A crate of mass 300kg is at rest on rough horizontal ground. The coefficient of friction between the crate and the ground is 0.5. A force of magnitude XN, acting at an angle α above the horizontal, is applied to the crate, where sin α = 0.28. Find the greatest value of X for which the crate remains at rest.

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

1. [M1] For attempt at resolving horizontally or vertically (Allow sin/cos mix. Allow sign error. Allow g missing. Correct number of terms.)
2. [A1] R = 300g - 0.28X or R = 300g – X sin16.3 (α = 16.26...)
3. [A1] 0.96X - F = 0 or 0.96X - 0.5(300g – X sinα) = 0 (Or X cos 16.3 – F = 0 or X cos 16.3-0.5(300g – X sin α) = 0) (Or using their F)
4. [M1] Use of F = 0.5R (Use to get an equation in X only. Allow sin/cos mix. Allow sign error. Allow g missing. Must be from 2 term R, which is a linear combination of 300(g) and a component of X)
5. [A1] X = 1360 [1363.63...]