Cambridge IGCSE0972

Forces

Physics 0972 Chapter Notes

What this chapter covers

Forces - Effects of forcesForces - Turning effect of forcesForces - Centre of gravity
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In this chapter

  1. 1Understanding Resultant Forces
  2. 2Force, Mass, and Acceleration (F=ma)
  3. 3Weight, Mass and Gravity
  4. 4Friction and Air Resistance

1. Understanding Resultant Forces

A force is a push or a pull that can change an object's motion. Often, multiple forces act on an object at the same time. The 'resultant force' is the single force that has the same effect as all the individual forces combined. If forces act in a straight line, you can find the resultant force by simple addition or subtraction. Forces acting in the same direction are added together. Forces acting in opposite directions are subtracted, with the resultant force acting in the direction of the larger force. If the forces are balanced, the resultant force is zero, and the object's motion doesn't change (it stays still or continues at a constant velocity).

Resultant Force (same direction) = F₁ + F₂

Resultant Force (opposite direction) = F₁ - F₂

Key term

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

Common pitfall

Forgetting to state the direction of the resultant force, which is a vector quantity and requires both magnitude and direction for a complete answer.

Worked example 12 marks

A box has a forward thrust of 25 N and a backward frictional force of 10 N. What is the resultant force on the box?

  1. 1

    The forces act in opposite directions.

  2. 2

    Resultant Force = Larger Force - Smaller Force

  3. 3

    Resultant Force = 25 N - 10 N = 15 N

  4. 4

    The direction of the resultant force is the same as the larger force, so it is 15 N forwards.

Worked example 23 marks

A tug-of-war rope is pulled to the left with forces of 150 N and 200 N. It is pulled to the right with a force of 330 N. Find the magnitude and direction of the resultant force.

  1. 1

    Step 1: Calculate the total force to the left.

  2. 2

    Total Left Force = 150 N + 200 N = 350 N.

  3. 3

    Step 2: Compare the total left force with the right force.

  4. 4

    The forces are in opposite directions, so subtract the smaller from the larger.

  5. 5

    Resultant Force = 350 N (left) - 330 N (right) = 20 N.

  6. 6

    Step 3: State the direction.

  7. 7

    The resultant force is in the direction of the larger force, which is to the left.

Recap

  • A force is a push or a pull measured in Newtons (N).
  • The resultant force is the overall force on an object.
  • Add forces that act in the same direction.
  • Subtract forces that act in opposite directions.
  • A zero resultant force means the forces are balanced and there is no change in motion.

Quick check

  1. A rocket has an upward thrust of 5000 N and a downward weight of 4000 N. What is the resultant force?1 mark

2. Force, Mass, and Acceleration (F=ma)

Newton's Second Law of Motion describes the relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. This means a larger resultant force produces a larger acceleration, while a larger mass results in a smaller acceleration for the same force. This fundamental relationship is summarised by the equation F = ma.

Resultant Force = mass × acceleration

F = ma

Key term

Newton (N): The unit of force, defined as the force required to give a mass of 1 kg an acceleration of 1 m/s².

Examiner insight

Examiners frequently set multi-step problems. A common sequence is to first calculate the resultant force, then use F=ma. Always show your calculation for the resultant force as a separate step to secure marks.

Common pitfall

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

Fun fact

When a large ship turns off its engines, its huge mass means it has enormous inertia. It can take several miles for the ship to stop, even with resistive forces from the water.

Worked example 13 marks

A car of mass 1200 kg has a driving force of 4000 N and resistive forces totalling 1600 N. Calculate the acceleration of the car.

  1. 1

    Step 1: Find the resultant force on the car.

  2. 2

    Resultant Force (F) = Driving Force - Resistive Forces

  3. 3

    F = 4000 N - 1600 N = 2400 N.

  4. 4

    Step 2: Use Newton's Second Law (F = ma) to find the acceleration.

  5. 5

    2400 N = 1200 kg × a

  6. 6

    a = 2400 / 1200 = 2 m/s².

Worked example 23 marks

A ball of mass 0.5 kg is pushed along the ground with a force of 10 N. It accelerates at 12 m/s². Calculate the force of friction acting on the ball.

  1. 1

    Step 1: Calculate the resultant force needed to cause the acceleration.

  2. 2

    Resultant Force (F) = ma = 0.5 kg × 12 m/s² = 6 N.

  3. 3

    Step 2: Understand the forces involved.

  4. 4

    The resultant force is the difference between the push force and friction: F = Push - Friction.

  5. 5

    Step 3: Rearrange to find the frictional force.

  6. 6

    Friction = Push - Resultant Force

  7. 7

    Friction = 10 N - 6 N = 4 N.

Recap

  • Newton's Second Law links resultant force, mass, and acceleration.
  • The equation is F = ma.
  • Force (F) must be in Newtons (N), mass (m) in kilograms (kg), and acceleration (a) in m/s².
  • The 'F' in F=ma always stands for the resultant force.
  • If the resultant force is zero, acceleration is zero.

Quick check

  1. What is the force needed to accelerate a 5 kg object at 3 m/s²?1 mark
  2. An object of mass 10 kg experiences a resultant force of 50 N. What is its acceleration?1 mark

3. Weight, Mass and Gravity

Mass and weight are often confused, but they are different concepts. Mass is the measure of how much matter is in an object, measured in kilograms (kg). It's a scalar quantity and is the same everywhere in the universe. Weight is the force of gravity acting on an object's mass, measured in Newtons (N). It's a vector quantity, as it always acts downwards towards the centre of the planet. The weight of an object depends on its mass and the gravitational field strength(g) of its location. On Earth, g is approximately 9.8 N/kg (often rounded to 10 N/kg in IGCSE exams).

