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39.An electric motor turns a flywheel through a drive belt that joins a pulley on the motor and a pulley that is rigidly attached to the flywheel, as shown in Figure P10.39.  The flywheel is a solid disk with a mass of 80.0 kg and a diameter of 1.25 m.  It turns on a frictionless axle.  Its pulley has much smaller mass and a radius of 0.230 m.  If the tension in the upper (taut) segment of the belt is 135 N and the flywheel has a clockwise angular acceleration of 1.67 rad/s2, find the tension in the lower (slack) segment of the belt.

Figure P10.39

Section 10.8 Work, Power, and Energy in Rotational Motion

40.Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 60.0 kg, and a minute hand 4.50 m long with a mass of 100 kg.  Calculate the total rotational kinetic energy of the two hands about the axis of rotation.  (You may model the hands as long thin rods.)

41.In a city with an air-pollution problem, a bus has no combustion engine.  It runs on energy drawn from a large, rapidly rotating flywheel under the floor of the bus.  The flywheel is spun up to its maximum rotation rate of 4 000 rev/min by an electric motor at the bus terminal. Every time the bus speeds up, the flywheel

slows down slightly.  The bus is equipped with regenerative braking, so that the flywheel can speed up when the bus slows down.  The flywheel is a uniform solid cylinder with mass 1 600 kg and radius 0.650 m.  The bus body does work against air resistance and rolling resistance at the average rate of 18.0 hp as it travels with an average speed of 40.0 km/h.  How far can the bus travel before the flywheel has to be spun up to speed again?

42.The top in Figure P10.42 has a moment of inertia of 4.00 10–4 kg·m2 and is initially at rest.  It is free to rotate about the stationary axis AA'.  A string, wrapped around a peg along the axis of the top, is pulled in such a manner as to maintain a constant tension of 5.57 N.  If the string does not slip while it is unwound from the peg, what is the angular speed of the top after 80.0 cm of string has been pulled off the peg?

Figure P10.42

43.In Figure P10.43 the sliding block has a mass of 0.850 kg, the counterweight has a mass of 0.420 kg, and the pulley is a hollow cylinder with a mass of 0.350 kg, an inner radius of 0.020 0 m,  and an outer radius of 0.030 0 m.  The coefficient of kinetic friction between the block and the horizontal surface is 0.250.  The pulley turns without friction on its axle.  The light

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