A spring is pulled by a force, and its extension depends on that force in a linear way.
Complete the idea: in a linear system, say what happens to the extension for each extra 1 N of force.
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Each extra 1 N makes the extension increase by the same amount, so the extension rises in equal steps.
How the marks are earned
- One mark: the extension (or length) of the spring goes up.
- One mark: it goes up in equal steps, or in proportion. Stating the same increase in extension for each newton earns both marks, and an increase of 1 unit, for example 1 cm, is accepted for this second mark. Saying the extension is squared earns nothing, and mentioning the spring constant is ignored.
Why it scores
The first mark is for saying the extension increases. The second is for the equal steps, which is what makes the relationship linear, a straight line on a force-extension graph. The extension must not be squared or changed in some other way.
Revise Forces & Their EffectsA spring has spring constant 15 N/m and extension 0.01 m. Find the energy stored, in standard form, in J.
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Choose the equation:. energy = ½ × spring constant × extension2
Substitute:. energy = ½ × 15 × 0.012. energy = ½ × 15 × 0.0001
Evaluate:. energy = 0.00075 J
Standard form has one digit before the point:. 0.00075 = 7.5 × 10-4 J
How the marks are earned
- One mark: choose the equation energy stored = ½ × spring constant × extension2. A correct substitution also earns this mark.
- One mark: substitute: ½ × 15 × 0.012.
- One mark: the value 0.00075 J.
- One mark: write that value in standard form, 7.5 × 10-4 J. Clear working that gives a wrong number, correctly written in standard form, earns this mark, for example 7.5 × 10-2 from forgetting to square.
- A correct answer in standard form with no working is worth at least three of the four marks, so show your working.
Why it scores
This earns the equation mark. The work is choosing it and noticing that the extension is squared.
Square the extension first: 0.01 × 0.01 = 0.0001. Leaving out the squaring is the common slip and gives an answer 100 times too big.
7.5 × 0.0001 = 0.00075, which earns the value mark.
Standard form has one non-zero digit before the decimal point, here 7.5, times a power of ten. The decimal point moves four places, so the power is −4.
Revise Forces & Their Effects