Standard +0.8 This is a challenging equilibrium problem requiring resolution of forces in two directions on an inclined plane, consideration of limiting friction in two opposite directions (up and down the slope), and solving simultaneous equations twice. It goes beyond standard single-direction friction problems and requires careful geometric reasoning about the force components and friction direction, making it moderately harder than average A-level mechanics questions.
\includegraphics{figure_3}
A particle of mass 2.5 kg is held in equilibrium on a rough plane inclined at 20° to the horizontal by a force of magnitude \(T\) N making an angle of 60° with a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.3.
Find the greatest and least possible values of \(T\). [8]
Question 3:
3 | Tsin60+R=25cos20 | B1
Attempt at resolving in any direction | M1
T cos 60 = F + 25 sin 20 | A1
T cos 60 + F = 25 sin 20 | A1
Use of F =μR | M1
Tcos60=25sin20±0.3(25cos20−Tsin60)
25sin20±0.3×25cos20
T =
cos60±0.3sin60 | M1
T =6.26 | A1
T =20.5 | A1
8
Question | Answer | Marks
\includegraphics{figure_3}
A particle of mass 2.5 kg is held in equilibrium on a rough plane inclined at 20° to the horizontal by a force of magnitude $T$ N making an angle of 60° with a line of greatest slope of the plane (see diagram). The coefficient of friction between the particle and the plane is 0.3.
Find the greatest and least possible values of $T$. [8]
\hfill \mbox{\textit{CAIE M1 2020 Q3 [8]}}