them. This 'extra' force is what we call the resultant force.

📖 Definitions

🔍 Worked example — Easy

A toy car of mass 2.0 kg is pushed with a horizontal force of 10 N to the right. There is a constant frictional force of 2.0 N acting to the left. Calculate the acceleration of the car.

🔍 Worked example — Standard

A 500 g ball is moving at 5 m/s due North. A horizontal force of 10 N is applied to the ball towards the East. Calculate the acceleration of the ball.

🔍 Worked example — Exam-style

A skydiver of mass 80 kg is falling at terminal velocity. The air resistance acting upwards is 785 N. Calculate the weight of the skydiver (use g = 9.81 m/s^2).

⚠️ Common errors

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🎯 Exam question

(a) Calculate the resultant force acting on the block. (b) Calculate the acceleration of the block. [3 marks]

Key ideas — Force, mass and acceleration

F = ma

🧑‍🏫 Teacher's explanation

Imagine you are pushing a heavy shopping trolley. If you push with a force of 10 N and your friend pushes from the other side with 10 N, the trolley doesn't move because the forces cancel out. This is a 'balanced' situation. However, if you push harder than your friend, there is a 'resultant' (or net) force that causes the trolley to speed up or slow down. This is an 'unbalanced' situation.

📖 Definitions

🔍 Worked example — Easy

A toy car of mass 0.5 kg is pushed with a constant force of 2.0 N. Calculate the acceleration of the car.

🔍 Worked example — Standard

A crate of mass 50 kg is being pulled across a floor. A horizontal force of 150 N is applied to the crate, while a friction force of 50 N acts in the opposite direction. Calculate the acceleration of the crate.

🔍 Worked example — Exam-style

An object experiences a resultant force of 12 N to the left. The object has a mass of 4.0 kg. If the force is doubled, what is the new acceleration?

⚠️ Common errors

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🎯 Exam question

Key ideas — Newton's third law

*When object A exerts a force on object B, then object B exerts an equal and opposite force on object A.* The two forces in a third-law pair:

🧑‍🏫 Teacher's explanation

Imagine you are wearing rollerblades and you push against a wall. Even though you are the one doing the pushing, you feel the wall pushing back against your hands, causing you to roll backward. This happens because forces never exist in isolation; they always come in pairs.

📖 Definitions

🔍 Worked example — Easy

A book rests on a table. The book exerts a downward contact force of 15 N on the table. What is the magnitude and direction of the force exerted by the table on the book?

🔍 Worked example — Standard

A magnet exerts a magnetic force of 0.5 N towards the right on a small iron nail. Describe the force exerted by the nail on the magnet.

🔍 Worked example — Exam-style

A heavy truck exerts a contact force of 5000 N on a concrete barrier. What is the magnitude and direction of the force exerted by the barrier on the truck?

⚠️ Common errors

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🎯 Exam question

(a) State the magnitude and direction of the force exerted by the floor on the person. (b) Explain why these two forces do not cancel each other out. [3 marks]

Worked example

Example 1: resultant force and acceleration. For the car in the diagram, the driving force is 3000 N, the total resistive force is 1200 N and the mass is 1200 kg.

🔍 Worked example — Easy

A toy car of mass 2.0 kg is pushed with a forward force of 10 N. The friction force acting against the motion is 4.0 N. Calculate the acceleration of the car.

🔍 Worked example — Standard

A crate of mass 50 kg is being pulled up a slope by a tension force of 600 N. The weight of the crate acting downwards is 490 N. If the crate moves at a constant speed, what is the magnitude of the resistive force acting down the slope?

🔍 Worked example — Exam-style

A rocket of mass 5000 kg is launched vertically upwards. The thrust from the engines is 70,000 N. Calculate the acceleration of the rocket immediately after launch. (Use g = 9.81 m/s^2)

⚠️ Common errors

Common mistakes

Practice

Answers: (1) (a) weight / gravitational force, (b) air resistance (drag), (c) tension. (2) 2500 - 900 = 1600\ N forwards. (3) a = 3.0/0.60 = 5.0\ m/s^2. (4) An object either remains at rest or continues to move in a straight line at constant speed unless acted on by a resultant force. (5) The rocket exerts a force on the gas backwards; the gas exerts an equal and opposite force on the rocket, forwards. (6) Weight downwards and air resistance upwards, equal in size (arrows the same length); resultant force = 0.

Ch 5 · 1.5.1 Balanced and Unbalanced Forces · O Level Physics 5054

All chapters in Motion, Forces and Energy