Higher June 2018 Paper 1 Q17
17.
(a) The pressure, P, in newtons per square metre, made by an object resting on a table-top is inversely proportional to the area, A m2, of the object in contact with the table.
A book is placed on the table.
The area, A, of the book in contact with the table is 0·08 m2.
The pressure, P, made by the book on the table is 30 N/m2.
Find the relationship between pressure and area for any object of this weight. [3]
(b) A different book of the same weight is placed on the table.
The pressure exerted on the table by the book is 80 N/m2.
The pressure exerted on the table by the book is 80 N/m2.
Find the area of this book that is in contact with the table. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(P \propto \dfrac{1}{A}\) or \(P = \dfrac{k}{A}\) or equivalent | B1 | seen or implied; if variables seen, must be P and A but allow any other letter for \(k\); may be implied by e.g. \(x \div 0.08 = 30\) |
| \((k =)\ 0.08 \times 30\) | M1 | |
| \(P = \dfrac{2.4}{A}\) or \(P = \dfrac{12}{5A}\) or equivalent | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| \((A =)\ \dfrac{2.4}{80}\) or equivalent | M1 | FT ‘their 2.4’, provided \(k\) is not an integer. |
| \((A =)\ 0.03\) (m2) or equivalent ISW | A1 | FT |
| (5) |