Exercises for Chapter 1 Kinematics
1. An impulsive retarding force of 3 seconds duration acts on a particle which is moving with a forward velocity of 60 m/s. The oscilloscope record of the deceleration is shown. Determine the approximate velocity of the particle at t = 9 s. [answer: -58 m/s] 2. A car can decelerate at 0.8 ‘g’ on a certain road. Find the total emergency stopping distance measured from the point where the driver first sights the danger for a speed of 100 km/hr. The time taken for the driver to identify the hazard, decide on a course of action, and apply the brakes is 0.75 s. [Answer: 70 m] 3. An underground train on the Mass Transit Railway moves away from a station with an initial acceleration of 0.9 m/s2. The acceleration decreases uniformly with time until after half a minute it is 0.3 m/s2. Calculate the speed reached and the distance travelled during this time. [Answer: 18 m/s, 315 m] 4. The magnitude of the acceleration and deceleration of an express lift is limited to 0.4 ‘g’, and the maximum vertical speed is 400 m/min. Calculate the minimum time required for the lift to go from rest at the 10th floor to a stop at the 30th floor, a distance of 100 m. [Answer: 16.7 s] 5. A cam rotates at 500 rev/min and imparts ‘parabolic’ motion (i.e. Constant acceleration and deceleration) to a reciprocating follower. The total lift of the follower is 20 mm and this takes place during 90 degrees of cam rotation.
If the acceleration and deceleration are a1 and a2 respectively, determine vmax, a1 and a2 for the following conditions: (1) a1 = 1.5 a2 and (2) a1 = a2. [answer: 111.1 m/s2, 74.1 m/s2, 1.33 m/s 88.9 m/s2, 88.9 m/s2, 1.33 m/s] 6. A circular cam of radius R rotates at rad/s and moves a flat-ended follower up and down. The eccentricity of the cam is d (i.e. distance from axis of rotation to centre of circle). Derive expressions for the follower velocity and acceleration. If the speed is 2000 rev/min, R = 20mm and d = 5 mm, determine the velocity...
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