A scientific sensor module AAA, of mass 1.5 kg, is positioned on a rough track inclined at an angle α \alpha\,α to the horizontal, where sinα=0.6\sin\alpha = 0.6sinα=0.6. A light, inextensible cable is fastened to A A\,A and runs parallel to the line of greatest slope until it passes over a smooth fixed pulley at the top of the track. The other end of the cable is connected to a weighted canister BBB, of mass 8.5 kg, which is suspended vertically so that the cable is taut.
The system is released from rest and B B\,B descends vertically with an acceleration of 0.7g ms-2. Show that the coefficient of friction, μ\muμ, between A A\,A and the track is 0.5.
In this part of the question use g=9.8 ms−2g = 9.8 \text{ ms}^{-2}g=9.8 ms−2. At the instant the speed of the sensor module A A\,A reaches 4.2 ms-1, the cable snaps. (i) Calculate the distance travelled by A A\,A from the moment the cable snaps until it first comes to instantaneous rest. (ii) Suggest one physical factor omitted from this model that could influence the calculated distance.
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.