Standard +0.8 This is a challenging M1 mechanics problem requiring resolution of forces in two directions (parallel and perpendicular to the slope), calculation of the normal reaction including the component of the horizontal force, determination of friction force, and solving simultaneous equations. The horizontal force adds significant complexity compared to standard inclined plane problems, and the multi-step nature with 10 marks indicates above-average difficulty for M1, though still within the standard syllabus.
\includegraphics{figure_2}
A particle \(P\) of mass 2 kg is pushed up a line of greatest slope of a rough plane by a horizontal force of magnitude \(X\) newtons, as shown in Figure 2. The force acts in the vertical plane which contains \(P\) and a line of greatest slope of the plane. The plane is inclined to the horizontal at an angle \(\alpha\), where \(\tan\alpha = \frac{3}{4}\).
The coefficient of friction between \(P\) and the plane is 0.5
Given that the acceleration of \(P\) is 1.45 m s\(^{-2}\), find the value of \(X\). [10]
Second A2 for a correct equation; -1 each error. (Allow \(F\) at this stage)
B1 for \(F = 1/2 R\)
Third M1 dependent on previous two M's for eliminating \(R\).
Fourth M1 dependent on previous M for solving for \(X\)
Third A1 for \(X = 45\).
$R = X \sin \alpha + 2g \cos \alpha$ | M1 A2 |
$X \cos \alpha - F - 2g \sin \alpha = 2 \times 1.45$ | M1 A2 |
$F = 0.5R$ | B1 |
Eliminating $R$: solving for $X$ | DM1;DM1 |
$X = 45$ | A1 |
**Notes for Question 5:**
First M1 for resolving perp to the plane.
First A2 for a correct equation; -1 each error.
Second M1 for resolving parallel to the plane.
Second A2 for a correct equation; -1 each error. (Allow $F$ at this stage)
B1 for $F = 1/2 R$
Third M1 dependent on previous two M's for eliminating $R$.
Fourth M1 dependent on previous M for solving for $X$
Third A1 for $X = 45$.
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\includegraphics{figure_2}
A particle $P$ of mass 2 kg is pushed up a line of greatest slope of a rough plane by a horizontal force of magnitude $X$ newtons, as shown in Figure 2. The force acts in the vertical plane which contains $P$ and a line of greatest slope of the plane. The plane is inclined to the horizontal at an angle $\alpha$, where $\tan\alpha = \frac{3}{4}$.
The coefficient of friction between $P$ and the plane is 0.5
Given that the acceleration of $P$ is 1.45 m s$^{-2}$, find the value of $X$. [10]
\hfill \mbox{\textit{Edexcel M1 2015 Q5 [10]}}