Vlad needs to draw water from a deep well. He is using a bucket that is connected by rope (negligible mass) to a wooden axle at the top of the well. By cranking a handle at the end of the axle, Vlad is able to unwind the rope around the axle and move the bucket downward. The radius of the axle is R = 30 cm. The bucket is traveling downward at speed vi = 25 cm/s when the handle slips out of Vlad’s hand. As the rope unwinds and the bucket falls downward, the axle spins freely with an angular acceleration whose magnitude is α = 4.5 rad/s^2. The bucket falls through a distance of d = 7.0 m before crashing into the water. 1. What is the angular speed ωf of the axle when the bucket first hits the water?  2. As d → 0, what limit does ωf approach and why?

In an amusement park ride, a child stands against the wall of a cylindrical room that is then made to rotate. The floor drops downward and the child remains pinned against the wall. If the radius of the room is 2.15 m and the relevant coefficient of friction between the child and the wall is 0.600, with what minimum speed is the child moving if he is to remain pinned against the wall? 07.26 m/s O3.93 m/s O 12.1 m/s 5.93 m/s 9.80 m/s

A puck of mass m = 1.30 kg slides in a circle of radius r = 22.0 cm on a frictionless table while attached to a hanging cylinder of mass M= 2.30 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? M Number i 2.227 Units m/s

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?

A bucket of mass equals 18.7 kg(mb) is knocked off the side of a wall. The bucket falls 18.6 m to the bottom of the well. Attached to the bucket is a light rope that wraps around a cylinder of radius equals 48.7 cm and mass(mc) equals 3.26 kg. How fast is the bucket falling just before it hits the ground

On a carnival ride, you stand next to a wall of a circular drum which spins around the center. When drum is spinning fast enough the floor drops away and you remain stuck to the wall and do not slide down to the floor until the drum slows down some. Assume a rider has a mass of 55.0 kg, and the drum has a radius of 6.00 m. The average linear speed that a rider is traveling with around the drum is 7.80 m/s. What is the normal force that the drum is exerting on the rider to keep her from sliding down to the floor?

A tire is tied to a rope that is tied to the branch of a tree so that the tire swings in a circular trajectory of radius h1 = 15.31 m. A child takes the tire to the top of a platform that is a height h2 = 12.60 m above the ground, sits in the tire, and swings from rest from the platform. The combined mass of the tire and child is 36 kg. The rope is taut when the child leaves the platform and you may neglect the mass of the rope. At the bottom of the circular trajectory, the child and tire are a height h3 = 0.99 m above the ground. include a diagram showing the physical sites (a) Calculate the speed of the child/tire at the bottom of the circular trajectory.  m/s (b) Calculate the maximum tension in the rope as the child/tire swing back and forth.  N

A pulley has a negligible mass (that means, the radius is not relevant).  It is supported with a pin at the center (and is free to rotate).  A rope goes over the pulley.  Block A, which has a mass of 5.723 kg is connected to one side of the rope.  On the other side, Block B, with a mass of 12.602 kg is connected.   The system is released from rest. What is the speed of block B, after B has traveled 0.716 m?  Please enter a positive value in m/s (but without units) regardless of the direction of the motion of B

You have a horizontal grindstone (a disk) that is 87 kg, has a 0.31 m radius, is turning at 94 rpm (in the positive direction), and you press a steel axe against the edge with a force of 23 N in the radial direction. The kinetic coefficient of friction between steel and stone is 0.20. What is the number of turns, N, that the stone will make before coming to rest?

A 83-kg pilot in training sits in a centrifuge that spins his seat around a central axis. When the seat is moving in its circular path at a speed of 3.0 m/s, he feels a 585-N force pressing against his back (the seat faces the axis). What is the radius of the centrifuge?