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Q. 3 (2 marks) Before hitting the apple, the 0.2 kg arrow has a velocity of 12 m/s. It becomes embedded in the 0.1 kg apple which leaves the top of the post together with the arrow. If the post is 1.712m high, determine the speed of the apple with the arrow in it just before it hits the ground. 1 Q. 4 (2 marks) The cylinder has a diameter 0.15 m and mass 4.0 kg. Calculate the distance x that the cylinder rolls down the ramp (starting from rest) during the time t = 2.424 s. Assume the cylinder rolls without slipping. D х O=159
Q. 5 (3 marks) The 10 kg steel bar has a length L = 16.12 m is pinned at one end. At its initial position, the angle between the rod and the vertical is 0 = 20° and its angular velocity is zero. Determine: i) the angular velocity of the bar when it reaches the vertical position. ii) the reaction forces on the pin when the bar reaches the vertical position. e L Q. 6 (4 marks) In the planetary gearbox shown, the ring gear B has a radius rb of 40 mm and is fixed so that it does not rotate. The planet gears, P each have a radius of 15 mm and mass 0.100 kg, while the sun has a radius of 10 mm and mass of 0.050 kg. The carrier C supports the bearings for the planet gears and rotates with the bearings at their centers. If a constant torque of 0.25 N.m is applied to the sun gear S, and the load on the carrier has a radius of gyration of 55 mm and a mass of 2.000 kg (including the mass of the carrier), determine the number of revolutions of the sun gear required for the carrier to reach 1512 rpm, starting from rest. In relation to calculating rotational mass moments of inertia, you may treat the gears as cylinders. You may neglect the size of the bearings and neglect losses due to friction. Hint: Consider using the work-energy approach. B B