Standard +0.3 This is a standard mechanics equilibrium problem requiring moment balance about one point and force balance. The setup is straightforward with clearly defined geometry, and the algebraic manipulation to reach the required form is routine. Slightly easier than average due to being a 'show that' question with a clear target and standard technique.
A uniform rod is resting on two fixed supports at points \(A\) and \(B\).
\(A\) lies at a distance \(x\) metres from one end of the rod.
\(B\) lies at a distance \((x + 0.1)\) metres from the other end of the rod.
The rod has length \(2L\) metres and mass \(m\) kilograms.
The rod lies horizontally in equilibrium as shown in the diagram below.
\includegraphics{figure_17}
The reaction force of the support on the rod at \(B\) is twice the reaction force of the support on the rod at \(A\).
Show that
$$L - x = k$$
where \(k\) is a constant to be found.
[4 marks]
Question 17:
17 | Forms a dimensionally correct
moment in L and x
May see :
(L−x)R
(L−(x+0.1))2R
(L−x)mg
(2L−(2x+0.1))2R
OE | 3.3 | B1 | The reaction at A is R
(L−x)R= (L−(x+0.1))2R
L−x=2(L−(x+0.1))
L−x=2L−2x−0.2
L−x=0.2
Forms dimensionally correct
moments equation with at least
one term correct
May also see:
(L−x)mg =(2L−(2x+0.1))2R
Or
(L−(x+0.1))mg =(2L−(2x+0.1))R
Condone missing brackets | 1.1a | M1
Obtains a fully correct equation in
L and x only | 1.1b | A1
Completes reasoned argument to
obtain L – x = 0.2
Must show expansion of all
brackets before the final answer | 2.1 | R1
Question 17 Total | 4
Q | Marking instructions | AO | Marks | Typical solution
A uniform rod is resting on two fixed supports at points $A$ and $B$.
$A$ lies at a distance $x$ metres from one end of the rod.
$B$ lies at a distance $(x + 0.1)$ metres from the other end of the rod.
The rod has length $2L$ metres and mass $m$ kilograms.
The rod lies horizontally in equilibrium as shown in the diagram below.
\includegraphics{figure_17}
The reaction force of the support on the rod at $B$ is twice the reaction force of the support on the rod at $A$.
Show that
$$L - x = k$$
where $k$ is a constant to be found.
[4 marks]
\hfill \mbox{\textit{AQA Paper 2 2024 Q17 [4]}}