192 MOTION UNDEE CONSTANT FOECES 



7. A body was observed to take t seconds in falling past a hatchway to the 

 bottom of a hold h feet deep. Prove that it fell 



and struck with velocity 



- 4- - gt feet per second. 

 t 2 



8. A chain 12 feet long hangs from its upper end. If this be released, find 

 the time the chain will take in passing a point 60 feet below the initial position 

 of the highest point. 



9. A body whose mass is 5 pounds, moving with a speed of 160 feet per 

 second, suddenly encounters a constant resistance equal to the weight of 

 ^ pound, which lasts until the speed is reduced to 96 feet per second. For 

 what time and through what distance has the resistance acted ? 



10. Two wagons, coupled together, are pulled along a horizontal track by 

 a steady force, and move over 100 feet in the first ten seconds from rest. The 

 rear wagon is then uncoupled, and it is found that at the end of the next ten 

 seconds the interval between the two wagons is 150 feet. Compare the masses 

 of the two wagons, all resistance being neglected. 



11. A balloon of weight W is rising with acceleration /. If a weight w of 

 sand be emptied out of the car, find the increase in the acceleration of the 

 balloon, neglecting the resistance of the air and the buoyancy of the sand. 



MOTION ON AN INCLINED PLANE 



158. Suppose we allow a particle to slide down an inclined 

 plane, the contact between the two being supposed perfectly 



smooth. If m is the mass of the par- 

 ticle, the forces acting on it are its 

 weight mg, and the reaction R normal 

 to the plane. The component down the 

 plane is mg sin a, so that the particle 

 moves with uniform acceleration g sin a. 

 We can obtain the distance described 



FIG. 105 



in the time t from the usual formula. 



If the particle starts from rest, the distance described in time t 

 is ^ g sin a t 2 . 



159. Suppose that through a point we have a great number of 

 smooth wires on which smooth beads are free to slide. Let these" 



