In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2.
A warehouse technician attempts to reposition a heavy industrial crate of mass 40 kg on a rough horizontal concrete floor. The coefficient of friction between the crate and the floor is 0.6.
The technician pushes the crate with a strictly horizontal force of 230 N. Prove that the crate remains in equilibrium.
The technician subsequently attaches a strap and pulls the crate. The strap is inclined at an angle of 30∘ 30^\circ\,30∘ above the horizontal. The technician exerts a tension of 230 N in the strap.
Determine whether the crate remains stationary under these conditions. Justify your answer with calculations.
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.