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Physics: Forces and energy

Science Stage 8 Chapter Notes

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Physics: Forces and energy
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In this chapter

  1. 1Introduction to Forces
  2. 2Balanced Forces and Constant Motion
  3. 3Unbalanced Forces and Acceleration
  4. 4Common Forces and Force Diagrams

1. Introduction to Forces

A force is simply a push or a pull. Forces are all around us and they can do several things to an object: make it start moving, make it stop moving, change its speed, change its direction, or change its shape. Because forces have both a size (magnitude) and a direction, they are known as vector quantities. The standard unit for measuring force is the Newton, abbreviated as N. We can represent forces on diagrams using arrows. The length of the arrow shows the size of the force (a bigger force gets a longer arrow), and the direction the arrow points shows the direction the force is acting in. These diagrams are called force diagrams or free-body diagrams.

Key term

Force: A push or a pull that acts on an object, capable of changing its state of motion or its shape, measured in Newtons (N).

Examiner insight

Examiners award marks for correctly drawn force diagrams where arrows are labelled with the name of the force (e.g., 'Weight') and originate from the object.

Common pitfall

Drawing force arrows of incorrect relative lengths for the situation described, for example drawing the weight arrow smaller than the upward contact force for an object resting on a table.

Fun fact

The force of gravity on a standard apple is about 1 Newton. So you can feel what 1 N of force is like by holding an apple in your hand.

Worked example 13 marks

A book with a weight of 5 N is resting on a horizontal table. Identify the two main forces acting on the book and draw a simple, labelled force diagram to represent them.

  1. 1

    Step 1: Identify the forces. The Earth's gravity pulls the book downwards. This force is its weight.

  2. 2

    Step 2: The table pushes upwards on the book, preventing it from falling. This is called the normal contact force or reaction force.

  3. 3

    Step 3: Draw the diagram. Represent the book as a simple box. Draw an arrow pointing downwards from the centre of the box, and label it 'Weight (5 N)'.

  4. 4

    Step 4: Draw another arrow of the same length pointing upwards from the centre of the box, and label it 'Contact Force (5 N)'. The arrows must be of equal length because the book is not moving up or down, meaning the forces are balanced.

Recap

  • A force is a push or a pull, measured in Newtons (N).
  • Forces are vector quantities, meaning they have both magnitude and direction.
  • Forces can change an object's speed, direction, or shape.
  • Force diagrams use arrows to show the size and direction of forces acting on an object.

Quick check

  1. What is the standard unit of force?1 mark
  2. If one force is 10 N and another is 20 N, how would you show this difference on a force diagram?1 mark

2. Balanced Forces and Constant Motion

When multiple forces act on an object, they can cancel each other out. If the forces acting on an object are equal in size and opposite in direction, we say they are 'balanced'. When forces are balanced, the total force, known as the 'resultant force', is zero. According to Newton's First Law of Motion, an object with zero resultant force acting on it will not change its motion. This means two things: if the object is stationary, it will remain stationary. If the object is already moving, it will continue to move at a constant speed in a straight line (this is called constant velocity). A car travelling at a steady 70 mph on a motorway has balanced forces: the forward thrust from the engine is exactly equal to the backward forces of air resistance and friction.

For balanced forces, Resultant Force = 0 N

Key term

Balanced Forces: Two or more forces acting on an object that are equal in size and opposite in direction, resulting in a zero resultant force and no change in motion.

Examiner insight

Students who explicitly state that 'constant speed' or 'constant velocity' implies balanced forces (and therefore a resultant force of zero) demonstrate a clear understanding and are rewarded.

Common pitfall

Thinking that an object moving at a constant speed has no forces acting on it. There are forces, but they are balanced, so the resultant force is zero.

Worked example 13 marks

A parachutist is falling at a constant speed, known as terminal velocity. Her weight is 600 N.a) What is the name of the upward force acting on her?b) What is the size of this upward force? Explain your answer.

  1. 1

    a) The upward force is air resistance (or drag).

  2. 2

    b) The size of the upward force (air resistance) is 600 N.

  3. 3

    Explanation: The question states she is falling at a 'constant speed'. This means her motion is not changing, so the forces on her must be balanced. Therefore, the upward force of air resistance must be equal in size and opposite in direction to her downward force of weight.

