The spring-held follower AB has a mass of 0.5 kg and moves back and forth as its end rolls on the contoured surface of the cam, where r = 0.15 m and z = (0.02 cos 2θ) m. If the cam is rotating at a constant rate of 30 rad/s, determine the force component Fz at the end A of the follower when θ = 30°. The spring is uncompressed when θ = 90°. Neglect friction at the bearing

of stion The man stands on the platform at O and runs out toward the edge such that when he is at A, y = 5 ft, his mass center has a velocity of 2 ft/s and an acceleration of 3 ft/s², both measured relative to the platform and directed along the positive y axis. If the platform has an angular velocity of 0.4 rd/s and angular acceleration of 0.2 rad/s² as shown in the figure below, determine the following: Note that i, j represent the unit vectors of x and y axes, respectively. Z The velocity of his mass center at this instant is The acceleration of his mass center at this instant is 00 # ft/s. W # ft/s². A

The helical path is wound around the circular cylinder with radiusR . The step h= 2*pi*R. The object A is sliding through the path guide under gravity (acting in the negative zdirection). There is no air resistance 1)Draw the force diagrams in (theta ,Z ) plane (tangent to the cylinder) and in( r,theta ) plane. 2) If the initial speed is 0, find the speed after 3 full circles. Given: R, g, m, u.[Hint: Use the work-energy principle.]

P= 900 N 4) The uniform 40 kg slender rod is being pulled by a cable that passes over the small smooth peg at A, and a vertical force F is applied at the edge 0.8 m as shown. If the rod has an angular velocity of w=6 rad/s 6 rad/s at the instant, determine the tangential and normal components of reaction forces at the F=150 N pin 0, and the angular acceleration of the rod. tosmt 0.6 m 0.3 m

The clock pendulum consists of the slender rod of length I and mass m and the bob of mass 7m. Neglect the effects of the radius of the bob and determine lo in terms of the bob position x. Calculate the ratio R of Io evaluated for x = ³/1 to Io evaluated for x = 1. 7m x m 1

3. The uniform bar has a mass m and length 7. If it is released from rest when 0 = 0°, determine its angular velocity as a function of the angle before it slips. 3 23

In the figure, rod AB has a mass of 10 kg, and must slide within the slots as shown. If the spring is unstretched when θ = 0°, determine the angular velocity of the bar when it reaches that angle after being released from θ = 30°.

*13=108. The collar, which has a weight of 3 lb, slides along the smooth rod lying in the horizontal plane and having the shape of a parabola r = 4/(1 – cos 0), where 0 is in radians and r is in feet. If the collar's angular rate is constant and equals ò = 4 rad/s, determine the tangential retarding force P needed to cause the motion and the normal force that the collar exerts on the rod at the instant 0 = 90°.

When in the mode of adsorbing, the vertical shaft is rotating with an angular velocity of 3 rad/s at 0 = 0°. When picking up trashes, a force F needs to be applied to the collar so that 0 = 90°. Help students determine the angular velocity of the shaft at 0 = 90°. Also, find the work done by force F from 0 = 0° to 0 = 90°. Neglect the mass of rods GH and EF and the collars I and J. The rods AB and CD each have a mass of 10 kg. 0.3 m E 0.3 m 0.1 m 0.3 m A 0.1 m H F 0 0.3 m B

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°.