Weight = mass × gravitational field strength

W = mg

Key term

Gravitational Field Strength (g): The force of gravity acting per unit of mass at a specific location, measured in Newtons per kilogram (N/kg).

Examiner insight

Marks are often awarded for clearly distinguishing between mass and weight. If a question involves moving between planets, remember that mass stays constant while weight changes.

Fun fact

If you were on Jupiter, where the gravitational field strength is about 24 N/kg, you would weigh about 2.4 times more than you do on Earth!

Worked example 13 marks

An astronaut has a mass of 75 kg. Calculate her weight:(a) on Earth, where g = 9.8 N/kg, and(b) on the Moon, where g = 1.6 N/kg.

  1. 1

    (a) On Earth:

  2. 2

    Weight = mass × g

  3. 3

    Weight = 75 kg × 9.8 N/kg = 735 N.

  4. 4

    (b) On the Moon:

  5. 5

    Weight = mass × g

  6. 6

    Weight = 75 kg × 1.6 N/kg = 120 N.

  7. 7

    Note that her mass (75 kg) remains the same in both locations.

Recap

  • Mass is the amount of matter in an object, measured in kg.
  • Weight is the force of gravity on an object, measured in N.
  • The formula linking them is W = mg.
  • An object's mass is constant, but its weight can change depending on the local gravity.
  • On Earth, g is approximately 9.8 N/kg or 10 N/kg.

Quick check

  1. What is the weight of a 5 kg bag of sugar on Earth? (Use g = 10 N/kg)1 mark
  2. An object weighs 300 N on a planet where g = 12 N/kg. What is its mass?2 marks

4. Friction and Air Resistance

Friction is a force that opposes motion between two surfaces in contact. Air resistance (or drag) is a type of friction that acts on objects moving through the air. These resistive forces are crucial in real-world scenarios. For a moving vehicle, they oppose the driving force from the engine. As an object speeds up, air resistance increases. Eventually, the air resistance can become large enough to balance the driving force. When this happens, the resultant force is zero, the object stops accelerating and moves at a constant maximum speed, called terminal velocity.

Key term

Terminal Velocity: The constant speed that a freely falling object eventually reaches when the resistance of the medium (e.g. air) through which it is falling prevents further acceleration.

Examiner insight

Questions about terminal velocity are common. Examiners look for the key idea that at terminal velocity, forces are balanced, the resultant force is zero, and therefore acceleration is zero.

Common pitfall

Thinking that an object with no resultant force on it must be stationary. It can also be moving at a constant velocity (Newton's First Law).

Worked example 13 marks

A skydiver of mass 80 kg is falling at a constant velocity. (Use g = 10 N/kg).(a) What is the skydiver's weight?(b) What is the magnitude of the air resistance force acting on the skydiver?

  1. 1

    (a) Calculate the weight:

  2. 2

    Weight (W) = mass × g = 80 kg × 10 N/kg = 800 N.

  3. 3

    (b) Determine the air resistance:

  4. 4

    The skydiver is falling at a constant velocity, which means their acceleration is zero.

  5. 5

    If acceleration is zero, the resultant force must be zero.

  6. 6

    This means the upward force (air resistance) must balance the downward force (weight).

  7. 7

    Therefore, Air Resistance = Weight = 800 N.

Recap

  • Friction and air resistance are forces that oppose motion.
  • Air resistance increases as the speed of an object increases.
  • Terminal velocity is reached when the driving force (or weight) is balanced by resistive forces.
  • At terminal velocity, the resultant force is zero and acceleration is zero.

Quick check

  1. A car is travelling at a constant speed on a level road. What is the relationship between the driving force and the total resistive forces?1 mark

End-of-chapter exercise

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

  1. A motorbike of mass 250 kg accelerates from rest to 15 m/s in 5.0 s. Calculate the resultant force required to cause this acceleration.4 marks
  2. A boat's engine provides a driving force of 5000 N. The resistive forces from the water total 1800 N. If the boat has a mass of 1600 kg, what is its acceleration?3 marks
  3. An apple of mass 150 g falls from a tree. Calculate its weight in Newtons. (Use g = 10 N/kg).2 marks
  4. A parachutist and their parachute have a total mass of 90 kg. When falling at terminal velocity, what is the magnitude of the upward air resistance force? (Use g = 9.8 N/kg).2 marks
  5. Two children push a large tyre. One pushes with a force of 80 N to the right. The other pushes with a force of 65 N to the right. A frictional force of 25 N opposes the motion. Calculate the resultant force on the tyre and state its direction.3 marks
  6. A space probe has a weight of 4900 N on Earth (g = 9.8 N/kg). What is the mass of the probe? The probe is sent to Mars where g = 3.7 N/kg. What is the weight of the probe on Mars?4 marks
  7. A block of mass 4.0 kg is pulled along a rough horizontal surface by a constant force. It accelerates from 1.0 m/s to 3.0 m/s in 4.0 s. Calculate the resultant force on the block.3 marks
  8. A car of mass 1500 kg is travelling at a constant velocity of 20 m/s. The total resistive forces are 800 N. What is the driving force produced by the engine?2 marks
  9. A force of 12 N gives an object an acceleration of 5 m/s². A force of 20 N gives the same object an acceleration of 9 m/s². Calculate the mass of the object and the constant frictional force acting on it.5 marks
  10. Explain why a falling object in air eventually reaches a terminal velocity. In your answer, refer to weight, air resistance, resultant force and acceleration.4 marks

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