You are riding in an amusement park ride consisting of a long horizontal arm that pivots from one end about a vertical axis. Attached to the far end of the arm is a container in which you stand with your face pointing towards the center, as shown in the diagram. As the ride's spin increases, you realize that when the container reaches a certain linear speed v, you can lift your feet off the ground and the frictional force on your back against the wall is sufficient to hold you suspended above the floor of the container. The length of the arm-plus-container (i.e. the distance from you to the axis of rotation) is L. The acceleration due to gravity is g. In terms of L and v, what is the coefficient of static friction between your back and the wall of the container? Axis of rotation L

A 0.50-kg ball that is tied to the end of a 1.4-m light cord is revolved in a horizontal plane, with the cord making a θ = 30° angle with the vertical. An illustration shows a ball suspended from a string. The string forms an angle θ with the vertical as its top end is held stationary in space while the ball moves along a horizontal circular path below. The center of the circular path is shown to be directly below the top end of the string.   (c) If the cord can withstand a maximum tension of 8.9 N, what is the highest speed at which the ball can move?

A certain amusement park ride consists of a large rotating cylinder of radius R = 3.15 m. As the cylinder spins, riders inside feel themselves pressed against the wall. If the cylinder rotates fast enough, the frictional force between the riders and the wall can be great enough to hold the riders in place as the floor drops out from under them. If the cylinder makes f 0.590 rotations/s, what is the magnitude of the normal force FN between a rider and the wall, expressed in terms of the rider's weight W? FN = W What is the minimum coefficient of static friction u, required between the rider and the wall in order for the rider to be held in place without sliding down? Hs 2

A uniform rod is set up so that it can rotate about an axis at perpendicular to one of its ends. The length and mass of the rod are 0.801 m and 1.25 kg, respectively. A force of constant magnitude F acts on the rod at the end opposite the rotation axis. The direction of the force is perpendicular to both the rod's length and the rotation axis. Calculate the value of F that will accelerate the rod from rest to an angular speed of 6.49 rad/s in 8.61 s. F =

Block A rests on a horizontal tabletop. A light horizontal rope is attached to it and passes over a pulley, and block B is suspended from the free end of the rope. The light rope that connects the two blocks does not slip over the surface of thè pulley (radius 0.080 m) because the pulley rotates on a frictionless axle. The horizontal surface on which block A (mass 3.70 kg) moves is frictionless. The system is released from rest, and block B (mass 6.00 kg) moves Part A What is the tension force that the rope exerts on block B? downward 1.80 m in 2.00 s. Express your answer with the appropriate units. HÁ TB = Value Units Submit Request Answer Part B What is the tension force that the rope exerts on block A? Express your answer with the appropriate units. HẢ 王新 TA= Value Units

A bicycle wheel is mounted on a fixed, frictionless axle, with a light string wound around its rim. The wheel has moment of inertia I=kmr2, where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular speed ω0, when at time t=0 someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel.   Suppose that after a certain time tL, the string has been pulled through a distance L. What is the final rotational speed ωfinal of the wheel? Express your answer in terms of L, F, I, and ω0.

One end of a string is wrapped several times around a pulley of mass  0.92 kgkg  that is oriented vertically. The other end of the string is connected to a block of mass 0.35 kg, which is then slowly lowered until the string becomes taut. After which the person lets go of the block completely, thus allowing the block to descend and the pulley to rotate in unison. What is the magnitude of the acceleration of the block after the person has let go?

An air puck of mass m1 = 0.27 kg is tied to a string and allowed to revolve in a circle of radius R = 1.1 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 0.8 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves. An overhead view of a table is shown. A string is used to whirl a puck of mass m1counterclockwise with velocity vector v on a horizontal circular path of radius R on the surface of the table. The string passes through a hole at the center of the circular path, and then extends down under the table where an object of mass m2 is attached. (a) What is the tension in the string (in N)? N (b) What is the horizontal force acting on the puck (in N)? N (c) What is the speed of the puck (in m/s)? m/s

An air puck of mass m1 = 0.25 kg is tied to a string and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 1.0 kg is tied to it (Fig. P7.27). The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck?

A uniform rod with a mass of 100 g and a length of 50.0 cm rotates in a horizontal plane about a fixed vertical, frictionless pin passing through the center of the rod. Two small beads, each having a mass of 30.0 g, are mounted on the rod so that they are able to slide without friction along its length. Initially, the beads are held by catches at positions 10.0 cm on each side of the rod’s center; at this time, the system rotates at an angular speed of 20.0 rad/s. Suddenly, the catches are released, and the small beads slide outward along the rod. Find (a) the angular speed of the system at the instant the beads reach the end of the rod and (b) the angular speed of the rod after the beads fly off the rod’s ends.