Cambridge Lower Secondary CheckpointStage 6

Physics: Forces and energy

Science Stage 6 Chapter Notes

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Physics: Forces and energy
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In this chapter

  1. 1Understanding Work Done
  2. 2Calculating Work Done
  3. 3Balanced and Unbalanced Forces
  4. 4Drawing and Using Force Diagrams
  5. 5Energy Transfers and Work Done

1. Understanding Work Done

In physics, 'work' has a very specific meaning. Work is done whenever a force causes an object to move a certain distance. For work to be done, two things must happen: a force must be applied, and the object must move in the direction of that force. If you push against a solid wall, you are applying a force, but since the wall doesn't move, no work is done on the wall. The energy you use is just dissipated as heat in your muscles. The amount of work done is a measure of the energy transferred from one form to another. For example, when you lift a book, you do work against gravity, and the energy you expend is transferred to the book as gravitational potential energy.

Work Done (J) = Force (N) × distance moved in the direction of the force (m)

W = Fd

Key term

Work Done: The energy transferred when a force moves an object through a distance in the direction of the force.

Examiner insight

Examiners look for a clear understanding that movement is essential for work to be done. In descriptive questions, stating 'the object moves' is a key marking point.

Common pitfall

Thinking that applying a force is the same as doing work. If the object does not move, no work is done.

Worked example 12 marks

A person pushes a large rock with a force of 500 N. The rock does not move. How much work is done on the rock? Explain your answer.

  1. 1
    1. State the formula for work done: Work Done = Force × distance.
  2. 2
    1. Identify the values given: Force = 500 N, distance moved = 0 m.
  3. 3
    1. Calculate the work done: Work Done = 500 N × 0 m = 0 J.
  4. 4
    1. Explanation: No work is done because although a force is applied, the rock does not move. For work to be done, there must be displacement in the direction of the force.

Recap

  • Work is done when a force causes an object to move.
  • The movement must be in the same direction as the applied force.
  • Work done is a measure of energy transferred.
  • If an object does not move, no work is done on it, no matter how large the force.
  • The unit for work done is the Joule (J).

Quick check

  1. A student holds a heavy bag of books stationary for 30 seconds. Is work being done on the bag? Explain why.1 mark

2. Calculating Work Done

We can calculate the amount of work done using a simple formula. The work done (W) is the product of the force applied (F) and the distance moved in the direction of the force (d). The standard unit for force is the Newton (N), for distance is the metre (m), and for work done is the Joule (J). One Joule of work is done when a force of one Newton moves an object one metre. It's crucial to use the correct units in your calculations; distances given in centimetres or kilometres must be converted to metres first.

W = F × d

Key term

Joule (J): The unit of work and energy, equivalent to the work done when a force of one Newton moves an object through a distance of one metre.

Examiner insight

Always show your working by writing down the formula, substituting the values, and then stating the final answer with the correct unit (J). This can earn you marks even if your final calculation is incorrect.

Common pitfall

Forgetting to convert units before calculating, especially converting centimetres to metres by dividing by 100.

Fun fact

Lifting an apple (which has a weight of about 1 N) from the floor to a table 1 metre high requires approximately 1 Joule of work.

Worked example 13 marks

A crane lifts a 1200 N steel girder 20 m vertically into the air. Calculate the work done by the crane.

  1. 1
    1. State the formula: Work Done = Force × distance (W = Fd).
  2. 2
    1. Identify the force. The force needed to lift the girder is equal to its weight, so F = 1200 N.
  3. 3
    1. Identify the distance: d = 20 m.
  4. 4
    1. Substitute the values into the formula: W = 1200 N × 20 m.
  5. 5
    1. Calculate the result: W = 24000 J (or 24 kJ).

Worked example 22 marks

A shopper pushes a trolley with a horizontal force of 35 N for a distance of 50 m. Calculate the work done by the shopper against friction.

  1. 1
    1. State the formula: W = Fd.
  2. 2
    1. Identify the force and distance: F = 35 N, d = 50 m.
  3. 3
    1. Substitute the values: W = 35 N × 50 m.
  4. 4
    1. Calculate the result: W = 1750 J.

Recap

  • The formula for work done is W = F × d.
  • Force (F) must be in Newtons (N).
  • Distance (d) must be in metres (m).
  • Work done (W) is measured in Joules (J).
  • Always convert units to standard SI units before calculating.

