Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R.

The cylinder rotates without friction about a horizontal axle along the cylinder axis. One end of the rope is attached to the cylinder.

The cylinder starts with angular speed ω0.

After one revolution of the cylinder the rope has unwrapped and, at this instant, hangs vertically down, tangent to the cylinder.

Find the angular speed of the cylinder at this time. You can ignore the thickness of the rope.

The car hoist allows the car to be driven onto the platform, after which the rear wheels are raised. if the loading from both rear wheels is 1380 lb, determine the force in the hydraulic cylinder ab. neglect the weight of the platform itself. member bcd is a right-angle bell crank pinned to the ramp at c. the force is positive if in tension, negative if in compression.

Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. the first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. assume that the positive direction is directed from the second satellite towards the first satellite. (a) calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.(b) what is the loss of kinetic energy in this inelastic collision? (c) repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity(d) loss of kinetic energy = ?

Identify some abiotic characteristics of the tundra biome.