Worked example 22 marks

Two teams are in a tug-of-war. Team A pulls to the left with a force of 500 N. The rope does not move. What is the size and direction of the force exerted by Team B?

  1. 1

    Step 1: Identify the state of motion. The rope is not moving, which means it has a constant velocity of zero.

  2. 2

    Step 2: Apply the concept of balanced forces. Since there is no change in motion, the forces must be balanced.

  3. 3

    Step 3: Determine the opposing force. For the forces to be balanced, Team B must be pulling in the opposite direction with an equal force.

  4. 4

    Answer: Team B is pulling to the right with a force of 500 N.

Recap

  • Balanced forces are equal in size and opposite in direction.
  • When forces are balanced, the resultant (net) force on the object is zero.
  • An object with balanced forces acting on it will either remain at rest or move at a constant velocity.
  • Constant velocity means constant speed in a straight line.

Quick check

  1. If a car is travelling at a constant speed of 30 m/s, are the forces on it balanced or unbalanced?1 mark

3. Unbalanced Forces and Acceleration

When the forces acting on an object are not equal and opposite, they are 'unbalanced'. This results in a non-zero 'resultant force'. A resultant force will always cause a change in the object's motion. This change in motion is called acceleration. Acceleration doesn't just mean speeding up! It can be:

  1. Speeding up (accelerating): If the resultant force is in the same direction as the object's motion.
  2. Slowing down (decelerating): If the resultant force is in the opposite direction to the object's motion.
  3. Changing direction: If the resultant force acts at an angle to the object's motion.

For example, when you press the accelerator in a car, the engine's thrust becomes greater than the resistive forces, creating a resultant force forwards, and the car speeds up. When you press the brakes, the braking force creates a resultant force backwards, and the car slows down.

For unbalanced forces, Resultant Force ≠ 0 N

Key term

Resultant Force: The single force that has the same effect as all the individual forces acting on an object combined.

Examiner insight

Examiners look for a clear link between the existence of a resultant force and the resulting acceleration. High-scoring answers will also state the direction of this force and acceleration.

Common pitfall

Confusing 'slowing down' with 'no force'. An object that is slowing down has a resultant force acting on it, but in the opposite direction to its movement.

Worked example 13 marks

A rocket has a weight of 20,000 N. At lift-off, its engines produce an upward thrust of 35,000 N.a) Calculate the resultant force on the rocket.b) Describe the motion of the rocket.

  1. 1

    a) The forces are in opposite directions, so we subtract the smaller force from the larger one. Resultant Force = Thrust - Weight = 35,000 N - 20,000 N = 15,000 N.

  2. 2

    The direction of the resultant force is upwards, as the thrust is larger than the weight.

  3. 3

    b) Because there is a resultant force acting upwards, the rocket will accelerate upwards (it will speed up in the upward direction).

Worked example 23 marks

A cyclist is travelling at 10 m/s. The forward thrust from pedalling is 120 N and the total resistive forces (air resistance and friction) are 80 N. Is the cyclist speeding up, slowing down, or travelling at a constant speed? Explain your answer.

  1. 1

    Step 1: Compare the opposing forces. The forward thrust (120 N) is greater than the total resistive forces (80 N).

  2. 2

    Step 2: Determine if the forces are balanced or unbalanced. Since the forces are not equal, they are unbalanced.

  3. 3

    Step 3: Find the resultant force. Resultant Force = 120 N - 80 N = 40 N in the forward direction.

  4. 4

    Step 4: Relate the resultant force to motion. Because there is a resultant force in the direction of travel, the cyclist is accelerating (speeding up).

Recap

  • Unbalanced forces occur when forces are not equal and opposite.
  • An unbalanced force results in a non-zero resultant force.
  • A resultant force causes an object to accelerate (speed up, slow down, or change direction).
  • The object accelerates in the same direction as the resultant force.

Quick check

  1. If a ball is slowing down as it rolls along the floor, in which direction is the resultant force acting?1 mark

4. Common Forces and Force Diagrams

To solve problems in mechanics, you need to be able to identify, name, and draw the specific forces acting on an object. Here are the most common ones:

  • Weight: The force of gravity pulling an object towards the centre of the Earth. It always acts vertically downwards.
  • Normal Contact/Reaction Force: The force exerted by a surface on an object pressing against it. It always acts at a right angle (90°) to the surface.
  • Friction: A force that opposes motion when two surfaces are in contact. It acts parallel to the surface, against the direction of motion (or attempted motion).
  • Air Resistance (or Drag): The frictional force an object experiences when moving through a fluid (like air or water). It opposes the motion.
  • Thrust (or Driving Force): The forward force from an engine or muscles that pushes an object along.
  • Tension: The pulling force transmitted through a string, rope, cable or chain when it is pulled tight by forces acting from opposite ends.

