Standard +0.3 This is a standard friction equilibrium problem requiring resolution of forces parallel and perpendicular to the plane, consideration of limiting friction in two directions, and straightforward algebraic manipulation. While it involves multiple steps and understanding that friction can act either up or down the slope, it follows a well-practiced method with no novel insight required, making it slightly easier than average.
A particle of mass \(3\text{ kg}\) is on a rough plane inclined at an angle of \(20°\) to the horizontal. A force of magnitude \(P\text{ N}\) acting parallel to a line of greatest slope of the plane is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is \(0.35\). Show that the least possible value of \(P\) is \(0.394\), correct to 3 significant figures, and find the greatest possible value of \(P\). [6]
Question 5:
5 | R=3gcos20° | B1 | Correct normal reaction stated or used
[F =0.35×3gcos20°] | M1 | For use of F =µR
[P +F =3gsin20°]
1 | M1 | Attempted resolving equation for minimum case
P =0.394 (AG)
1 | A1 | Correct given answer from correct work
[P =F+3gsin20°]
2 | M1 | Attempted resolving equation for maximum case
P =20.1(N)
2 | A1
Total: | 6
Question | Answer | Marks | Guidance
A particle of mass $3\text{ kg}$ is on a rough plane inclined at an angle of $20°$ to the horizontal. A force of magnitude $P\text{ N}$ acting parallel to a line of greatest slope of the plane is used to keep the particle in equilibrium. The coefficient of friction between the particle and the plane is $0.35$. Show that the least possible value of $P$ is $0.394$, correct to 3 significant figures, and find the greatest possible value of $P$. [6]
\hfill \mbox{\textit{CAIE M1 2018 Q5 [6]}}