Question 13
In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
Two blocks AAA, of mass 2 kg, and BBB, of mass 3 kg, are connected by a light inextensible string.
Initially A A\,A is held at rest on a smooth plane inclined at an angle θ \theta\,θ to the horizontal, where tanθ=34\displaystyle \tan\theta = \frac{3}{4}tanθ=43. The string passes over a smooth fixed pulley at the top of the plane, parallel to a line of greatest slope, and B B\,B hangs freely 1.5 m above the ground.
The blocks are released and A A\,A moves up the plane. The blocks are modelled as particles.
a.[5]
Find the acceleration of the blocks and the tension in the string.
b.[2]
Find the speed of the blocks immediately before B B\,B reaches the ground.
c.[2]
After B B\,B reaches the ground, the string becomes slack. Find the additional distance travelled by A A\,A before it comes instantaneously to rest.
3.3 Forces and Newton's Laws Questions
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.