Resultant Forces

✏️ Paper first! Work out every question on paper before you tap Show solution. Write down every step – the equation, the numbers with units, the rearranging and the answer with its unit. In the exam, if your final answer is wrong you can still get marks for correct working, but only if the examiner can see it.

When several forces act on an object, their combined effect is the resultant force. It decides whether the object speeds up, slows down, changes direction or stays as it is. Answer each question on paper first, then tap to check. Use g = 9.8 N/kg. Questions marked (H) are Higher tier. ← Forces topic

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The RESULTANT FORCE is the single force that has the same effect as all the forces acting together.
• Forces in the SAME direction: ADD them.
• Forces in OPPOSITE directions: SUBTRACT the smaller from the larger. The resultant acts in the direction of the larger force.
• Resultant force = 0 → forces are BALANCED → the object stays still, or keeps moving at a constant velocity.
• Resultant force ≠ 0 → the object ACCELERATES in the direction of the resultant (F = ma). If the resultant is opposite to the motion, the object slows down.

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A FREE BODY DIAGRAM shows all the forces acting on ONE object, drawn as labelled arrows from its centre. Longer arrow = bigger force.
(H) Forces at an angle can be added with a SCALE DRAWING (head-to-tail), and one force can be RESOLVED into two components at right angles.

Forces in a straight line

Q1 (1 mark) Two people push a stuck car to the right with forces of 250 N and 300 N. Calculate the resultant force.

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Same direction, so add: 250 + 300 = 550 N to the right (1)

Q2 (2 marks) A box has a force of 12 N pulling it right and a force of 7 N pulling it left. Calculate the resultant force.

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Opposite directions, so subtract: 12 − 7 = 5 N (1) to the right (1) – the direction of the larger force.

Q3 (2 marks) In a tug of war, team A pulls left with 1200 N and team B pulls right with 1200 N. What is the resultant force, and what happens to the rope?

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Resultant = 0 N (1). The forces are balanced, so the rope stays still – or, if it was already moving, keeps moving at a constant velocity (1).

Q4 (2 marks) A car has a driving force of 3000 N. Air resistance is 800 N and friction is 400 N. Calculate the resultant force and describe the car’s motion.

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Resultant = 3000 − (800 + 400) = 1800 N forwards (1)
The car is accelerating forwards (1).

Q5 (3 marks) A book rests on a table. Draw a free body diagram for the book. The book’s weight is 6 N. What is the size of the normal contact force, and what is the resultant force?

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Diagram: a downward arrow labelled “weight 6 N” and an upward arrow of the same length labelled “normal contact force 6 N” (1).
Normal contact force = 6 N upwards (1); resultant = 0 N (1) – the book is stationary, so the forces must be balanced.

Q6 (2 marks) A student says, “The weight of the book and the normal contact force are a Newton’s third law pair.” Explain why she is wrong.

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Both forces act on the same object (the book), but a third law pair acts on two different objects (1). They are also different types of force (gravitational and contact). The third law partner of the book’s weight is the book pulling the Earth upwards (1).

Q7 (2 marks) A plane flies at a constant velocity. Its engines provide 50 kN of thrust. What is the size of the drag force? Explain.

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Drag = 50 kN (1). At constant velocity the resultant force is zero, so drag must equal thrust (1).

Q8 (3 marks) A student pushes an 8.0 kg box across the floor with a force of 60 N. Friction is 20 N. Calculate (a) the resultant force and (b) the acceleration of the box.

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(a) 60 − 20 = 40 N in the direction of the push (1)
(b) a = F ÷ m = 40 ÷ 8.0 (1) = 5.0 m/s² (1)

Q9 (3 marks) A 1200 kg car is braking. The braking force is 6000 N and the air resistance is 300 N. Calculate (a) the resultant force and (b) the deceleration of the car.

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(a) Both forces act backwards, so add: 6000 + 300 = 6300 N backwards (1)
(b) a = F ÷ m = 6300 ÷ 1200 (1) = 5.25 m/s² deceleration (1)

Q10 (2 marks) A lift and its passengers have a weight of 10 000 N. The cable pulls up with a tension of 12 000 N. Calculate the resultant force. The lift is moving upwards – what is happening to its speed?

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Resultant = 12 000 − 10 000 = 2000 N upwards (1). The resultant is in the same direction as the motion, so the lift is speeding up (1).

Q11 (4 marks) A rocket has a mass of 2500 kg and its engines produce a thrust of 35 000 N at launch. Calculate (a) its weight, (b) the resultant force and (c) its acceleration.

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(a) W = mg = 2500 × 9.8 = 24 500 N (1)
(b) Resultant = 35 000 − 24 500 = 10 500 N upwards (1)
(c) a = F ÷ m = 10 500 ÷ 2500 (1) = 4.2 m/s² upwards (1)

Q12 (2 marks) A cyclist is moving along a flat road. The resultant force on her is zero. Her friend says, “That means she must be stopped.” Is the friend right? Explain.

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No (1). A resultant force of zero means her velocity doesn’t change. Since she is already moving, she keeps moving at a constant speed in a straight line – Newton’s first law (1).

Forces at an angle (H)

Use a scale drawing on squared paper (e.g. 1 cm = 1 N): draw the forces head-to-tail, then measure the line from the start of the first arrow to the end of the last. Measure angles with a protractor. You can check sizes with Pythagoras.

Q13 (3 marks – H) A 6.0 N force acts east and an 8.0 N force acts north on the same object. Find the size and direction of the resultant force.

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Scale drawing or √(6.0² + 8.0²) = √100 (1) = 10 N (1)
Direction: about 53° north of east (1)

Q14 (3 marks – H) A boat’s engine pushes it north with 400 N, and the river current pushes it east with 300 N. Find the resultant force on the boat.

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Scale drawing or √(400² + 300²) (1) = 500 N (1), about 37° east of north (1)

Q15 (2 marks – H) A child pulls a sledge with a rope at 30° above the horizontal. The tension in the rope is 20 N. Using a scale drawing, resolve this force into horizontal and vertical components.

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Draw a 20 N arrow (e.g. 10 cm) at 30° to the horizontal, then complete a right-angled triangle.
Horizontal component ≈ 17 N (1) – this pulls the sledge along
Vertical component = 10 N (1) – this lifts the sledge slightly

Q16 (2 marks – H) A lamp hangs in equilibrium from two cables. Describe the vector diagram of the three forces acting on the lamp, and explain why it looks like this.

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Drawn head-to-tail, the two tensions and the weight form a closed triangle (1). The lamp is in equilibrium, so the resultant force is zero – the arrows end where they started (1).

✅ Add up your marks out of 39 (or out of 29 for Q1–Q12 if you’re doing Foundation).

⚠️ Where students lose marks

  • Forgetting the direction of the resultant force – always say which way it acts.
  • “Zero resultant force means stopped.” It means constant velocity – which could be moving.
  • Using just one force in F = ma (e.g. the driving force) instead of the RESULTANT force.
  • Confusing balanced forces with a Newton’s third law pair. Balanced forces act on one object; a third law pair acts on two different objects.
  • Adding forces at an angle as if they were in a line – 6 N and 8 N at right angles make 10 N, not 14 N.

Next: Resultant force = mass × acceleration → · Terminal velocity questions