Evaluate — 2 marks
A student is investigating the relationship between the force applied to a spring and the extension it produces. She applies forces of 2 N, 4 N, 6 N and 8 N to an identical spring and measures the extensions as 4 cm, 8 cm, 12 cm and 16 cm respectively.
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(a) What is the ratio of force to extension for this spring? Express your answer in simplest form.
[1 mark]
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(b) Evaluate whether the spring obeys Hooke's Law based on the data provided. Explain your reasoning.
[1 mark]
Show mark scheme
- (a) Correct ratio of 1:2 or 0.5 N/cm (or equivalent such as 2:4, 50 N/m, showing the force is half the extension in cm)
- (b) Yes, the spring obeys Hooke's Law because the ratio of force to extension is constant across all measurements (or the extension is directly proportional to the force applied, or all data points show the same relationship)
Explain — 5 marks
A physics teacher is preparing two solutions for a class experiment. Solution A contains 3 grams of salt dissolved in 150 cm³ of water. Solution B contains 5 grams of salt dissolved in 250 cm³ of water. The teacher wants to understand which solution is more concentrated.
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(a) Calculate the ratio of salt to water in Solution A. Express your answer in the form 1:n.
[2 marks]
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(b) Calculate the ratio of salt to water in Solution B. Express your answer in the form 1:n.
[2 marks]
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(c) Explain which solution is more concentrated and how the ratios you calculated support your answer.
[1 mark]
Show mark scheme
- (a) Divides both sides by 3 to get 1:50 (1 mark for correct method/working)
- (a) States correct final ratio 1:50 (1 mark for correct answer)
- (b) Divides both sides by 5 to get 1:50 (1 mark for correct method/working)
- (b) States correct final ratio 1:50 (1 mark for correct answer)
- (c) Both solutions are equally concentrated because they have the same ratio of salt to water (1:50), meaning the same amount of salt is dissolved in the same amount of water in both cases (1 mark for explanation linking ratios to concentration)
Show — 4 marks
A physics teacher is preparing a practical experiment comparing the extension of two different springs. Spring A extends by 8 cm when a 2 N force is applied. Spring B extends by 12 cm when a 3 N force is applied.
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(a) Show that the ratio of extension to force for Spring A is 4:1.
[1 mark]
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(b) Calculate the ratio of extension to force for Spring B. Express your answer in the form n:1.
[2 marks]
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(c) Using your answers from parts (a) and (b), show which spring is stiffer by comparing the ratios.
[1 mark]
Show mark scheme
- (a) Divides 8 cm by 2 N to give 4 cm/N or equivalent ratio 4:1
- (b) Divides 12 cm by 3 N to give 4 cm/N (1 mark)
- (b) Expresses answer as 4:1 (1 mark)
- (c) States that both springs have the same stiffness (both have ratio 4:1) or equivalent conclusion that they are equally stiff
Describe — 4 marks
A student investigates the relationship between the extension of a spring and the force applied to it. She hangs different masses from a spring and measures the extension produced. Her results show that when a 100 g mass is added, the spring extends by 4 cm. When a 250 g mass is added, the spring extends by 10 cm.
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(a) Describe the relationship between the mass and the extension of the spring shown by these results.
[2 marks]
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(b) A 500 g mass is now added to the spring. Describe how you would use the ratio and proportion method to predict the extension produced.
[2 marks]
Show mark scheme
- (a) The extension is directly proportional to the mass (or force) applied
- (a) As mass increases, extension increases in the same ratio / when mass is multiplied by a factor, extension is multiplied by the same factor
- (b) Set up the ratio: 100 g : 4 cm (or equivalent simplified ratio of 25 g : 1 cm)
- (b) Use this ratio to calculate: 500 g would produce an extension of 20 cm (by multiplying both parts of the ratio by 5 or by scaling)
State — 4 marks
A recipe for granola uses oats, nuts, and dried fruit in the ratio 3 : 2 : 1 by weight. A café uses 450 grams of oats when making a large batch.
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(a) State the total weight of nuts and dried fruit used in this batch.
[2 marks]
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(b) The café wants to make a smaller batch using 300 grams of ingredients in total. State the weight of oats required.
[2 marks]
Show mark scheme
- (a) M1 for method: 450 ÷ 3 (= 150) or sight of 3 parts for nuts and fruit combined
- (a) A1 for 450 grams
- (b) M1 for method: 300 ÷ 6 × 3 or 300 × 3/6 or equivalent
- (b) A1 for 150 grams
GCSE Perfect