ENGR220 Dynamics. Final Exam

Transcription

1 Spring Semester ENGR220 Dynamics Final Exam Instructions: 110 minutes to complete. Closed-book, 4 exam reference sheets allowed. Turn computations and exam in to instructor at the end of the exam period. 1. (30 Points) A particle with an initial position of s=-0.3 m at t=0 experiences the discontinuous velocity shown. v, m/s 3 m/s t=10 sec t=20 sec a. (20 Points) Derive mathematical formulae for the acceleration a(t) and position s(t) for the two time intervals 0<t<10s and 10<t<20s. Time t should be the only variable in these formulae. b. (10 Points) Sketch a plot of the acceleration a(t) and position s(t) versus time for the entire time interval 0<t<20s. The plot should be numerically correct at the time segment endpoints.

2 Spring Semester (15 Points) A bumper, consisting of three nested springs, is used to arrest the horizontal motion of a large mass that is traveling at 40 ft/s as it contacts the bumper. The spring causes a deceleration versus position as shown in the graph. For the positions in the interval 0<x<0.5 ft, the deceleration is given by 2000x ft/s 2, while in the interval 0.5<x<1 ft, the deceleration is given by (x- 0.5) ft/s 2. In these formulae, x is given in units of ft. a. (5 Points) Compute the velocity of the mass at x=0.5 ft. b. (10 Points) Compute the compression of the spring set when the mass has reached zero velocity. 3. (20 Points) The 50 lb slider in the position shown has an initial velocity v o = 2 ft/s on the inclined rail and slides under the influence of gravity and friction. The kinetic coefficient of friction µ k is µ k =0.5, and the spring constant is k=1 lb/ft. Compute the velocity of the mass when the spring has been compressed 4 in.

3 Spring Semester (20 Points) The supertanker has a total displacement (weight) of 150,000 long tons (one long ton is 2240 lb). At the instant shown, it is lying still in the water. The tugboat begins to tow the supertanker by applying a tension of 50,000 lb to the cable. Compute the time that it takes the supertanker to reach a speed of mi/hr (1 knot). (5280ft= 1mi, 3600s/hr). 5. (30 Points) A container for waste materials is dumped by the hydraulicactuated linkage shown. This linkage imposes a velocity and acceleration to point A of the waste container. The piston rod starts from rest in the position indicated and has an acceleration of 0.5 m/s 2 in the direction shown. a. (10 Points) Write the necessary vector equation(s) that will allow for the determination of the initial angular acceleration of the container. b. (10 Points) Specify the individual vectors in the vector equation(s) from part a. c. (10 Points) Derive N equations that will determine N unknowns, among which one of the unknowns is the initial angular acceleration of the waste container.

4 Spring Semester The 30 kg bar OB is secured to the accelerating cart in the 30 o position from the horizontal by the pin at O and the roller at A. The horizontal acceleration of the cart is a=20 m/s 2. You may redefine the orientation of the xy coordinate system if you wish. a. Sketch a free body diagram, including all of the required components, for the bar OB. b. Write Newton s laws for the bar OB. c. List the unknowns in Newton,s laws. d. Write a vector kinematic constraint that will help determine all of the unknowns. e. Identify (specify) all of the vectors in the kinematic constraint. f. Derive N equations that will determine the N unknowns.

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