Addis Ababa University Addis Ababa Institute of Technology School Of Mechanical and Industrial Engineering Extension Division` Assignment 1

Transcription

1 Assignment 1 1. Vehicle B is stopped at a traffic light, as shown in the figure. At the instant that the light turns green, vehicle B starts to accelerate at m/s 2. At this time vehicle A is 91.44m behind vehicle B, travelling at a speed of 13.4m/s. A. At what distance past the light will vehicle A overtake B? B. At what distance past the light will vehicle B overtake vehicle A? C. For what range of values of constant acceleration of vehicle B could vehicle A not overtake this vehicle? 2. The graph of the bullet train is shown. If the train starts from rest, determine the elapsed time before it again comes to rest. What is the total distance traveled during this time interval? Construct the v t and s t graphs. 1

2 Assignment 2 1. Pin P at the end of the telescoping rod in the Figure slides along the fixed parabolic path y 2 = 40x, where x and y are measured in millimeters. The y coordinate of P varies with time t (measured in seconds) according to y = 4t 2 + 6t mm. when y = 30 mm, compute the velocity vector of P and the acceleration of vector P and direction. 2. A volleyball player serves the ball with an initial velocity v0 of magnitude m/s at an angle of 20 with the horizontal. Determine (a) if the ball will clear the top of the net, (b) how far from the net the ball will land. 2

3 Assignment 3 1. A highway engineer needs to find the least radius R of an exit circular ramp as shown schematically in the figure. His computations are to be based on a constant exit ramp speed of 75km/hr and that the passengers in the cars are subjected to accelerations not to exceed 1.1m/s 2. What should be the least value of the radius R? 2. A rocket travelling above the atmosphere at an altitude of 500km would have a free - fall acceleration g = 8.43m/s 2 in the absence of forces other than gravitational attraction. Because of thrust, however, the rocket has an additional acceleration component a 1 of 8.80 m/s 2 tangent to its trajectory, which makes an angle of 30 0 with the vertical at the instant considered. If the velocity v of the rocket is 30,000km/hr at this position, compute the radius of curvature ρ of the trajectory and the rate at which v is changing with time. 3

4 Assignment 4 1. At the instant ϴ = 30, the cam rotates with a clockwise angular velocity of 5 rad/s and angular acceleration of 6 rad/s 2. Determine the magnitudes of the velocity and acceleration of the follower rod AB at this instant. The surface of the cam has a shape of a limaçon defined by r = ( cos ϴ) mm. 2. Link AB rotates through a limited range of the angle β, and its end a causes the slotted link AC to rotate also. For the instant represented where β = 60 0 and β = 0.6 rad/s constant, determine the corresponding values of r,r, Θ and Θ. Make use of polar equations of velocity and acceleration. 4

5 Assignment 6 1. Car A travels at a constant speed of 70 ft/s while car B travels at a constant speed V B as shown in figure. Both cars pass point o at the same instant, and 5s latter, car B appears to an observer in car A to be moving at ft/s in a direction that makes an angle of with the negative x axis. Determine (a) the constant speed V B of car B and ϴ defining its path and (b) the position of car B, 5s after point o, as measured by the observer in car A. 2. Two airplanes A and B are flying with constant velocity at the same altitude. The position of the plane at time t = 0 are shown in figure. The xy reference frame is fixed in space. Determine (1) the velocity of plane A relative to B; (2) the position vector of A relative to B as a function of time; and (3) the minimum distance between the planes and the time when this occurs. 1mi = 1, meter, 1 mi/ h = m/s 3. Collar A and block B are connected by a cable passing over three pulleys C, D, and E as shown. Pulleys C and E are fixed, while D is attached to a collar which is pulled downward with a constant velocity of 3 in/s. At t = 0s, collar A starts moving downward from position K with a constant acceleration and no initial velocity. Knowing that the velocity of collar A is 12 in/s as it passes through point L, determine the change in elevation, the velocity, and the acceleration of block B when collar A passes through L. 5

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