NAME: Exam 03: Chapters 16 and 17 INSTRUCTIONS Solve each of the following problems to the best of your ability. Read and follow the directions carefully. Solve using the method required by the problem statement. Show all your work. Work as neatly as you can. If you need additional paper, please be sure to staple all pages in the proper order. It is permissible to use your calculator or an online solver (like Wolframα) to perform derivatives or integrals. If you do, state this explicitly. Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units. You must submit your exam paper no later than Wednesday, March 28. You should submit the paper to me directly, or, if I am not in my office, please turn it in to Mrs. McDaniel in the department office (LSC 171), no later than 12:00PM. You may not slide the paper under my door. Late papers will not be accepted. Your work will be scored according to the following point structure: Problem 01: /15 Problem 06: /15 Problem 02: /15 Problem 07: /15 Problem 03: /15 Problem 08: /15 Problem 04: /15 Problem 09: /15 Problem 05: /15 Problem 10: /15
Problem 01 A mill in a textile plant uses the belt- and- pulley arrangement shown to transmit power. When t = 0 an electric motor is turning pulley A with an initial angular velocity ωo = 3rad/s. If this pulley is subjected to a constant counterclockwise angular acceleration αa = 1.5rad/s 2, determine the angular velocity of pulley B after B turns 5 revolutions. The hub at D is rigidly connected to pulley C and turns with it. 16.3: Rotation About a Fixed Axis ωa, αa EXAM 03 PAGE 2/11
Problem 02 If the angular velocity of link AB is ωa = 5rad/s, determine the velocity of the block at C and the angular velocity ωc of the connecting link CB at the instant θ = 45 and D = 30. 16.5: Relative Motion Analysis ωa = 5rad/s ωa vb vc/b vc ωb vb EXAM 03 PAGE 3/11
Problem 03 If the collar at C is moving downward to the left at vc = 8m/s, determine the angular velocities ωa and ωc of links AB and BC at the instant shown. 16.6: Instantaneous Center of Zero Velocity vc = 8m/s vb ωa vb 45 60 vc rc 75 rb ωc EXAM 03 PAGE 4/11
Problem 04 At a given instant, the gear has the angular motion shown. Determine the accelerations of points A and B on the link and the link s angular acceleration at this instant. 16.7: Relative Motion Analysis: Acceleration va ω O. IC aa/o]n aa/o]t ao α. O. IC vb ωab va ab αab aa EXAM 03 PAGE 5/11
Problem 05 16.8: Relative Motion Analysis Using Rotating Axes Collar C moves along rod BA with a velocity vc/b = 2m/s and an acceleration ac/b = 0.5m/s 2, both directed from B towards A and measured relative to the rod. At the same instant, rod AB rotates with the angular velocity ωb = 4rad/s and angular acceleration αb = 1.5rad/s 2. Determine the collar s velocity and acceleration at this instant. ωb = 4rad/s αb = 1.5rad/s 2 vc/b = 2m/s ac/b = 0.25m/s 2 Z X Y EXAM 03 PAGE 6/11
Problem 06 If the cart is given a constant acceleration a = 6ft/s 2 up the inclined plane, determine the force developed in rod AC and the horizontal and vertical components of force at pin B. The crate has a weight W = 150lb with center of gravity at G, and it is secured on the platform, so that it does not slide. Neglect the platform s weight. (Hint: You don t need the applied force P, because it s not being applied to the crate. Treat the crate and platform as a single rigid body.) = 30 ma FC 60 W By Bx EXAM 03 PAGE 7/11
Problem 07 The lift truck has a mass m1 = 80kg and mass center at G. Determine the largest upward acceleration of the spool (m2 = 120kg) so that no reaction of the wheels on the ground exceeds 600N. m2a = 2NA m1g m2g 2NB First case is the correct solution, a = 3.39m/s 2. In the second case, NA exceeds the limit of 600N. EXAM 03 PAGE 8/11
Problem 08 The disk has a mass m = 25kg and is originally spinning at the end of the strut with an angular velocity of ω = 50rad/s. If it is then placed against the wall, for which the coefmicient of kinetic friction is µk = 0.20, determine the time required for the motion to stop. What is the force in strut BC during this time?.. µkn = N IBα FB mg EXAM 03 PAGE 9/11
Problem 09 Determine the angular acceleration of the diving board (m = 25kg) and the horizontal and vertical components of reaction at the pin A the instant the man jumps off. Assume that the board is uniform and rigid, and that at the instant he jumps off the spring is compressed by a maximum amount l = 250mm, v = 0, and the board is horizontal. Assume k = 7.5kN/m. Ax Ay mg = man mat k l Iα EXAM 03 PAGE 10/11
Problem 10 The slender rod AB (m = 25kg) rests in the position shown when the horizontal force P = 50N is applied. Determine the initial angular acceleration of the rod. Neglect the mass of the rollers. NA G = mg IGα max may P NB aa aa/g]t aa/g]n = ax ay ab ab/g]n ab/g]t EXAM 03 PAGE 11/11