Question 39
In this question use g=9.8g = 9.8g=9.8 m s−2^{-2}−2.
Two heavy boxes, M M\,M and NNN, are connected securely by a length of rope.
The mass of M M\,M is 40 kilograms and the mass of N N\,N is 60 kilograms.
M M\,M is placed near the bottom of a rough slope inclined at 30° 30°\,30° above the horizontal. The rope passes over a smooth pulley at the top of the slope so that N N\,N hangs with the rope vertical. The boxes are held with the rope taut and running parallel to a line of greatest slope.
When the boxes are released, M M\,M moves up the slope as N N\,N descends, with acceleration a a\,a m s−2^{-2}−2. The tension in the rope is T T\,T newtons.
a.[1]
Explain why the equation of motion for N N\,N is 60g−T=60a60g - T = 60a60g−T=60a.
b.[2]
Show that the normal reaction force between M M\,M and the slope is 203g 20\sqrt{3}g\,203g newtons.
c.[5]
The coefficient of friction, μ\muμ, between the slope and M M\,M is such that 0≤μ≤10 \le \mu \le 10≤μ≤1. Show that a≥(2−3)g5\displaystyle a \ge \frac{(2 - \sqrt{3})g}{5}a≥5(2−3)g.
d.[1]
State one modelling assumption you have made throughout this question.
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.