Quick check

  1. A force of 10 N moves an object 3 m. How much work is done?1 mark
  2. If 500 J of work is done moving an object 25 m, what force was used?2 marks

3. Balanced and Unbalanced Forces

Forces almost always act in pairs. If the forces acting on an object are equal in size and opposite in direction, we say they are 'balanced'. Balanced forces result in no change in motion. The object will either remain stationary or continue to move at a constant velocity. If one force is larger than the opposing force, the forces are 'unbalanced'. Unbalanced forces cause a change in motion: the object will accelerate, decelerate, or change direction. The overall force on an object is called the 'net force' or 'resultant force'. For balanced forces, the net force is zero. For unbalanced forces, there is a non-zero net force.

Net Force (F_net) = Larger Force - Smaller Force (for forces in opposite directions)

Key term

Net Force: The overall force acting on an object when all the individual forces acting on it are added together, taking their directions into account.

Examiner insight

When describing the motion of an object, be precise. Use terms like 'constant velocity' for balanced forces on a moving object, and 'accelerates' for an object with a net force in its direction of motion.

Common pitfall

Confusing 'no motion' with 'no forces'. A stationary object on a table has balanced forces acting on it (weight down, normal contact force up); it does not mean there are no forces at all.

Worked example 13 marks

A car's engine provides a forward thrust of 2000 N. The resistive forces (friction and air resistance) total 1500 N.a) Are the forces on the car balanced or unbalanced?b) Calculate the net force on the car.c) Describe the motion of the car.

  1. 1
    1. (a) The forward thrust (2000 N) is greater than the resistive forces (1500 N). Therefore, the forces are unbalanced.
  2. 2
    1. (b) Net Force = Thrust - Resistive Forces. Net Force = 2000 N - 1500 N = 500 N.
  3. 3
    1. (c) Since there is a net force in the forward direction, the car will accelerate (speed up).

Recap

  • Balanced forces are equal and opposite, resulting in a net force of zero.
  • An object with balanced forces acting on it will not change its motion; it stays still or moves at a constant velocity.
  • Unbalanced forces result in a non-zero net force.
  • A net force causes an object to accelerate, decelerate, or change direction.

Quick check

  1. A parachutist is falling at a constant speed. What can you say about the forces acting on them?1 mark

4. Drawing and Using Force Diagrams

A force diagram (or free-body diagram) is a simple drawing that shows all the forces acting on a single object. We represent the object as a simple box or dot, and each force is shown as an arrow pointing away from the object. The direction of the arrow shows the direction of the force. The length of the arrow is often used to represent the relative size (magnitude) of the force; a larger force is shown with a longer arrow. Common forces to include are Weight (acting vertically downwards), Normal Contact Force (or Reaction Force, acting perpendicular to a surface), Thrust (or Driving Force), and resistive forces like Friction or Air Resistance.

Key term

Force Diagram: A diagram showing the direction and relative magnitude of all the forces acting on an object.

Examiner insight

Examiners award marks for correctly labelled forces with arrows that start on the object and point in the correct direction. For balanced forces, arrows should be of equal length.

Common pitfall

Drawing the arrows pointing towards the object instead of away from it, or confusing weight (a force) with mass (a scalar quantity).

Worked example 12 marks

A book with a weight of 5 N is resting on a horizontal table. Draw a force diagram for the book.

  1. 1
    1. Draw a dot or a box to represent the book.
  2. 2
    1. Draw an arrow pointing vertically downwards from the centre of the box. Label this 'Weight = 5 N'.
  3. 3
    1. Draw an arrow pointing vertically upwards from the centre of the box. This represents the force from the table pushing up. Label this 'Normal Contact Force = 5 N'.
  4. 4
    1. Ensure both arrows are of equal length, as the forces are balanced and the book is not accelerating.

Worked example 22 marks

Draw a force diagram for a rocket accelerating vertically upwards after launch.

  1. 1
    1. Draw a box to represent the rocket.
  2. 2
    1. Draw a large arrow pointing vertically upwards from the base of the rocket. Label this 'Thrust'.
  3. 3
    1. Draw a smaller arrow pointing vertically downwards from the centre of the rocket. Label this 'Weight'.
  4. 4
    1. The upward arrow for Thrust must be visibly longer than the downward arrow for Weight, as there is a net upward force causing acceleration.

