A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Work, Power, and Efficiency in Mechanics — mark scheme explained
The short answer
In this section, we will explore the concepts of work, power, and efficiency, particularly focusing on how these principles apply to mechanical systems and electric motors. Understanding these concepts is crucial for solving problems related to energy transfer and the performance of machines.
The question
A force of 10 N is applied to move an object 5 m along a horizontal surface. The angle between the force and the direction of displacement is 30°. Calculate the work done. [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
Identify the given values: F = 10 N, s = 5 m, θ = 30°.
- S2
Use the formula for work done: W = F × s × cos(θ).
- S3
Calculate cos(30°) = √3/2 ≈ 0.866.
- S4
Substitute the values into the formula: W = 10 N × 5 m × 0.866.
- S5
W = 43.3 J.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: F = 10 N, s = 5 m, θ = 30°.
- S2
Use the formula for work done: W = F × s × cos(θ).
- S3
Calculate cos(30°) = √3/2 ≈ 0.866.
- S4
Substitute the values into the formula: W = 10 N × 5 m × 0.866.
- S5
W = 43.3 J.
Final answer: 43.3 J
Common mistakes
- Forgetting to include the cosine term in the work done formula when the force is not applied in the direction of displacement. — Always check if the force is applied at an angle and use the cosine term accordingly.
- Confusing work done with power in problems involving time. — Remember that work is energy transferred (W = F × s × cos(θ)), while power is the rate at which work is done (P = W / t or P = F × v).
- Using incorrect units for force, displacement, and time. — Always ensure that all values are in the correct SI units (N for force, m for displacement, s for time).
- Forgetting to convert efficiency into a percentage when required. — Always remember to express efficiency as a percentage by multiplying the result by 100%.
- Incorrectly identifying random and systematic errors in experiments. — Review the definitions of random and systematic errors and practice identifying them in different experimental scenarios.
- Failing to account for the area under a force-displacement graph when calculating work done by a variable force. — Always remember that the area under a force-displacement graph gives the work done. Practice integrating or using geometric methods to find this area.
Where the marks go
- Full worked solution (all marking points)4 marks