June 2024 Paper 1 Q3
3 A particle hangs at the end of a string. A horizontal force of magnitude \(F\) N acting on the particle holds it in equilibrium so that the string makes an angle of \(20^\circ\) with the vertical, as shown in the diagram. The tension in the string is 12 N.
(a) Find the value of \(F\). [2]
(b) Find the mass of the particle. [3]
| Scheme | Marks | AO |
|---|---|---|
| Resolve horizontally \(F = 12\sin 20\) | M1 | 1.1a |
| \(F = 4.10\) | A1 | 1.1 |
| [2] |
Notes
M1: Resolving horizontally – allow sin/cos interchange.
Allow if \(F = T\sin 20\) or similar seen
A1: www
| Scheme | Marks | AO |
|---|---|---|
| Resolve vertically \([mg =]\,12\cos 20\) | M1 | 3.1b |
| \(m = \dfrac{12\cos 20^\circ}{g} = 1.15\ \text{kg}\) | M1 A1 | 3.4 1.1 |
| [3] |
Notes
M1: Resolve to find vertical component of tension. Allow sin/cos interchange if consistent with (a)
If triangle of forces used, allow attempt to find by Pythagoras
M1: Equating weight to their component of tension and dividing their weight by \(g\) soi
A1: cao