A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Gravitational Force Between Point Masses — mark scheme explained
The short answer
Gravity is a fundamental force of nature that acts between all masses in the universe. It is an attractive force, meaning it always pulls objects together rather than pushing them apart. The strength of this gravitational force can be calculated using Newton's law of universal gravitation.
The question
Calculate the gravitational force between a planet with mass 6 × 10 24 kg and its moon with mass 7 × 10 22 kg, separated by 3.8 × 10 8 meters. [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: m 1 = 6 × 10 24 kg, m 2 = 7 × 10 22 kg, r = 3.8 × 10 8 m.
- S2
Use the gravitational force formula: F = G × (m 1 × m 2 ) / r 2 .
- S3
Substitute the values into the formula: F = 6.674 × 10 -11 × (6 × 10 24 × 7 × 10 22 ) / (3.8 × 10 8 ) 2 .
- S4
Calculate the numerator: 6 × 10 24 × 7 × 10 22 = 4.2 × 10 47 kg 2 .
- S5
Calculate the denominator: (3.8 × 10 8 ) 2 = 1.444 × 10 17 m 2 .
- S6
Divide the numerator by the denominator: 4.2 × 10 47 / 1.444 × 10 17 ≈ 2.91 × 10 30 .
- S7
Multiply by G: F = 6.674 × 10 -11 × 2.91 × 10 30 ≈ 1.94 × 10 20 N.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: m 1 = 6 × 10 24 kg, m 2 = 7 × 10 22 kg, r = 3.8 × 10 8 m.
- S2
Use the gravitational force formula: F = G × (m 1 × m 2 ) / r 2 .
- S3
Substitute the values into the formula: F = 6.674 × 10 -11 × (6 × 10 24 × 7 × 10 22 ) / (3.8 × 10 8 ) 2 .
- S4
Calculate the numerator: 6 × 10 24 × 7 × 10 22 = 4.2 × 10 47 kg 2 .
- S5
Calculate the denominator: (3.8 × 10 8 ) 2 = 1.444 × 10 17 m 2 .
- S6
Divide the numerator by the denominator: 4.2 × 10 47 / 1.444 × 10 17 ≈ 2.91 × 10 30 .
- S7
Multiply by G: F = 6.674 × 10 -11 × 2.91 × 10 30 ≈ 1.94 × 10 20 N.
Final answer: 1.94 × 10 20 N
Common mistakes
- Using the wrong value for G (gravitational constant). — Always use the standard value of G = 6.674 × 10 -11 N·m 2 /kg 2 .
- Forgetting to square the distance (r) in the denominator. — Ensure that you always square the distance (r 2 ) when using the gravitational force formula.
- Using the wrong units for mass or distance. — Always convert masses to kilograms and distances to meters before using the formula.
- Confusing gravitational force with other forces (e.g., electrostatic force). — Ensure you are using the correct formula for gravitational force: F = G × (m 1 × m 2 ) / r 2 .
- Not converting altitude to distance from the center of the Earth. — Always add the altitude to the radius of the Earth to get the correct distance (r) between the masses.
- Rounding too early in calculations. — Perform all calculations with full precision and only round the final answer to the required number of significant figures.
Where the marks go
- Full worked solution (all marking points)6 marks