Up= 3.23 m S
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- 2. The spheres have a mass of 7.50 kg each and are moving at v = 3.50 m/s at time t = 0 as shown. The shaft and frame have negligible mass. A time dependent driving moment M=4-t² is applied. Calculate the speed of the spheres at time t = 6.00 s. M 0.5 mIn the system that starts to move without speed, the masses of 22.2 kg each reach an angular velocity of 242 rev/min in t second at a radius of R=293 mm with the effect of the 37 N force T. Since the radius of the pulley is r = 63 mm, find t ignoring friction and all masses except the four.The disk D, which has weight W = 15 lb, starts from rest on an incline when the constant moment M is applied to it. The disk is attached at its center to a wall by a spring of constant k = 7 ft/lb. The spring is unstretched when the disk is at its starting position. The disk rolls down the incline without slipping. Take R = 5 ft, 0 = 25° and g = 32.2 ft/s². Use for the moment of inertia of the disk about G, IG: Figure D Part B R M mR² wwww 1 of 1 Part A - Draw a free body diagram of the disk. Indicate which forces and/or couples do work on the disk. Determine the value of the moment M for the disk to stop after rolling down a distance d = 5 ft down the incline. You must use the work-energy theorem to solve this question.
- The small block B is attached to the vertex A of the right circular cone using a light cord. The cone is rotating at a constant angular velocity about the vertical z-axis such that the block attains a speed of 0.6 m/sec. If the mass of the block is 0.3 kg, determine the tension in the cord by neglecting friction and the size of the block. Present your answer in Newtons using 3 significant figures. 200 mm B 300 mm A 400 mmThe four balls, each of mass m = 2.8 kg, are rigidly mounted to the rotating frame and shaft, which are initially rotating freely about the vertical z-axis at the angular rate of 15.7 rad/s clockwise when viewed from above. The distances r = 0.28 m and R = 0.57 m. If a constant torque M = 25.7 N-m is applied to the shaft, calculate the time t to reverse the direction of rotation and reach an angular velocity 0 = 15.7 rad/s in the same sense as M. 3 m R Answer: t = i - R M m m S0 A solid cylinder with a radius of r = 0.34 m and a mass of m = 8 kg is attached to a spring with a spring N constant of k = 25. Assume that the cylinder rolls down the ramp without slipping and that the spring m is initially at its natural length (not stretched or compressed). We ro If the ramp is at an angle of 0 = 63° from horizontal, what is the cylinder's angular velocity when it has traveled a distance of d = 0.25 m? rad ∙d. S
- The flat circular disk rotates about a vertical axis through O with a slowly increasing angular velocity w. Prior to rotation, each of the 0.52-kg sliding blocks has the position x = 28 mm with no force in its attached spring. Each spring has a stiffness of 430 N/m. Determine the value of x for each spring for a steady speed of 279 rev/min. Also calculate the normal force N exerted by the side of the slot on the block. The force N is positive if it pushes from the side labeled A. Neglect any friction between the blocks and the slots, and neglect the mass of the springs. (Hint: Sum forces along and normal to the slot.) Answers: X = wwwwwwww N = i i -74-74- mm mm mm NPart A The smooth surface of the vertical cam is defined in part by the curve r = (0.2 cos 0+0.3) m. The forked rod is rotating with an angular acceleration of 0 = 2 rad/s as shown in (Figure 1), and when 0 = 45°, the angular velocity is 6 = 6 rad/s. Determine the force the cam and the rod exert on the 1.8-kg roller at this instant. The attached spring has a stiffnesss k = 100 N/m and an unstretched length of 0.1 m. Express your answers in newtons using three significant figures separated by a comma. ? Neam, Frud = N Submit Request Answer Figure 1 of 1 Provide Feedback Next >The robot arm is elevating and extending simultaneously. At a given instant, 0 = 29°, 0 = 36 deg/s, Ö = 112 deg/s², 1 = 0.62 m, i = 0.32 m/s, and 7 = -0.38 m/s². Compute the radial and transverse forces F, and F that the arm must exert on the gripped part P, which has a mass of m = 12.8 kg. Compare with the case of static equilibrium in the same position. Assume d = 0.82 m. SARAJE Answers: Dynamic: Fr= i N, Fe= i N Static: F₁ = i N, F₂= i N
- A mechanical engineering student has been practicing his yoyo tricks because he has too much free time. For one trick, he spins the yoyo such that it contacts the ground and rolls forward, emulating someone walking their dog. If the yoyo has a radius of gyration 0.01 m and a mass of m = 0.2 kg, determine the acceleration and angular acceleration of the yoyo when the tension in the string is found to be T = 0.3 N. Assume the string is at its full extent and does not roll up as the yoyo rolls. Assume there is also no friction where the string slips around the yoyo's inner axle. The coefficients of static and kinetic friction are found to be 0.25 and 0.1 respectively. The angle = 40 degrees and the radius of the yoyo is r = 0.04 m. Take the initial angular velocity of the yoyo to be w = 6 - CW rad 8 Does the yoyo slip? Ꮎ aG₂ Slips Does not Slip What is the acceleration of the yoyo's center of gravity (G) and angular acceleration (a)? Round all answers to three significant figures. a (22 k…The four balls, each of mass m = 2.3 kg, are rigidly mounted to the rotating frame and shaft, which are initially rotating freely about the vertical z-axis at the angular rate of 19.5 rad/s clockwise when viewed from above. The distances r = 0.25 m and R = 0.52 m. If a constant torque M = 23.1 N·m is applied to the shaft, calculate the time t to reverse the direction of rotation and reach an angular velocity = 19.5 rad/s in the same sense as M. m R m r M m R m2. 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.