In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2. A heavy limestone block of mass 40 kg40 \text{ kg}40 kg is being dragged up a rough incline during the construction of a monument. The incline is 25 metres25 \text{ metres}25 metres long and is angled at 25∘25^\circ25∘ above the horizontal. The base of the incline is designated as point OOO.
An industrial winch pulls the block from a starting position, point AAA, where it is initially at rest. The winch cable remains taut and parallel to the line of greatest slope throughout the motion.
The tension in the cable is maintained at 350 N350 \text{ N}350 N, causing the block to accelerate up the incline at 2.4 m s−22.4 \text{ m s}^{-2}2.4 m s−2. Calculate the coefficient of friction, μ\muμ, between the block and the incline.
The block takes exactly 3.2 seconds3.2 \text{ seconds}3.2 seconds to reach the top of the incline. Calculate the distance OAOAOA.
Other than air resistance, state one assumption you have made about the limestone block in your calculations for part (b)(i).
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.