Standard +0.3 This is a standard equilibrium problem with friction on an inclined plane. Students must resolve forces parallel to the plane, consider limiting friction in both directions (up and down the plane), and solve two inequalities to find the range of m. While it requires careful consideration of two cases and involves multiple force components, the techniques are routine for M1 and the problem structure is familiar from textbook exercises.
\includegraphics{figure_4}
Blocks \(P\) and \(Q\), of mass \(m\) kg and 5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a rough plane inclined at 35° to the horizontal. Block \(P\) is at rest on the plane and block \(Q\) hangs vertically below the pulley (see diagram). The coefficient of friction between block \(P\) and the plane is 0.2. Find the set of values of \(m\) for which the two blocks remain at rest. [6]
For resolving forces along the plane in either case
5g – mg sin 35 – 0.2 mg cos 35
Answer
Marks
Guidance
= 0
1
A1
5g – Mg sin 35 + 0.2 Mg cos 35
Answer
Marks
Guidance
= 0
1
A1
m = 6.78 or M = 12.2
1
M1
6.78 ⩽ mass ⩽ 12.2
1
A1
6
Marks
Question 4:
4 | F = 0.2 × mg cos 35 | 1 | B1 | Maximum value of F
1 | M1 | For resolving forces along the plane in either case
5g – mg sin 35 – 0.2 mg cos 35
= 0 | 1 | A1 | Equilibrium, on the point of moving up the plane
5g – Mg sin 35 + 0.2 Mg cos 35
= 0 | 1 | A1 | Equilibrium, on the point of moving down the plane
m = 6.78 or M = 12.2 | 1 | M1 | For solving either
6.78 ⩽ mass ⩽ 12.2 | 1 | A1
6
Marks
\includegraphics{figure_4}
Blocks $P$ and $Q$, of mass $m$ kg and 5 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small smooth pulley which is fixed at the top of a rough plane inclined at 35° to the horizontal. Block $P$ is at rest on the plane and block $Q$ hangs vertically below the pulley (see diagram). The coefficient of friction between block $P$ and the plane is 0.2. Find the set of values of $m$ for which the two blocks remain at rest. [6]
\hfill \mbox{\textit{CAIE M1 Q4 [6]}}