When drawing force diagrams, always draw the arrows starting from the centre of the object, pointing outwards, and label each one clearly.

Key term

Weight: The force acting on an object due to gravity, which always acts vertically downwards towards the centre of the Earth.

Examiner insight

Marks are consistently lost for poorly labelled force diagrams. Always use standard names for forces (e.g., 'Weight', 'Air Resistance', 'Normal Contact Force') and ensure arrows are correctly directed.

Common pitfall

Confusing weight and mass. Mass is the amount of 'stuff' in an object (measured in kg), while weight is the force of gravity on that mass (measured in N).

Worked example 14 marks

An aeroplane is flying at a constant height and a constant speed. Draw a labelled force diagram showing the four main forces acting on it.

  1. 1

    Step 1: Identify the vertical forces. The plane's Weight acts downwards. The Lift from the wings acts upwards.

  2. 2

    Step 2: Identify the horizontal forces. The Thrust from the engines acts forwards. Air Resistance (or Drag) acts backwards.

  3. 3

    Step 3: Consider the motion. 'Constant height' means vertical forces are balanced. 'Constant speed' means horizontal forces are balanced.

  4. 4

    Step 4: Draw the diagram. Draw a box/shape for the plane. Draw an upward arrow for Lift and a downward arrow for Weight of equal length. Label them.

  5. 5

    Step 5: Draw a forward arrow for Thrust and a backward arrow for Air Resistance of equal length. Label them. All arrows should start from the centre of the plane.

Recap

  • Weight is the force of gravity and always acts downwards.
  • The Normal Contact Force acts perpendicular to a surface.
  • Friction and Air Resistance are forces that oppose motion.
  • Thrust is a forward, driving force.
  • In force diagrams, label each force and ensure arrow lengths reflect if forces are balanced or unbalanced.

Quick check

  1. What is the name of the force that prevents you from falling through the floor?1 mark
  2. A car is parked on a hill. In which direction does its weight act?1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Define 'balanced forces' and give an example of a situation where an object has balanced forces acting on it.2 marks
  2. A car has a weight of 12,000 N and is travelling along a straight, level road at a constant speed. The engine provides a forward thrust of 2,500 N. a) What is the size of the upward contact force from the road on the car? b) What is the total size of the resistive forces acting on the car? Explain your answer.3 marks
  3. Draw a labelled force diagram for a helicopter that is accelerating vertically upwards. Your arrows should be of appropriate relative lengths to show this motion.3 marks
  4. Explain the difference between an object moving at a constant speed and an object accelerating, using the idea of resultant force.3 marks
  5. A box is pushed across a rough floor with a horizontal force of 60 N. The frictional force opposing the motion is 45 N. Calculate the magnitude of the resultant force and state the effect it has on the box's motion.3 marks
  6. A boat is floating stationary in the water. Its weight is 8000 N. What is the size of the upthrust force from the water on the boat? Explain your reasoning.2 marks
  7. Two teams are in a tug-of-war. Team A pulls to the left with a force of 950 N. Team B pulls to the right with a force of 1020 N. a) Calculate the magnitude and state the direction of the resultant force. b) Describe the motion of the rope.3 marks
  8. An aeroplane has a weight of 600,000 N. Its engines produce a total thrust of 180,000 N. At a certain moment, the lift force is 600,000 N and the force of air resistance is 150,000 N. Describe and explain the aeroplane's motion, considering both horizontal and vertical movement.4 marks
  9. A cyclist is travelling at a constant speed. They then stop pedalling. Describe the forces acting on the cyclist and explain what happens to their speed.3 marks
  10. A skydiver jumps from a plane. A few seconds into her fall, her weight is 700 N and the force of air resistance on her is 400 N. a) Calculate the resultant force on the skydiver. b) As she falls faster, the force of air resistance increases. Explain what effect this has on her acceleration.4 marks

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