Turn over 7  Question 2 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 2 is 12 marks) 8   3. B θ A 2a Figure 2 A beam AB has mass m and length 2a. The beam rests in equilibrium with A on rough horizontal ground and with B against a smooth vertical wall. The beam is inclined to the horizontal at an angle θ, as shown in Figure 2. The coefficient of friction between the beam and the ground is μ The beam is modelled as a uniform rod resting in a vertical plane that is perpendicular to the wall. Using the model, (a) show that μ  1 2 cot θ (5) A horizontal force of magnitude kmg, where k is a constant, is now applied to the beam at A. This force acts in a direction that is perpendicular to the wall and towards the wall. Given that tan θ = 5 4 , μ = 1 2 and the beam is now in limiting equilibrium, (b) use the model to find the value of k. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________