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MAE-2102 Practice Exam #1 Kinematics & Kinetics of Particles Show all work for partial credit Projectiles 1. A boy at A throws a ball 45o from the horizontal such that it strikes the slope at B. Determine the speed at which the ball is thrown and the time of flight. Friction, linear, constant acceleration 2. The double inclined plane supports two blocks A and B, each having a weight of 10 lb. If the coefficient of kinetic friction between the blocks and the plane is μk = 0.1, determine the acceleration along the plane for each block. Assume the blocks start at rest. Cylindrical Coordinates 3. Using a forked rod, a smooth cylinder P, having a mass of 0.4 kg, is forced to move along the vertical slotted path r = (0.6 θ) m, where θ is in radians. If the forked rod has a constant angular speed of θ& =0.2 rad/s, determine the force of the rod and the normal force of the slot on the cylinder at the instant θ = π rad. Assume the cylinder is in contact with only one edge of the rod and slot at any instant. 1 MAE-2102 Practice Exam #1 Kinematics & Kinetics of Particles Power & Efficiency 4. The 50-lb load is hoisted by the pulley system and motor M. If the crate starts from rest and by constant acceleration attains a speed of 15 ft/s after rising 6 ft, determine the power that must be applied to the motor at this instant. The motor has an efficiency ε = 0.76. Neglect the mass of the pulleys and cable. Principal of Work and Energy 5. Roller coasters are designed so that riders will not experience more than 3.5 times their weight (i.e. normal force + weight = 3.5*weight) as a normal force against the seat of the car. Determine the smallest radius of curvature ρ of the track at its lowest point if the car has a speed of 5 ft/s at the crest of the drop. Neglect friction. Conservation of Linear Momentum 6. The 20-lb cart B is supported on rollers of negligible size. If a 10-lb suitcase A is thrown horizontally on it at 10 ft/s, determine the time t and the distance B moves before A stops relative to B. The coefficient of kinetic friction between A and B is μk =0.4. 2 MAE-2102 Practice Exam #1 Kinematics & Kinetics of Particles Conservation of Angular Momentum 7. Determine the total angular momentum HO (along the z-axis) for the system of three particles about point O. All the particles are moving in the x-y plane. Extra Credit Dependant Motion Impact 3