‘ 
32 APPLIED MECHANICS 
Exercises IIIb. 
_ 1, A railway train has a speed of 30 miles per hour. How far will this train 
travel, after steam is shut off, under a resistance of 15 lbs. per ton? Also, what 
additional resistance, in lbs. per ton, must be applied to stop the train in a 
distance of 100 yards ? > Sit 
2. Through what distance must a force of 74 lbs. act on a body weighing 
20 lbs., in the direction of its motion, in order to change its velocity from 15 to 
25 feet per second ? ‘ 
3. What must be the magnitude of a force acting on a body weighing 50 lbs. 
through a distunce of 10 feet, in the direction of its motion, which will double 
the kinetic energy of the body, if the velocity when the force begins to act 
is 200 feet per minute? 
4. To draw a waggon weighing 10 tons up an incline 50 feet high requires 
the expenditure of 530 foot-tons of work. Ifthe waggon is liberated at the top of 
the incline, what speed, in miles per hour, will it have when it reaches the 
bottom? Assume that the frictional resistances are the same coming down as 
going up the incline. Further, if the brake is applied during the descent, and 
the velocity acquired at the foot of the incline is 25 miles per hour, how many 
foot-tons of work have been absorbed by the brake ? 
5. How far will a train, moving at the rate of 40 miles per hour, run up an 
incline of 1 in 150 after steam is shut off? In addition to the resistance of 
gravity there is a mean resistance of 12 lbs. per ton in the direction opposite to 
that of the motion. 
6. A vehicle weighing 4 tons is proceeding at the rate of 10 miles an hour 
along a level road; the pull on it is suddenly stopped: supposing the whole 
resistance equivalent to 500 lbs. applied to the rim of one of the wheels 4 feet 
in diameter, calculate how far the vehicle will run before stopping. [Inst.C.E.] 
7. A fly-wheel alters in speed from 99 to 101 revolutions per minute when 
its kinetic energy alters by the amount of 500,000 ft.-lbs. What is its 
moment of inertia? What is its kinetic energy when making 1 revolution per 
minute ? [Inst.C.E.] 
8. A fly-wheel of a shearing machine has 150,000 ft.-lbs. of kinetic energy 
stored in it when its speed is 250 revolutions per minute; what energy does 
it part with during a reduction of speed to 200 revolutions per minute? If 
82 per cent. of this energy given out is imparted to the shears during a stroke of 
2 inches, what is the average force due to this on the blade of the shears? [B.E.] 
9. A fly-wheel when running at 90 revolutions per minute has a stored 
energy of 3,000,000 ft.-lbs. By reason of additional load it is slowed down to 
86 revolutions per minute in two seconds. By how much will the stored energy 
be reduced, and what is the average HP. produced by the slowing down of the 
fly-wheel ? [Inst.C.E.] 
10. A machine is found to have 300,000 ft.-Ibs. stored in it as kinetic energy 
when its main shaft makes 100 revolutions per minute. A similar machine (that 
is, made to the same drawings but on a different scale) is made of the same 
material but with all its dimensions 20 per cent. greater ; what will be its store 
of kinetic energy at 70 revolutions per minute? If when at 70 revolutions 
per minute energy is being stored for a short time at the rate of 1 horse-power, 
how does the speed alter during this time? [B. E.] 
11. When the fly-wheel of a certain traction engine lessens in speed from 
150 to 140 revolutions per minute there is a loss of kinetic energy (on the 
motion of the whole engine as well as the fly-wheel) of 25,000 ft.-lbs. If 
the speed is 160 revolutions per minute, how far will the engine travel up 
an ascent of 1 in 100, before coming to rest, if engine and truck together weigh 
30 tons, and there is a constant frictional resistance on a level road of 20 Ibs. to 
the ton? [B.E.] 
12. An electric tram-car has a total weight of 10 tons. The driving axle and 
driving wheels weigh 1050 lbs., and the other axle and its wheels weigh 650 Ibs. 
Each axle with its wheels has a radius of gyration of 1l inches. The diameter 
of the wheels at the tread is 30 inches. What is the total kinetic energy of this 
car in foot-tons when it is travelling at 15 miles per hour? What fraction of 
the total energy of the car is due to the rotation of the wheels and axles ? 
