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8.3 Resultant Forces

GCSE Physics · AQA · Chapter 8: Forces in Balance

A free GCSE Physics lesson for AQA (8463) from OBA School: finding the resultant of forces along a line, balanced and unbalanced forces, and free-body diagrams. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Explain what is meant by the resultant force on an object
  • Calculate the resultant of forces acting along the same line
  • Use Newton’s first law to describe what happens when the resultant force is zero
  • Describe how the motion changes when the resultant force is not zero
  • (Higher tier) draw and use free-body force diagrams

Key words

  • Resultant force: The single force that has the same effect as all the forces acting on an object together.
  • Balanced forces: Forces whose resultant is zero.
  • Unbalanced forces: Forces whose resultant is not zero; the motion of the object changes.
  • Newton’s first law: If the resultant force on an object is zero, a stationary object stays at rest and a moving object keeps moving at the same speed in the same direction.
  • Free-body diagram: (Higher tier) A diagram of one object showing every force acting on it as a labelled arrow, and nothing else.

The resultant force

Most objects have several forces acting on them at once. The resultant force is the single force that would have the same effect as all of them together. For forces acting along one line:

  • 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.

Worked example: a tug-of-war

The red team pulls left with forces of 380 N, 410 N and 350 N. The blue team pulls right with 420 N, 390 N and 360 N.
Red total = 380 + 410 + 350 = 1140 N to the left. Blue total = 420 + 390 + 360 = 1170 N to the right.
Resultant = 1170 − 1140 = 30 N, in the direction of the larger force.

Answer: 30 N to the right (towards the blue team)

Balanced forces: Newton’s first law

If the resultant force on an object is zero, the forces are balanced and the object’s motion does not change (Newton’s first law):

  • an object at rest stays at rest
  • a moving object keeps moving at the same speed in the same direction (constant velocity).

A puck on an air-hockey table floats on a layer of air, so there is almost no friction. Once hit, it glides across the table at a steady speed in a straight line. A cyclist whose driving force exactly matches the resistive forces also moves at a constant velocity.

Exam tip: Zero resultant force does not mean the object is stationary. It means its velocity is not changing: it is either at rest or moving at a constant speed in a straight line.

If only two forces act on an object and the resultant is zero, the two forces must be equal in size and act in opposite directions.

Unbalanced forces change the motion

If the resultant force is not zero, the object’s speed or direction (or both) changes. A resultant force in the direction of motion speeds the object up; a resultant force opposite to the motion slows it down; a resultant force at an angle to the motion changes its direction.

Worked example: a rocket at lift-off

The engines of a small rocket give an upward thrust of 52 000 N. Its weight is 38 000 N.
Resultant = 52 000 − 38 000 = 14 000 N upwards, so the rocket speeds up as it rises.

Answer: 14 000 N upwards

Free-body force diagrams (Higher tier)

A free-body diagram shows one object and all the forces acting on it, and nothing else. Each force is a labelled arrow starting on the object and pointing in the direction the force acts. Forces that the object exerts on other things are not shown.

Worked example: using the free-body diagram of the car

Vertical: upward forces = 5400 + 6600 = 12 000 N = weight, so the vertical resultant is zero (the car does not rise or sink).
Horizontal: resultant = 2500 − 1900 = 600 N forwards.

Answer: resultant force = 600 N forwards, so the car speeds up

Common mistakes

  • Thinking a moving object must have a resultant force on it. A constant velocity needs zero resultant force.
  • Adding forces that act in opposite directions instead of subtracting them.
  • Giving a resultant force without a direction. The resultant is a vector, so say which way it acts.
  • (Higher tier) Drawing forces that act on other objects in a free-body diagram, or forgetting to label the arrows.

Revision questions

Try these, then check your answers below each one.

Question 1. A force of 45 N acts to the left on a box and a force of 70 N acts to the right. What is the size of the resultant force?

Answer: 25 N

Working: 70 − 45 = 25 N, to the right (direction of the larger force).

Question 2. A puck slides across ice at 3 m/s with zero resultant force on it. What happens next? (Choose from: it keeps moving at 3 m/s in the same direction, it slows down and stops, it speeds up, it changes direction.)

Answer: it keeps moving at 3 m/s in the same direction

Working: With zero resultant force its velocity does not change (Newton’s first law), so it carries on at 3 m/s in a straight line.

Question 3. True or false? An object with zero resultant force on it must be stationary.

Answer: False

Working: False. Zero resultant force means no change in velocity: the object is either at rest or moving at constant speed in a straight line.

Related lessons

Continue in the full course

This lesson is section 8.3 (AGCPH0803) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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