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P8.3 Resultant Forces

GCSE Combined Science · AQA · Chapter P8: Forces in Balance

A free GCSE Combined Science: Trilogy lesson for AQA (8464) 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
  • Describe what happens to an object when the resultant force on it is zero, and when it is not zero
  • (Higher tier) draw and use free-body diagrams to describe the forces on an isolated object

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 360 N, 400 N and 330 N. The blue team pulls right with 410 N, 370 N and 345 N.
Red total = 360 + 400 + 330 = 1090 N to the left. Blue total = 410 + 370 + 345 = 1125 N to the right.
Resultant = 1125 − 1090 = 35 N, in the direction of the larger force.

Answer: 35 N to the right (towards the blue team)

Balanced forces: zero resultant

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 person standing on a floor: weight down, normal contact force up, equal in size
  • a moving object keeps moving at the same speed in the same direction (constant velocity) – a car on a straight motorway whose driving force equals the air resistance.

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 75 000 N. Its weight is 58 000 N.
Resultant = 75 000 − 58 000 = 17 000 N upwards, so the rocket speeds up as it rises.

Answer: 17 000 N upwards

Free-body 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; the object can be drawn as a box or a dot. Forces that the object exerts on other things are not shown.

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

Vertical: upward forces = 6300 + 7700 = 14 000 N = weight, so the vertical resultant is zero (the car does not rise or sink).
Horizontal: resultant = 3100 − 2200 = 900 N forwards.

Answer: resultant force = 900 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. The diagram shows the horizontal forces acting on a box. Calculate the size of the resultant force on the box.

Answer: 50 N

Working: To the right: 65 + 25 = 90 N. To the left: 40 N. Resultant = 90 − 40 = 50 N to the right.

Question 2. An ice puck is sliding at 2 m/s across smooth ice. The resultant force on it is zero. What happens next? (Choose from: It keeps moving at 2 m/s in the same direction, It slows down and stops, It speeds up, It stops immediately.)

Answer: It keeps moving at 2 m/s in the same direction

Working: With zero resultant force the velocity does not change, so the puck keeps moving at 2 m/s in a straight line (Newton’s first law).

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

Answer: False

Working: False. It can be at rest or moving at a constant velocity.

Related lessons

Continue in the full course

This lesson is section P8.3 (AGCSC3703) of our free GCSE Combined Science 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 Combined Science course.

 

 

 

 

 

 

 

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