In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
A block of mass 4 kg rests on a rough horizontal plane. The coefficient of friction between the block and the plane is 0.5.
A force of magnitude P P\,P newtons is applied to the block at an angle θ \theta\,θ above the horizontal, and the block is on the point of moving.
Show that P=2gcosθ+0.5sinθ\displaystyle P = \frac{2g}{\cos\theta + 0.5\sin\theta}P=cosθ+0.5sinθ2g.
Find the value of θ \theta\,θ for which P P\,P takes its least value, and find that least value of PPP.
87 exam-style questions on OCR (MEI) A Level Maths 3.4 Forces, covering 3.4.1 Language relating to forces, 3.4.2 Acceleration due to gravity, 3.4.3 Identify forces and draw force diagrams, 3.4.4 Resultant of concurrent forces, 3.4.5 Equilibrium of a particle, 3.4.6 Resolve a force into components (A-level only), 3.4.7 Equilibrium condition for resultant zero (A-level only), 3.4.8 Forces in equilibrium sum to zero (A-level only), 3.4.9 Equations for a particle in equilibrium (A-level only), 3.4.10 Frictional force and normal contact force (A-level only), 3.4.11 Model friction with F ≤ μR (A-level only), and 3.4.12 Apply Newton's Laws to friction problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.