Page 67 - Fisika Terapan for Engineers and Scientists

Problems 267

*90. The power supplied to an electric circuit decreases exponen- that the descending water delivers to the wheel? Assume that
tially with time according to P P e t/ , where P the water flowing onto the top of the wheel has roughly the
0
0
2.0 W and 5.0 s are constants. What is the total energy same speed as the wheel and exerts no horizontal push on the
supplied to the circuit during the time interval 0 t 5.0 s? wheel. [Hint: The kinetic energy of the water is the same
During 0 t ? when the water enters the bucket and when it spills out (since
*91. Each of the two Wright Cyclone engines on a DC-3 airplane the speed of the bucket is constant); hence the kinetic energy
generates a power of 850 hp. The mass of the loaded plane is of the water does not affect the answer.]
10900 kg. The plane can climb at the rate of 260 m/min.
When the plane is climbing at this rate, what percentage of
the engine power is used to do work against gravity?
*92. A fountain shoots a stream of water 10 m up in the air. The
base of the stream is 10 cm across. What power is expended to
send the water to this height?
*93. The record of 203.1 km/h for speed skiing set by Franz Weber
at Velocity Peak in Colorado was achieved on a mountain slope
inclined downward at 51 . At this speed, the force of friction
(air and sliding friction) balances the pull of gravity along the
slope, so the motion proceeds at constant velocity.
(a) What is the rate at which gravity does work on the skier?
Assume that the mass of the skier is 75 kg. FIGURE 8.23 An overshot waterwheel.
(b) What is the rate at which sliding friction does work?
Assume that the coefficient of friction is 0.03. *99. Suppose that in the undershot waterwheel shown in Fig.
k
8.24, the stream of water against the blades of the wheel has a
(c) What is the rate at which air friction does work?
speed of 15 m/s, and the amount of water is 30 liters per
*94. A windmill for the generation of electric power has a propeller second (or 30 kg per second). If the water gives all of its
of diameter 1.8 m. In a wind of 40 km/h, this windmill delivers kinetic energy to the blades (and then drips away with zero
200 W of electric power. horizontal speed), how much mechanical power does the
(a) At this wind speed, what is the rate at which the air car- water deliver to the wheel?
ries kinetic energy through the circular area swept out by
3
the propeller? The density of air is 1.29 kg/m .
(b) What percentage of the kinetic energy of the air passing
through this area is converted into electric energy?
3
*95. A small electric kitchen fan blows 8.5 m /min of air at a speed
3
of 5.0 m/s out of the kitchen. The density of air is 1.3 kg/m .
What electric power must the fan consume to give the ejected
air the required kinetic energy?
*96. The final portion of the Tennessee River has a downward
slope of 0.074 m per kilometer. The rate of flow of water in
3
the river is 280 m /s. Assume that the speed of the water is
constant along the river. How much power is dissipated by
FIGURE 8.24 An undershot waterwheel.
friction of the water against the riverbed per kilometer?
*97. Off the coast of Florida, the Gulf Stream has a speed of
3
3
4.6 km/h and a rate of flow of 2.2 10 km /day. At what *100. (a) With its engines switched off, a small two-engine airplane
rate is kinetic energy flowing past the coast? If all this kinetic of mass 1100 kg glides downward at an angle of 13 at a
energy could be converted into electric power, how many speed of 90 knots. Under these conditions, the weight of
kilowatts would it amount to? the plane, the lift force (perpendicular to the direction of
*98. Figure 8.23 shows an overshot waterwheel, in which water motion) generated by air flowing over the wings, and the
flowing onto the top of the wheel fills buckets whose weight frictional force (opposite to the direction of motion)
causes the wheel to turn. The water descends in the buckets to exerted by the air are in balance. Draw a “free-body” dia-
the bottom, and there it is spilled out, so the ascending buck- gram for these forces, and calculate their magnitudes.
ets are always empty. If in a waterwheel of diameter 10 m the (b) Suppose that with its engine switched on, the plane
amount of water carried down by the wheel is 20 liters per climbs at an upward angle of 13 at a speed of 90 knots.
second (or 20 kg per second), what is the mechanical power Draw a “free-body” diagram for the forces acting on the