292 APPLIED MECHANICS 
(2) A body weighing 1 ton is-lifted vertically by a rope, there being 
a damped spring balance to indicate the pulling force F of the rope. 
There is a constant frictional resistance of 1000 lbs. to the motion of the 
body. When the body has been lifted « feet from its position of rest, 
the pulling force in Ibs. is automatically recorded, and is given in the — 
second column of the table below. It is required to find the velocity » of 
the body in feet per second for the given values of «, also the time ¢ in 
seconds to rise the distance «. 
. u < Increase | 
% ae bg ap ou Total | Velocity Tim ‘ime 
Pal ea bro ch phen eta Kinetic (). # | pices ae 
(xe the: (P). during during Energy, | Feet per , Interval. | Start (¢). 
Feet, Lbs. | Interval. | Interval. K. Sec. Sec. Sec. 
Ft.-lbs. 
0 5580 2340 p 0 0 ; 0 | 
10 | 5450 | 2210 | 2275 | 58,75) | 99,750| 2557 | 0782 | ong 
20 5260 2020 1900 19.000 48,900 | 35°53 0-256 Ti 
30 5020 1780 1675 16.750 62,900 | 42°52 0-221 137 
40 4810 1570 1465 14.650 79,650 | 47°85 0:200 1°59 
50 4600 1360 1278 12.750 94,300 | 52-07 0'186 179 
60 4430 1190 1110 11100 107,050 | 55°48 0176 1:97 
70 4270 1030 ? 118,150 | 58:28 2°15 
Unbalanced effort, P = F — (2240 + 1000) = F — 3240, 
The mean value of P during any interval is half the sum of the values 
of P at the beginning and end of that interval. 
The increase in the kinetic energy of the body during any interval is 
the work done by P 
during that interval, _%°° wm? es fe: 
namely, the mean 3 alae $ ‘ 
value of P during the s”°°° 1% meat Pog 
interval multiplied by x at See ehne-——t40 N.. os 
10. ae VN phe 3 8 
K, the total kinetic S j599 VA a 30 J Lee 
energy in the body at 5 s — 
the end of anyinterval, "y 1000 < 208110 & 
is the sum of all the in- /: fo 2 & 
terval increases of kin- KR s00-t/, 10 §}.0'5 
etic energy up to and “8 = 
including thatinterval. > ° ie So ad se 0 o—to 
9x 3F-2K Doshece (2c) in Feet. 
v= 'Y = oa10 7. Fia. 457, 
The time taken over any interval is 10, the distance moved, divided — 
by the mean velocity during the interval. The mean velocity during an 
interval is taken as half the sum of the velocities at the beginning and 
end of that interval. 
The time taken from the start to the end of any interval is the sum 
of all the interval times up to and including that interval. 
The results are shown plotted on a distance base in Fig, 457. 
