Higher November 2018 Unit 1 Q12
12. Catrin is measuring the force between a pair of magnets in a physics laboratory. It is known that the force, \(F\), between the magnets is inversely proportional to the square of the distance, \(d\), between them.
Catrin measures the force to be 4 newtons when the distance between the magnets is 10 m.
What is the distance between the magnets when the force is 100 newtons? [5]
| Scheme | Marks | Comments |
|---|---|---|
| \(F \;\alpha\; 1/d^{\,2}\) OR \(F = k/d^{\,2}\) | B1 | Allow \(F \;\alpha\; k/d^{\,2}\) |
| \(4 = k/10^2\) OR \(k = 400\) | M1 | M1 implies B1. F.T. for use of \(F \;\alpha\; d^{\,2}\) or \(F \;\alpha\; 1/d^{\,n}\) with \(n \gt 0\) and \(n \neq 2\). |
| \(F = 400/d^{\,2}\) | A1 | May be implied by further work. |
| \(100 = 400/d^{\,2}\) or equivalent | M1 | F.T. (for M1 only) from consistent \(F \;\alpha\; d^{\,2}\) or \(F \;\alpha\; 1/d^{\,n}\) with \(n \gt 0\) and \(n \neq 2\). |
| \(d = 2\) (m) | A1 | CAO. Ignore presence of '±' for the value of \(d\). Use of \(F \;\alpha\; 1/d\), leading to \(F = 40/d\) (and an answer of \(d = 0{\cdot}4\) (m)), is awarded B0 FT M1 A1 M1 A0. Use of \(F \;\alpha\; d^2\), leading to \(F = 0.04d^2\) (and an answer of \(d = 50\) (m)), is awarded B0 FT M1 A1 M1 A0. Use of \(F \;\alpha\; 1/\sqrt{d}\), leading to \(F = 4\sqrt{10}/\sqrt{d}\) (and an answer of \(d = 0{\cdot}016\) (m)), is awarded B0 FT M1 A1 M1 A0. |