In this question use g=9.8 m s−2g = 9.8 \text{ m s}^{-2}g=9.8 m s−2. A scientific payload of mass 40 kg40 \text{ kg}40 kg is being tested on a rough inclined trackway that is 20 m20 \text{ m}20 m long and makes an angle of 25∘25^\circ25∘ with the horizontal. The origin, point OOO, is located at the foot of the trackway.
A payload is initially at rest at point AAA on the trackway. A winch line, kept parallel to the trackway, pulls the payload directly up the slope.
When the tension in the winch line is 320 N320 \text{ N}320 N, the payload is observed to accelerate up the slope at 1.2 m s−21.2 \text{ m s}^{-2}1.2 m s−2. Calculate the coefficient of friction, μ\muμ, between the payload and the trackway surface.
The payload takes 3.5 seconds3.5 \text{ seconds}3.5 seconds to reach the top of the trackway. Determine the distance OAOAOA.
Other than air resistance, state one assumption you have made about the payload in answering 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.