A-Level · Mathematics · AQA · Mark scheme decoded
AQA A-Level Mathematics: Newton’s Third Law and Equilibrium of Forces — mark scheme explained
The short answer
In this section, we will explore Newton's third law, the equilibrium of forces on a particle, motion in a straight line under specific conditions, problems involving smooth pulleys and connected particles, resolving forces in two dimensions, and the equilibrium of a particle under coplanar forces.
The question
A particle of mass 2 kg is acted upon by two forces: F 1 = 5 N at 30° to the horizontal and F 2 = 8 N horizontally. Determine if the particle is in equilibrium. [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Resolve F 1 into its horizontal and vertical components: F 1x = 5 cos 30° = 4.33 N, F 1y = 5 sin 30° = 2.5 N.
- S2
The horizontal component of the total force is ΣF x = F 1x + F 2 = 4.33 + 8 = 12.33 N.
- S3
The vertical component of the total force is ΣF y = F 1y = 2.5 N.
- S4
Since ΣF x ≠ 0 and ΣF y ≠ 0, the particle is not in equilibrium.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Resolve F 1 into its horizontal and vertical components: F 1x = 5 cos 30° = 4.33 N, F 1y = 5 sin 30° = 2.5 N.
- S2
The horizontal component of the total force is ΣF x = F 1x + F 2 = 4.33 + 8 = 12.33 N.
- S3
The vertical component of the total force is ΣF y = F 1y = 2.5 N.
- S4
Since ΣF x ≠ 0 and ΣF y ≠ 0, the particle is not in equilibrium.
Final answer: The particle is not in equilibrium.
Common mistakes
- Forgetting to resolve forces into components — Always check if the problem involves forces at angles. If so, resolve each force into its x and y components before applying equilibrium conditions or Newton's laws.
- Incorrectly applying Newton's third law — Remember that for every action, there is an equal and opposite reaction. Ensure that the forces are drawn in the correct directions on your diagram.
- Forgetting to consider all forces acting on a particle — Always list all the forces acting on the particle and ensure they are included in your calculations. Double-check your force diagram.
- Incorrectly calculating the resultant force — Use vector addition to find the resultant force. Ensure you are adding and subtracting components correctly.
- Confusing equilibrium conditions — Remember that a particle is in equilibrium if ΣF x = 0 and ΣF y = 0. Ensure you are applying these conditions correctly.
- Incorrectly solving simultaneous equations — Double-check your algebra and ensure you are solving the equations correctly. It can be helpful to substitute values back into the original equations to verify your solution.
- Forgetting to check units — Always check that all forces are in the same unit (e.g., Newtons) and that masses are in kilograms. Ensure your final answer has the correct units.
- Incorrectly interpreting force diagrams — Take your time to draw and label the force diagram accurately. Ensure you understand the direction and magnitude of each force before setting up your equations.
Where the marks go
- Full worked solution (all marking points)4 marks