Standard +0.3 This is a standard M1 friction problem requiring resolution of forces in two directions, application of F ≤ μR, and solving a linear equation. The angle is given in convenient form (sin α = 0.28), making calculations straightforward. It's slightly above average difficulty due to requiring careful setup of the limiting friction condition, but follows a well-practiced method with no conceptual surprises.
A crate of mass 300 kg is at rest on rough horizontal ground. The coefficient of friction between the crate and the ground is 0.5. A force of magnitude \(X\) N, acting at an angle \(\alpha\) above the horizontal, is applied to the crate, where \(\sin \alpha = 0.28\).
Find the greatest value of \(X\) for which the crate remains at rest. [5]
For attempt at resolving horizontally or vertically
M1
number of terms.
Answer
Marks
Guidance
R = 300g – 0.28X or R300gXsin16.3
A1
α = 16.26…
0.96X – F = 0 or 0.96X 0.5(300gXsin)0
Answer
Marks
Guidance
Or X cos 16.3 – F = 0 or X cos 16.30.5(300gXsin)0
A1
Or using their F
Use of F = 0.5R
M1
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
Answer
Marks
X = 1360 [1363.63…]
A1
5
Answer
Marks
Guidance
Question
Answer
Marks
Question 3:
3 | For attempt at resolving horizontally or vertically | M1 | Allow sin/cos mix. Allow sign error. Allow g missing. Correct
number of terms.
R = 300g – 0.28X or R300gXsin16.3 | A1 | α = 16.26…
0.96X – F = 0 or 0.96X 0.5(300gXsin)0
Or X cos 16.3 – F = 0 or X cos 16.30.5(300gXsin)0 | A1 | Or using their F
Use of F = 0.5R | M1 | 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
X = 1360 [1363.63…] | A1
5
Question | Answer | Marks | Guidance
A crate of mass 300 kg is at rest on rough horizontal ground. The coefficient of friction between the crate and the ground is 0.5. A force of magnitude $X$ N, acting at an angle $\alpha$ above the horizontal, is applied to the crate, where $\sin \alpha = 0.28$.
Find the greatest value of $X$ for which the crate remains at rest. [5]
\hfill \mbox{\textit{CAIE M1 2022 Q3 [5]}}