In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2.
A museum curator attempts to reposition a bronze sculpture of mass 40 kg40 \text{ kg}40 kg across a rough horizontal gallery floor. The coefficient of friction between the sculpture and the floor is 0.550.550.55.
The curator first tries to push the sculpture with a horizontal force of 210 N210 \text{ N}210 N. Show that the sculpture does not move.
The curator then attaches a harness and pulls the sculpture. The harness acts at an angle of 25∘25^\circ25∘ above the horizontal. The curator exerts a tension of 210 N210 \text{ N}210 N in the harness. Determine whether the sculpture 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.