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P8.6 Resolution of Forces

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

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: (Higher tier) Splitting a force into two perpendicular components with a scale drawing, forces on slopes, and equilibrium. 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

  • (Higher tier) explain what is meant by resolving a force into two perpendicular components
  • (Higher tier) resolve a force using a scale drawing, including the weight of an object on a slope
  • (Higher tier) state the condition for an object to be in equilibrium
  • (Higher tier) use components or a closed vector diagram to decide whether an object is in equilibrium

Key words

  • Component: One of two perpendicular forces that together have the same effect as the original force.
  • Resolving a force: Replacing a force by two perpendicular components whose resultant is the original force.
  • Parallel component: The component of a force that acts along a slope.
  • Perpendicular component: The component of a force that acts at 90° to a slope.
  • Equilibrium: The state of an object when the resultant force on it is zero.
  • Vector diagram: A scale drawing in which force arrows are joined tip to tail; a closed shape means the resultant is zero.

Resolving a force into two components

Resolving is the opposite of finding a resultant. One force is replaced by two perpendicular components that together have exactly the same effect. Usually we choose horizontal and vertical directions, or directions along and at 90° to a slope.

1. Draw the force to scale as an arrow from a point O, at the correct angle.

2. Draw two lines from O in the two chosen perpendicular directions.

3. Draw a rectangle with these lines as two sides and the force arrow as its diagonal.

4. Measure the two sides of the rectangle and convert with the scale: these are the components.

Worked example: the trolley case handle

Draw the 60 N pull at 35° to the horizontal (e.g. 1 cm ≡ 6 N, so 10.0 cm long) and complete the rectangle.
Horizontal side ≈ 8.2 cm → 49 N, which pulls the case forwards.
Vertical side ≈ 5.7 cm → 34 N, which partly lifts the case and reduces its push on the ground.

Answer: components ≈ 49 N horizontally and 34 N vertically

Forces on a slope

It is harder to cycle uphill because part of your weight acts down the slope. Resolve the weight of an object on a slope into a component parallel to the slope and a component perpendicular to it.

  • The parallel component (≈ 27 N) tries to make the box slide down. If the box stays at rest, friction acts up the slope and is equal to it (27 N).
  • The perpendicular component (≈ 75 N) presses the box onto the slope. The slope pushes back with an equal normal contact force.
  • The steeper the slope, the bigger the parallel component and the smaller the perpendicular component.

Exam tip: In a scale drawing on a slope, the rectangle’s sides must be parallel and perpendicular to the slope, not horizontal and vertical.

Equilibrium

An object at rest, or moving at a constant velocity, is in equilibrium: the resultant force on it is zero. There are two ways to check this with a scale drawing:

  • Components: resolve every force into components along the same two perpendicular directions (e.g. horizontal and vertical). The components must balance in each direction.
  • Vector diagram: draw the force arrows to scale tip to tail. For an object in equilibrium they form a closed shape (a triangle for three forces), so there is no gap for a resultant.

Worked example: tension in the cables

Horizontal: the two tensions are equal, so their horizontal components cancel.
Vertical: a scale drawing of a force at 30° to the horizontal shows that its vertical component is half its size.
The vertical components must balance the weight: ½T + ½T = 90 N, so T = 90 N.

Answer: each cable has a tension of 90 N

Key fact: If the force arrows drawn tip to tail leave a gap, the arrow needed to close the gap (from the start of the first to the tip of the last) is the resultant, and the object is not in equilibrium.

Common mistakes

  • Drawing the components so that they do not make a rectangle with the force as the diagonal.
  • On a slope, resolving the weight horizontally and vertically instead of along and perpendicular to the slope.
  • Thinking friction on a resting object is always as big as possible. It only matches the parallel component needed to stop sliding.
  • Checking only one direction for equilibrium. The components must balance in both perpendicular directions.

Revision questions

Try these, then check your answers below each one.

Question 1. (Higher tier) What does resolving a force mean? (Choose from: Replacing it by two perpendicular components that together have the same effect, Adding two forces to find the resultant, Measuring the force with a newtonmeter, Finding the force that balances it.)

Answer: Replacing it by two perpendicular components that together have the same effect

Working: Resolving splits one force into two components at right angles whose combined effect equals the original force.

Question 2. (Higher tier) A box of weight 50 N rests on a slope at 30° to the horizontal. Use a scale drawing to find the component of its weight acting down the slope.

Answer: 25 N

Working: A scale drawing gives a component of 25 N along the slope (and about 43 N into the slope). For a 30° slope the component down the slope is half the weight.

Question 3. (Higher tier) True or false? A parachutist falling at a constant velocity is in equilibrium.

Answer: True

Working: True. Constant velocity means zero acceleration, so the resultant force is zero: air resistance balances weight.

Related lessons

Continue in the full course

This lesson is section P8.6 (AGCSC3706) 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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