148 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



to be 0.008 foot per second per second. After the boat has 

 gained a certain amount of velocity, say, 3 feet per second, the 

 drag of the water is f of 50 pounds, so that 30 pounds of the 

 propelling force is used to overcome the drag of the water and 

 the remainder, 20 pounds, is used to produce acceleration. 

 Therefore the acceleration is 0.0032 foot per second per second. 

 At the very start when the velocity of the boat is zero no work 

 is being done upon the boat. When the velocity of the boat 

 becomes 3 feet per second, the propelling force does work at the 

 rate of 150 foot-pounds per second; a portion of this power 

 is expended in overcoming the friction of the water, and the 

 remainder goes to increase the kinetic energy of the moving boat. 

 The portion of power which is used to overcome the friction of 

 the water is found by multiplying the velocity of the boat by the 

 portion of the force which is used to overcome the frictional drag. 

 This gives 90 foot-pounds per second. The portion of the power 

 which goes to increase the kinetic energy of the boat is found by 

 multiplying the portion of the propelling force which produces 

 acceleration by the velocity of the boat. This gives 60 foot- 

 pounds per second. 



(&) An electric generator has an electromotive force of 50 volts 

 and it acts upon a circuit of which the resistance is 10 ohms, so 

 that the steady current that may be produced by the electro- 

 motive force is 5 amperes according to Ohm's law. The induc- 

 tance of the circuit is, say, 2 henrys. At the instant when the 

 electromotive force begins to act on the circuit the current is 

 zero, and all of the electromotive force is used to cause the cur- 

 rent to increase so that the rate of increase of the current is 25 

 amperes per second, according to equation (49). After the cur- 

 rent has reached a value of, say, 3 amperes, a portion of the 

 electromotive force of the generator is used to overcome the 

 resistance of the circuit and a portion is used to cause the current 

 to increase. The electromotive force which is used to overcome 

 the resistance is found by multiplying the resistance of the circuit 

 by the current which gives 30 volts, and the remaining 20 volts 



