294 APPLIED MECHANICS 
friction of the water in the pipes will increase the resistance, and the line 
H,J will not be parallel to A,B,. To stop the downward motion, the — 
steam under the piston is shut in when the piston reaches the point M, 
and the resistance then increases, as shown by the line JE,K,, due to the 
compression of the steam on the lower side of the piston. In constructing 
the curve JE, K,, it must be remembered that while the steam below the 
piston is being compressed the steam above is expanding, and this must 
be allowed for, so that JE,K, may show the effective increase in the 
resistance. The velocity curve A,L,B, is determined as before. 
During the up stroke the steam above the piston is exhausted into 
the condenser. To prevent damage to the cylinder in the event of the 
prearranged stroke being exceeded, there are buffer beams against which 
the cross-head strikes. i 
Exercises XVIIa. 
1. An effort-space diagram is drawn to the scales, 1 inch to 60 Ibs. and 1 
inches to 1 foot. The length of the diagram is 2°3 inches, and its area is 2°4 
square inches. How many ft.-lbs. of work does the area of the diagram repre- 
sent, and what is the space average of the effort ? F 
2. A body weighing 80 Ibs. is moved from rest in a horizontal direction b 
an effort which varies uniformly from 112 lbs. at the beginning to 40 lbs. when 
the body has moved 8 feet. There is a uniform horizontal resistance of 60 Ibs. 
Represent this by a diagram to the scales, 1 inch to 50 lbs., and 1 inch to 2 feet. 
Calculate the kinetic energy and the velocity of the body when it has moved 
8 feet. Find also the maximum velocity. 
3. In an effort-time diagram, the effort being the unbalanced effort, the 
length of the diagram is 5 inches, and represents 30 seconds. The scale for the * 
effort is 1 inch to 100 lbs., and the area of the diagram is 12 square inches. If 
the weight of the body upon which the effort acts is 5 tons, what is the increase 
in its velocity, in miles per hour, in the time represented by the length of the 
diagram ? 
4. The pressure on the piston of a direct acting steam-engine is 150 lbs. per 
square inch for the first three-tenths of the stroke, and for the remainder of the 
stroke the pressure varies inversely as the distance of the piston from the be- 
ginning of the stroke. Draw on the same base, (a) the pressure-space diagram, 
(6) the pressure-time diagram, assuming an infinite connecting-rod,(c) the pressure- 
time diagram, taking the length of the connecting-rod twice the stroke of the 
piston. Find the mean pressure in lbs. per square inch of piston from each 
diagram. Assume that the crank is rotating at a uniform speed. ee 
5. A certain acceleration diagram on a time base has an area of 2-1 square 
inches. The base is 3°5 inches long, and represents 17°5 seconds. The accelera- 
tion scale is 1 inch to 5 feet per second per second. If the velocity is 8 feet per 
second at the beginning, what is the velocity at the end of the 17-5 seconds? ~~ 
6. In a diagram representing the unbalanced effort on a body weighing 800 
Ibs., the effort scale is 1 inch to 100 lbs, If the effort curve is also the accelera- 
tion curve, and the acceleration scale is x inches to 10 feet per second per second, 
find x. : ; 
7. The tangent at a certain point of a certain velocity curve on a time base is 
inclined at 35° to the base (tan. 35°=0°7). If the time scale is 1 inch to 5 
seconds, and the velocity scale is 1 inch to 20 feet per second, what is the 
acceleration in feet per second per second at the point considered. 
8. The area of an acceleration diagram on a space base was measured with a 
planimeter and found to be 7°85 square inches. The base ON of the diagram was 
4 inches long, and represented 20 feet. The acceleration scale was 1 inch to 10 
feet per second per second, and the velocity at O was 2 feet per second. 
Calculate the velocity at N. 
9. At a particular point on the curve of a velocity-space diagram the inclina- 
tion of the tangent is 30°. The ordinate of the point represents a velocity of 
feet per second, and the sub-normal measures 1°35 inches, If the distance scale 
