Moderate -0.5 This is a straightforward equilibrium problem on an inclined plane requiring resolution of forces in two directions and basic trigonometry. While it involves two separate scenarios and careful angle work, the method is standard M1 fare with no conceptual surprises—slightly easier than average due to the direct application of equilibrium conditions.
2
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Small blocks \(A\) and \(B\) are held at rest on a smooth plane inclined at \(30 ^ { \circ }\) to the horizontal. Each is held in equilibrium by a force of magnitude 18 N . The force on \(A\) acts upwards parallel to a line of greatest slope of the plane, and the force on \(B\) acts horizontally in the vertical plane containing a line of greatest slope (see diagram). Find the weight of \(A\) and the weight of \(B\).
(Triangle of forces / resolving parallel to slope)
M1
For a triangle of forces with sides 18, \(R\) and \(W\) for \(A\) or \(B\); or for resolving forces acting on \(A\) or \(B\) parallel to line of greatest slope
For \(A\): right angle between 18 and \(R\), \(30°\) opposite 18, or \(W_A \sin 30° = 18\); or For \(B\): \(W_B \sin 30° = 18\cos 30°\)
A1
For \(B\): \(W_B \sin 30° = 18\cos 30°\); or For \(A\): \(W_A \sin 30° = 18\)
B1
Weight of \(A\) is \(36\) N and weight of \(B\) is \(31.2\) N
A1
[Total: 4]
## Question 2:
| Answer/Working | Mark | Guidance |
|---|---|---|
| (Triangle of forces / resolving parallel to slope) | M1 | For a triangle of forces with sides 18, $R$ and $W$ for $A$ or $B$; or for resolving forces acting on $A$ or $B$ parallel to line of greatest slope |
| For $A$: right angle between 18 and $R$, $30°$ opposite 18, **or** $W_A \sin 30° = 18$; **or** For $B$: $W_B \sin 30° = 18\cos 30°$ | A1 | |
| For $B$: $W_B \sin 30° = 18\cos 30°$; **or** For $A$: $W_A \sin 30° = 18$ | B1 | |
| Weight of $A$ is $36$ N and weight of $B$ is $31.2$ N | A1 | **[Total: 4]** |
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\includegraphics[max width=\textwidth, alt={}, center]{ffefbc81-402f-4048-8741-23c8bae30d5a-2_385_621_488_762}
Small blocks $A$ and $B$ are held at rest on a smooth plane inclined at $30 ^ { \circ }$ to the horizontal. Each is held in equilibrium by a force of magnitude 18 N . The force on $A$ acts upwards parallel to a line of greatest slope of the plane, and the force on $B$ acts horizontally in the vertical plane containing a line of greatest slope (see diagram). Find the weight of $A$ and the weight of $B$.
\hfill \mbox{\textit{CAIE M1 2014 Q2 [4]}}