Standard +0.3 This is a standard mechanics equilibrium problem requiring resolution of forces parallel and perpendicular to an inclined plane, with consideration of friction acting in two opposite directions for minimum and maximum P. It involves routine application of F=μR and Newton's laws with straightforward trigonometry, making it slightly easier than average but still requiring careful setup of two cases.
\includegraphics{figure_3}
A particle of mass \(0.6\) kg is placed on a rough plane which is inclined at an angle of \(21°\) to the horizontal. The particle is kept in equilibrium by a force of magnitude \(P\) N acting parallel to a line of greatest slope of the plane, as shown in the diagram. The coefficient of friction between the particle and the plane is \(0.3\). Show that the least possible value of \(P\) is \(0.470\), correct to \(3\) significant figures, and find the greatest possible value of \(P\). [6]
Question 3:
3 | R = 0.6g cos 21 [= 5.60] | B1
F = 0.3R = 1.8 cos 21 [= 1.68] | M1 | Using F = µR
P + F = 6 sin 21[ = 2.15] | M1 | Slipping down
P = 2.15 – 1.68 = 0.470 AG | A1 | Least possible value
P – F = 6 sin 21 | M1 | Slipping up
P = 2.15 + 1.68 = 3.83 | A1 | Greatest possible value
Total: | 6
Question | Answer | Marks | Guidance
\includegraphics{figure_3}
A particle of mass $0.6$ kg is placed on a rough plane which is inclined at an angle of $21°$ to the horizontal. The particle is kept in equilibrium by a force of magnitude $P$ N acting parallel to a line of greatest slope of the plane, as shown in the diagram. The coefficient of friction between the particle and the plane is $0.3$. Show that the least possible value of $P$ is $0.470$, correct to $3$ significant figures, and find the greatest possible value of $P$. [6]
\hfill \mbox{\textit{CAIE M1 2017 Q3 [6]}}