Recap

  • Force diagrams show all the forces acting on one object.
  • The object is shown as a dot or box.
  • Forces are shown as arrows pointing away from the object.
  • The direction of the arrow shows the force's direction.
  • The length of the arrow represents the force's magnitude.
  • All forces on a diagram should be clearly labelled.

Quick check

  1. Name two forces that would act on a car driving along a level road.2 marks

5. Energy Transfers and Work Done

The Principle of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one store to another. Doing work is the mechanism for transferring energy. When work is done on an object, energy is transferred to it. For example, when you lift a box, you do work against gravity. The chemical energy from your muscles is transferred to the box as gravitational potential energy (GPE). If you push a box along the floor, you do work against friction. The energy is transferred to the box and the floor, increasing their thermal energy (making them slightly warmer). The work done on an object is equal to the energy it gains.

Work Done = Energy Transferred

Key term

Conservation of Energy: The principle that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

Examiner insight

In questions linking work and energy, be explicit about the energy stores involved. For example, state that 'work done against gravity increases the gravitational potential energy'.

Common pitfall

Forgetting that work done against friction results in a transfer to thermal energy, not a 'useful' energy store like kinetic or potential energy.

Fun fact

When a meteor enters the atmosphere, it's travelling incredibly fast. Work is done against air resistance, transferring the meteor's huge kinetic energy store to a thermal energy store, causing it to glow brightly and burn up.

Worked example 14 marks

A 2 kg ball is lifted 3 m vertically.a) Calculate the work done on the ball.b) What form of energy has the ball gained? (Take gravitational field strength, g = 10 N/kg)

  1. 1
    1. (a) First, find the weight of the ball. Weight = mass × g = 2 kg × 10 N/kg = 20 N. This is the force needed to lift it.
  2. 2
    1. (a) Now, calculate work done. Work Done = Force × distance = 20 N × 3 m = 60 J.
  3. 3
    1. (b) By lifting the ball against gravity, it has gained Gravitational Potential Energy (GPE).
  4. 4
    1. (b) The amount of GPE gained is equal to the work done, so it has gained 60 J of GPE.

Recap

  • Doing work on an object transfers energy to it.
  • Work Done is equal to Energy Transferred.
  • Lifting an object does work against gravity, increasing its Gravitational Potential Energy.
  • Pushing an object against friction does work, increasing the thermal energy of the object and its surroundings.
  • Energy is always conserved in any interaction.

Quick check

  1. If 200 J of work is done to lift an object, how much gravitational potential energy does it gain?1 mark

End-of-chapter exercise

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

  1. Define 'work done' in physics and state its unit.2 marks
  2. A weightlifter holds a 1500 N barbell stationary above their head for 5 seconds. How much work is done on the barbell during this time?1 mark
  3. A boy pulls a sled with a horizontal force of 40 N over a distance of 150 m on level, snowy ground. Calculate the work done by the boy.2 marks
  4. Draw a labelled force diagram for a car that is accelerating along a horizontal road. Use arrows of appropriate relative lengths to represent the forces.3 marks
  5. A motor does 4500 J of work to lift a crate. If the crate has a weight of 900 N, how high was it lifted?3 marks
  6. A boat is moving through the water at a constant velocity. The engine provides a forward thrust of 5000 N. What is the magnitude of the total resistive force (drag) from the water? Explain your answer.3 marks
  7. A person of mass 60 kg climbs a flight of stairs. The vertical height of the stairs is 4.5 m. a) Calculate the person's weight. (g = 10 N/kg) b) Calculate the work done by the person to climb the stairs. c) What is the person's gain in gravitational potential energy?4 marks
  8. A car has a driving force of 3000 N and experiences total resistive forces of 2200 N. a) Calculate the net force on the car. b) The driver then reduces the driving force to 2200 N. Describe the subsequent motion of the car.3 marks
  9. Explain why the front of a car is designed with a 'crumple zone' that collapses in a collision, in terms of forces and energy transfer.3 marks
  10. A pump lifts 50 kg of water per minute from a well that is 12 m deep. a) Calculate the weight of water lifted per minute. (g = 10 N/kg) b) Calculate the work done by the pump every minute.3 marks

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