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.
139 exam-style questions on OCR A Level Maths 3.3 Forces and Newton's Laws, covering 3.3.1 Concept and vector nature of a force, 3.3.2 Newton's first law, 3.3.3 Newton's second law in a straight line, 3.3.4 Newton's second law with vectors (A-level only), 3.3.5 Newton's second law with resolved forces (A-level only), 3.3.6 Weight, 3.3.7 Gravitational acceleration, 3.3.8 Newton's third law, 3.3.9 Normal reaction force, 3.3.10 Smooth contact model, 3.3.11 Equilibrium with connected particles and pulleys, 3.3.12 Newton's third law with resolved forces (A-level only), 3.3.13 Equilibrium by resolving (A-level only), 3.3.14 Equilibrium of forces in two dimensions using vectors (A-level only), 3.3.15 Resolving forces for advanced problems (A-level only), 3.3.16 Resultant forces and components (A-level only), 3.3.17 Dynamics of a particle in a plane (A-level only), 3.3.18 Concept of a frictional force (A-level only), 3.3.19 Contact force components (A-level only), 3.3.20 Coefficient of friction (A-level only), 3.3.21 Static and limiting equilibrium on a rough surface (A-level only), 3.3.22 Motion of a body on a rough surface (A-level only), and 3.3 Forces and Newton's Laws. Each one has a worked solution and a mark scheme showing where the marks go.