138 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



PROBLEMS. 



92. Let it be assumed that the force required to propel a canal 

 boat is proportional to the velocity of the boat. A force of 50 

 pounds is required to maintain a velocity of 5 feet per second. 

 (#) Find the value of the coefficient by which the velocity of the 

 boat must be multiplied to give the frictional drag and specify the 

 unit in terms of which this coefficient is expressed, (b) Find the 

 velocity at which the boat would be propelled by a force of 36 

 pounds. (<:) Find the rate at which work is done by a force of 

 36 pounds in propelling the boat. Ans. (a) 10 pounds per 

 (foot per second). (b) 3.6 feet/second, (c] 129.6 foot-pounds/ 

 second. 



93. When a force of 50 pounds is applied to the above canal 

 boat the boat starts from rest and after some time reaches its full 

 speed of 5 feet per second. At a given instant the velocity of the 

 boat is 3 feet per second. At this instant : (a) Find the rate at 

 which work is done on the boat by the propelling force. (b) Find 

 the dragging force which is acting on the boat. (<r) Find the rate 

 at which work is dissipated in overcoming the friction of the water. 

 (d} Explain what is becoming of the difference between (a) and 

 (<:). Ans. (a) 1 50 foot pounds/second, (b) 30 pounds, (c) 90 

 foot-pounds/second. 



94. An electromotive force of 50 volts acts on a circuit of which 

 the resistance is 10 ohms. At a certain instant during the time 

 that the current is growing from zero to its full value the current has 

 an actual value of 3 amperes. At this instant : (a) Find the rate 

 at which the generator delivers work to the circuit, (b) Find the 

 dragging force in volts which is opposing the flow of the current 

 through the circuit, (c] Find the rate at which work is dissipated 

 in overcoming the resistance of the circuit, (d} Explain what is 

 becoming of the difference between (a) and (<:). Ans. (a) 150 

 watts, (b} 30 volts, (c) 90 watts. 



95. A vertical wire 3 meters long is moved sidewise, towards 

 magnetic east or west, at a velocity of 25 meters per second. 



