24 KINETICS OF A PARTICLE. [46. 



46. Exercises. 



(1) A stone weighing 200 Ibs. is raised vertically by means of a 

 chain running over a fixed pulley. Determine the tension of the chain : 

 (a) when the motion is uniform ; (t>) when the motion is uniformly 

 accelerated upwards at the rate of 8 ft. per second ; (c) when the accel- 

 eration is 32 ft. per second downwards. Neglect the weight of the 

 chain and the axle-friction of the pulley. 



(2) A railroad car weighing 4 tons is pushed by four men over a 

 smooth horizontal track. If each man exerts a constant pressure of 

 100 pounds, (a) what is the velocity acquired by the car at the end 

 of 5 sec. ? (^) what is the distance passed over in these 5 sec. ? 



(3) (a) Determine the constant force required to give a train of 90 

 tons a velocity of 30 miles an hour in 5 min. after starting from rest. 

 () How far does the. train go in this time ? (c) If the same velocity 

 is to be acquired at the end of the first mile, what must be the tractive 

 force of the engine ? 



(4) If in Atwood's machine (Fig. 5) the two masses are each 2 lbs. r 

 and an additional mass of i oz. be placed on one of these masses, how 

 long will it take this mass to descend 6 ft. ? (g= 32.2.) 



(5) If in Ex. (4) an additional mass of half an ounce be placed on 

 each of the 2 Ib. masses, how would the tension in the cord differ from 

 the tension in Ex. (4) ? 



(6) Solve the problem of Art. 45 when the inclined planes are rough,. 

 the coefficients of friction being fi lt ^. 



"(?) A mass of 5 Ibs. rests on a smooth horizontal table, and has a 

 cord attached which runs over a smooth pulley on the edge of the table. 

 If a mass of i Ib. be suspended from the cord, find the acceleration and 

 the tension of the cord. 



(8) A sleigh weighing 500 Ibs. is drawn over a horizontal road, the 

 coefficient of friction being -fa. Find the pull exerted by the horses 

 when the motion is uniform. 



(9) When the U.S.S. Raritan was launched she was observed to 

 pass in ii sec. over an incline of 3 40', 54 ft. long. Find the coeffi- 

 cient of friction. 



(10) A coaster, after coming down a hill, runs up another hill a dis- 

 tance of 200 ft. (from its foot) in 10 sec., when it stops. If the slope 

 of the second hill be 6, find the coefficient of friction. 



