190 TIIK PIHKCT-rrUHKNT MoTnl! CH. IX 



Returning to the case when the motors have the 

 lowest possible resistance, we can calculate how much of 

 the energy taken from the line is lost in the rheostat. 

 The total energy expended on the first step is 

 500 x 100 x 100 watt-seconds, or 369 x 10 4 foot-pounds, 

 per motor. This is expended in three ways. 



1. In accelerating the car. At the end of 100 seconds 

 the car is found to be moving at 41'5 feet per second; 



Wv* 



taking half the weight, we find the kinetic energy, - 



'-'.! 



to be 120 x 10 4 foot-pounds. 2. In heating the rheostat 

 and motor. The mean resistance during 100 seconds is 2'7 

 ohms. The energy used in heating is thus 199 x 10 4 foot- 

 pounds. 3. In overcoming friction. This involves exerting 

 a force of 242 pounds through a distance of 2,075 feet, 

 giving 50 x 10 4 foot-pounds. We can then construct a 

 table of energy expended for one motor, thus : 



Kinetic energy . . 120 x 10' foot-pounds 32-5 per cent. 

 Heating . . . 199 x 10' 54-0 



Friction . 50x10' 13-5 



Total . . 369x10' 100-0 



An inspection of Fig. 47 shows the influence of the 

 acceleration period upon the distance travelled in a given 

 time. If the distance travelled is considerable, the rate at 

 which the car speeds up will have but a small influence 

 on the distance covered in a given time ; but if the distance 

 is small, the time occupied in getting up speed becomes of 

 great importance. 



CASE II. Motors started and run in series. 

 The terminal tension on each motor is now 250 volts, and 



