RT, ACCELERATION, AND VELOCITY DIAGRAMS 295 
is 1 inch to 10 feet, what is the acceleration, in feet per second per second, at the 
position considered ? 
40. An electric street car was found to have moved from rest 66, 245, 490, 
and 750 feet in 5, 10, 15, and 20 seconds respectively from the start. Construct 
- On a time base the displacement, velocity, and acceleration curves, and state the 
velocities in miles per hour, and the accelerations in miles per hour per second 
the times 5, 10, 15, and 20 seconds from the start. [Engineering News, Oct. 
_ 14, 1897, and Durley’s * Kinematics of Machinery,” p. 47.] 
_ ‘41. The angular position @ (in radians) of a rocking shaft at any time ¢ (in 
_ seconds) is measured from a fixed position. Successive positions at intervals of 
_ gy second have been determined as follows :— 
t 00 (002 |0°04 | 006 | 0°08 |0:10 | O12 (014 | 016 | 018 
6 0°106 | 0-208 | 0°337 | 0-487 | 0-651 | 0819 | 0-978 | 1-111 | 1-201 1-222 
Find the change of angular position during the first interval from t=0°0 
to t=0°02. Calculate the mean angular velocity during this interval in radians 
_ per second, and, on a time base, set this up as an ordinate at the middle of 
the interval. Repeat this for the other intervals, tabulating the results, and 
drawing the curve showing approximately angular velocity and time. In the 
same way find a curve showing angular acceleration and time. 
Read off angular velocity in radians per second, and angular acceleration in 
radians per second per second, when t=0°075 second. 
A wheel keyed to the shaft weighs 720 lbs., and has a radius of gyration of 
1°5 feet. What is the torque tending to fracture the shaft when t=0°16 
second? [B.E.] 
12. A weight W of 1000 lbs. is made to move along a horizontal plane. The 
frictional resistance R is uniform and equal to 100 lbs. The driving force P in 
lbs. varies uniformly, and is given by the formula P=Q(10-«), where x is the 
distance moved in feet from the starting point. Determine in each of the 
_ following cases (a) the distance moved in feet by W before coming to rest, (0) 
the um velocity of W in feet per second, (c) the distance in feet of W 
from the starting point when its velocity is a maximum, (d) the acceleration in 
feet on second per second when W is 2 feet from the starting point. Case I. 
Q=15; Case II. Q=20; Case ITI. Q=30. 
13. A body A weighing 1000 lbs. is moved horizontally by a force P Ibs. 
which is equal to 200 Ibs. for the first 2 feet, and afterwards varies according 
to the law Px=400, where « is the distance moved from the starting point. The 
frictional resistance R is constant, and equal to 100 lbs. Determine (a) the 
distance moved by A, in feet, before coming to rest ; (6) the maximum velocity 
of A, in feet per second; (c) the distance of A from the starting point, in feet, 
when its velocity is a maximum; (d) the acceleration, in feet per second per 
second, when A is 3 feet from the starting point. Plot P—R, and the velocity, 
on a space base. 
14. A body weighing 1610 lbs. is lifted vertically by a rope, there being a 
spring balance to indicate the pulling force F lb, of the rope. There is 
a constant frictional resistance of 740 lbs. to the motion of the body. When the 
body has been lifted x feet from its position of rest, the pulling force is automati- 
cally recorded as follows :— 
x 0 11 20 34 45 55 66 76 
F 4010 3915 3763 3532-3366 3208 3100 3007 
Using squared paper, find the velocity v feet per second for values of x of 10, 
30, 50, 70, and draw a curve showing the probable values of v for all values of x 
up to 80. In what time does the body get from z=45 tox=55? In what time 
does it get from «=0 to ~=75? [B.E.] 
