4.14. The system illustrated in Figure 4.26 is comprised of a board of length / with uniform mass per unit length of p. It sits on top of two counter-rotating cylinders, which are rotating with an angular velocity of w in the directions indicated and are separated by a distance 1/2. You may assume that w is large enough that the points of contact between the board and cylinders are always slipping and that the coefficient of dynamic friction between the board and cylinders is u. If the board is not centered on the two cylinders, then the normal force will be greater on the side to which it is displaced because more of the weight of the board will be supported on that side. For example, in the figure, the normal force between the board and cylinder will be greater at the left cylinder, and this will cause a net force to the right. Let x denote the distance that the center of the board is displaced from the center of the two cylinders, as is illustrated in the figure, and determine the differential equation for this system. Solve it if x(0) = 1/8 and x(0) = 0.

A machine part has the shape of a solid uniform sphere of mass 220 gg and diameter 3.50 cmcm . It is spinning about a frictionless axle through its center, but at a point at the top of the sphere, it is scraping against metal, resulting in a friction force of  0.0200 NN at that point. Find the angular acceleration of the sphere, including the direction (a positive value would indicate the +z direction and a negative value would indicate the -z direction).

Problems 3.64 and 3.65 Te stem shown is initially at rest when the bent bar starts to rotate about the vertical is AB with constant angular acceleration a son between the collar of mass m = intially d = 70 cm from the spin axis AB. 3 rad/s. The coefficient of static fric- 2 kg and the bent bar is u, = 0.35, and the collar is %3D %3D %3D Problem 3.64 Assuming the motion starts at 1 = 0, determine the time at which the allar starts to slip relative to the bent bar. Figure P3.64 and P3.65 of rotations undergone by the bent bar when the

Cam mechanisms are used in many machines. For example, cams open and close the valves in your car engine to admit gasoline vapor to each cylinder and to allow the escape of exhaust. The principle is illustrated in the figure below, showing a follower rod (also called a pushrod) of mass m resting on a wedge of mass M. The sliding wedge duplicates the function of a rotating eccentric disk on a camshaft in your car. Assume that there is no friction between the wedge and the base, between the pushrod and the wedge, or between the rod and the guide through which it slides. When the wedge is pushed to the left by the force F, the rod moves upward and does something such as opening a valve. By varying the shape of the wedge, the motion of the follower rod could be made quite complex, but assume that the wedge makes a constant angle of 0 = 19.0⁰. Suppose you want the wedge and the rod to start from rest and move with constant acceleration, with the rod moving upward 1.00 mm in 8.00 ms. Take m…

weighs 60 N on Earth. (3). A system consists of a pulley (vertical wheel) that is only allowed to rotate (spin). A cord is passed over the pulley and at each end there is a mass attached to the end of the cord. The mass attached on the left is m, =0.6 kg and at the right the mass is m2 = 0.8 kg. a) Calculate both the Tension in the cord and the acceleration of the system. b) What are the accelerations of both masses, if you were to cut the cord? Neglect the friction between cord and wheel,

A sphere of mass M and radius R is not necessarily solid or hollow. It has moment of inertia I= cMR2. As shown in the figure, the sphere starts from rest and rolls without slipping down a ramp from height H. It then moves back up the other side, but now with no friction at all between the sphere and the ramp. What height does the sphere reach?

A photograph shows two U.S. Coast Guard icebreakers in an ice field and a simple model for an ice breaking operation. The coefficients of static and kinetic friction for contact between the ship's bow and ice are 0.08 and 0.054, respectively, and the ship produces a thrust of 106 forces between the ship's hull and water except for the thrust. Ib. Assume the ship makes contact with the ice only on its bow, and neglect all 1170 T17° Determine the normal and friction forces acting on each side of the ship's bow as it moves through the ice field with constant velocity. The normal force is x 106 lb. The friction force is x 104 Ib.

i need the answer quickly

i need the answer quickly

An old vinyl record is a thin plastic disk of radius 0.25 m and mass 132 g. It is freely rotating at 45 rev/min. You are able to stop the record from rotating in 9 s by pressing your finer against the rim and exerting a radially directed force of 8 N. (Recommendation: If you don't know what a vinyl record is, please do a Google search for an image to help your understanding.) What is the coefficient of kinetic frictions between the record and your finger?? Your Answer: