(4.) A Porter governor has all four arms 250 mm long. The upper arms are attached on the axis of rotation and the lower arms are attached to the sleeve at a distance of 30 mm from the axis. The mass of each ball is 5 kg and the sleeve has a mass of 50 kg. The extreme radii of rotation are 150 mm and 200 mm. Determine the range of speed of the governor. Solution: Given: BP = BD=250 mm; DH = 30 mm; m = 5 kg; M = 50 kg; ri = 150 mm; r2= 200 mm First of all, let us find the minimum and maximum speed of the governor. The minimum and maximum position of the governor is shown in Fig. 6.8 (a) and (b) respectively. T mg 250 250 mg 250 250 B₁ Ma Mg 2 Fig. 6.8.

In a four bar mechanism the link AB rotates with angular velocity of 20rad/s and angular acceleration of 100 rad/s both in clockwise direction when it make an angle of 45° with link AD which is fixed .The length of various linkages are AB=CD=400 mm,BC=500mm and AD=750mm .Neglect the gravitational effect and friction.The mass of link is 5kg/m. Find the torque on output link E (2) (4) A (1) (1)

8. 2) Rods AB and BC are linked at Band have weights of 18 lb and 37 lb, respectively. The 8-lb collar C, which is connected to BC and the spring, slides freely along the smooth vertical guide. The lengths of the rods are 4 = 1.4 ft and 2 = 2.9 ft. If the system is released from rest when 0 = 0°, determine the magnitude of the angular velocity (in rad/s) of rod BC when 0 = 90°. The attached spring has spring constant k = 20 Ib/ft, and is unstretched when 0 = 0°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Take g= 32.2 ft/s2. k CO Your Answer: Answer

** correction to problem: angular speed is rad/ s

The gear train shown operates in a horizontal plane and is used to transmit motion to the rack D of mass mD = 4.9 kg. If an input torque M = 63 N●m is applied to gear A, what will be the magnitude of the resulting acceleration a of the unloaded rack? (The mechanism which it normally drives has been disengaged.) Gear C is keyed to the same shaft as gear B. Gears A, B, and C have pitch diameters dA = 185 mm, dB = 355 mm, and dC = 185 mm, and centroidal mass moments of inertia IA = 0.45 kg●m2, IB = 3.38 kg●m2, and IC = 0.45 kg●m2, respectively. All friction is negligible.

5. A motor is using a large pulley to pull a crate with a mass of m= 200 kg up a 30 degree incline. The pulley has a mass of m = 50 kg, a radius of r = 0.5 m and a radius of gyration of ko = 0.25 m. The motor supplies a torque of M = (500 +1500) N*m to the pulley. If the crate starts from rest and the coefficient of kinetic friction between the crate and ground is µ = 0.2 (assume the crate immediately starts moving, so no static friction analysis needed). Determine the speed of the crate after it travels 4m. M 777 30°

Problem 2 A load is to be raised 12 ft by the hoisting system shown, developed by ASCE Club students to lift various loads to the ceiling of the Construction Materials Laboratory. Assume gear A is initially at rest, then accelerates uniformly to a speed of 110 rpm in 5 s, and then maintains a constant speed of 110 rpm. Gear A has radius A 4.0 in, gear B has radius B = Drum C rotates with gear B. = 22 in, and drum C has radius rc = 18 in. Determine: (a) the number of revolutions executed by gear A in raising the load, (b) the time required to raise the load to 12 ft. TB B с Load rc

8. 1) Rods AB and BC are linked at Band have weights of 20 lb and 37 Ib, respectively. The 9-lb collar C, which is connected to BC and the spring, slides freely along the smooth vertical guide. The lengths of the rods are 4 = 1.3 ft and 2 = 3.2 ft. If the system is released from rest when 0 = 0°, determine the ratio r= WABI WBC of the angular velocities or rod AB and rod BC when e = 90°. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. 11 A В k C Your Answer: Answer

3. The pulley assembly shown in the figure weighs 150 lb and has a centroidal radius of gyration of 2 ft. The blocks are attached to the assembly by cords wrapped around the pulleys. Determine the acceleration of each body and the tension in each cord. a. Identify the direction of motion in the problem. b. Set up the equations of motion that is required to solve the problem. c. Solve for the unknown variables by substituting the given in the equations of motion that has been set up previously. 2' 3' A B 100 Ib 200 Ib

2. Consider the 5-1lb bar with length of 2½ feet and width of 2 inches. Small frictionless bearings are mounted to the ends, constraining the motion of the bar to the horizontal x and y slots. The bar starts at rest at positioned at 0= 45°. If an angular acceleration of 3 rad/s² is desired, what moment M must be applied to the bar? What are the reaction forces at A and B at that instant? Additional question: Does the width of the bar matter, or is it appropriate to consider the bar as a slender rod? Consider errors of less than 2% negligible.