CP A 15.0-kg bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m in diameter with mass 12.0 kg. The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.0 m to the water. (b) With what speed does the bucket strike the water?

A $400\mathrm{g}$ particle is moving in circular motion with a radius of $2.3\mathrm{m}$. At one instant in time its speed was $3.4\mathrm{m}/\mathrm{s}$ and it was slowing down at a rate of $2.2\mathrm{m}/{\mathrm{s}}^2$. What was the magnitude of the net force on the particle at this instant?

A hollow sphere with a radius of 0.31 m is placed on an inclined plane that makes an $11°$ angle with the floor. Assuming the sphere rolls without slipping, what will be the magnitude of the acceleration of the sphere down in the incline?

A cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. (b) Find the magnitude and direction of the force that the axle exerts on the wheel.

A 12.0-kg box resting on a horizontal, frictionless surface is attached to a 5.00-kg weight by a thin, light wire that passes over a frictionless pulley (Fig. E10.16). The pulley has the shape of a uniform solid disk of mass 2.00 kg and diameter 0.500 m. After the system is released, find

(b) the acceleration of the box, and

CP A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m, to a hanging book with mass 3.00 kg. The system is released from rest, and the books are observed to move 1.20 m in 0.800 s. (a) What is the tension in each part of the cord?

A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. (a) Find its angular acceleration.

A playground merry-go-round has radius 2.40 m and moment of inertia 2100 kg•m^2 about a vertical axle through its center, and it turns with negligible friction. A child applies an 18.0-N force tangentially to the edge of the merry-go-round for 15.0 s. If the merry-go-round is initially at rest (b) How much work did the child do on the merry-go-round?

CP A stone is suspended from the free end of a wire that is wrapped around the outer rim of a pulley, similar to what is shown in Fig. 10.10. The pulley is a uniform disk with mass 10.0 kg and radius 30.0 cm and turns on frictionless bearings. You measure that the stone travels 12.6 m in the first 3.00 s starting from rest. Find (b) the tension in the wire.