CHAP. 6]
WORK, ENERGY, AND POWER
from which
6.23
Power
77
777 kJ 97 kW 0:13 103 hp 8:0 s
In unloading grain from the hold of a ship, an elevator lifts the grain through a distance of 12 m. Grain is discharged at the top of the elevator at a rate of 2.0 kg each second, and the discharge speed of each grain particle is 3.0 m/s. Find the minimum-horsepower motor that can elevate grain in this way. The power output of the motor is change in KE change in PEG 12 m v2f v2i mgh t time taken m 1 2 2 2 9:0 m =s 9:81 m=s 12 m t 2 The mass transported per second, m=t, is 2.0 kg/s. Using this value gives the power as 0.24 kW. Power
Supplementary Problems 6.24
A force of 3.0 N acts through a distance of 12 m in the direction of the force. Find the work done. Ans. 36 J
6.25
A 4.0-kg object is lifted 1.5 m. (a) How much work is done against the Earth's gravity? (b) Repeat if the object is lowered instead of lifted. Ans. (a) 59 J; (b) 59 J
6.26
A uniform rectangular marble slab is 3.4 m long and 2.0 m wide. It has a mass of 180 kg. If it is originally lying on the ¯at ground, how much work is needed to stand it on end? Ans. 3.0 kJ
6.27
How large a force is required to accelerate a 1300-kg car from rest to a speed of 20 m/s in a distance of 80 m? Ans. 3.3 kN
6.28
A 1200-kg car going 30 m/s applies its brakes and skids to rest. If the friction force between the sliding tires and the pavement is 6000 N, how far does the car skid before coming to rest? Ans. 90 m
6.29
A proton m 1:67 10 27 kg) that has a speed of 5:0 106 m/s passes through a metal ®lm of thickness 0.010 mm and emerges with a speed of 2:0 106 m/s. How large an average force opposed its motion through the ®lm? Ans. 1:8 10 9 N
6.30
A 200-kg cart is pushed slowly up an incline. How much work does the pushing force do in moving the cart up to a platform 1.5 m above the starting point if friction is negligible? Ans. 2.9 kJ
6.31
Repeat Problem 6.30 if the distance along the incline to the platform is 7.0 m and a friction force of 150 N opposes the motion. Ans. 4.0 kJ
6.32
A 50 000-kg freight car is pulled 800 m up along a 1.20 percent grade at constant speed. (a) Find the work done against gravity by the drawbar pull. (b) If the friction force retarding the motion is 1500 N, ®nd the total work done. Ans. (a) 4.70 MJ; (b) 5.90 MJ
6.33
A 60-kg woman walks up a ¯ight of stairs that connects two ¯oors 3.0 m apart. (a) How much lifting work is done on the woman? (b) How much lifting work is done by the woman? (c) By how much does the woman's PEG change? Ans. (a) 1.8 kJ; (b) 1.8 kJ; (c) 1.8 kJ