Answer Happy

Q2. [25 marks] a) A motorized capstan is used to haul a rope, in order to secure a ship in its mooring berth. The rope is wrapped three times around the capstan and the rope's velocity is 15 m/min. The operator exerts a constant pull of 70 N on the free end. The coefficient of friction between the rope and capstan is 0.3. You may neglect centrifugal effects. i. Calculate the magnitude of the tension in the rope between the ship and the capstan. Calculate the power supplied by the capstan. ii. b) A company that manufactures flat belt drives is undertaking a review of the material it uses for its belts. It has identified the following two possibilities: Material Polypropylene Hard rubber Density kg/m³ 975 1,250 Material - on - Material Polypropylene on steel Hard rubber on steel [4] The coefficients of friction between these two possible belt materials and a steel pulley wheel are: ii. [4] Coefficient of friction 0.22 0.75 A prospective customer wants to use a flat belt on steel pulleys. The belts will be 25 mm wide and 6 mm thick. The maximum stress in the belt is not to exceed 4.5x105 N/m² and the angle of lap is 180º. The centrifugal effect must be considered in the following design calculations. i. For each of the two possible belt materials, calculate the speed of the belt when it is transmitting maximum power and operating at the maximum allowed stress. [7] For each of the two possible belt materials, calculate the maximum power that can be transmitted for that maximum speed. [10]