A 3-kg shaft CA passes through a smooth journal bearing at B. Springs are attached the bearing at B and the caps at C and A. Initially, the springs are unstretched when no force is applied to the shaft. In this position, s = s' = 250 mm and the shaft is at rest. If a horizontal force of F = 5 kN is applied, determine the speed of the shaft the instant whens = 100 mm and s'= 400 mm. %3!

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 m

The cylinder is at rest supported by the spring of stiffness 205 N/m when a torque of 78 Nm is applied as shown. The mass of the cylinder is 2.5 kg and its radius is 205 mm. If the wheel rolls without slipping, find the velocity of the centre of the wheel when it has moved a distance 352 mm up the slope with the angle ẞ= 25°.

At the instant shown, the uniform slender rod with mass m = 31 kg is pin-supported at point O. It is subjected to a counterclockwise moment M = 68 N•m, has a counterclockwise angular velocity of W= 5.3 rad/s, and the dimensions a = 0.10 m and b = 0.65 m. Determine magnitude of the support reaction at point O at this instant. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. Take g = 9.81 m/s2. a M

The 18-kg rod AB is pin-connected at A and subjected to a couple moment of M =15 N- m The rod is released from rest when the spring is unstretched at 0 = 30°. As the rod rotates, the spring always remains horizontal, because of the roller support at C. (Figure 1) Determine the rod' s angular velocity, measured clockwise, at the instant 0 = 60°. Express your answer using three significant figures. Enter positive value if the angular velocity is clockwise and negative value if the angular velocity is counterclockwise. vec rad/s k = 40 N/m 0.75 m M = 15 N- m

The 29-kg spool of outer radius ro​=530 mm has a centroidal radius of gyration k=355 mm and a central shaft of radius ri​=215 mm. The spool is at rest on the incline when a tension T=204 N is applied to the end of a cable which is wrapped securely around the central shaft as shown. Determine the acceleration aaa of the spool center GGG and the friction force FFF acting at the interface of the spool and incline. The friction coefficients there are μs=0.28 and μk​=0.17. The tension T is applied parallel to the incline and the angle θ=16. The acceleration aaa and the force F are both positive if up the incline, negative if down.

The 0.6-lb particle is guided along the circular path using the slotted arm guide. Motion occurs in the horizontal plane with negligible friction. Note that the circular part of the slot has the radius equal to 0.5 ft, and the radial position, r, is measured from the hinge and the angle is measured in the counter-clockwise direction. If the arm has an angular velocity = 4 rad/sec and an angular acceleration 6 - 8 rad/sec² at the instant when 0 = 30°, determine the force of the arm guide on the particle at the instant. Present your answer in lb using 3 significant figures. 0.5 ft 0 0.5 ft.

A simple pendulum of mass m = 10 kg and length r= 1 m is mounted on the flatcar, which has a constant horizontal acceleration a = 1 m/s as shown. If the pendulum is released from rest relative to the flatcar at the position 0 = 0 deg, determine the expression for the tension Tin the supporting light rod for 0 = 45 deg and A = 90 deg.

The spring-mounted 0.89-kg collar A oscillates along the horizontal rod, which is rotating at the constant angular rate θ˙=8.2θ˙=8.2 rad/s. At a certain instant, r is increasing at the rate of 700 mm/s. If the coefficient of kinetic friction between the collar and the rod is 0.63, calculate the friction force F exerted by the rod on the collar at this instant.

At the instant shown, link CD rotates with an angular velocity of W = 9.0 rad/s. If it is subjected to a couple moment M= 320 N-m, determine the magnitude of the vertical reaction force developed on pin D. The block has a mass of 50 kg and center of mass at G. Neglect the mass of links AB and CD. (Hint, since the mass of link AB or CD is negligible, the external force or moment acting on it sums up to 0.) Please pay attention: the numbers may change since they are randomized. Your answer must include 1 place after the decimal point, and proper unit. Take g = 9.81 m/s². 0.1 m 0.6 m В А 0.4 m' G 0.4 m D C M Your Answer: Answer units