ba 
* 
418 APPLIED MECHANICS 
tively. Find the resultant force on the axis when the disc is making 200 turns — 
per minute, and determine the angular position and magnitude of a mass place 
at 2°5 feet radius which will make the force on the axis zero at all speeds, E) 2 
[Inst.C.] 
3. A, B, and C are the centres of gravity of three masses revolving in the 
same plane about a centre O in that plane. OA=18 inches, OB=25 oe 
OC=15 inches, angle AOB=90°, angle BOC=120°. The weight of the C3 
mass is 5) lbs, Find the weights of the first and second masses, so that the — 
three masses may balance. a 
4, A locomotive wheel 6 feet in diameter is out of balance to the extent of 
200 lbs. at a radius of 1 foot. The load on the wheel, including its own wei 
is 7tons. What are the maximum and minimum pressures of the wheel on the 
rail, in tons, when the speed of the locomotive is 60'miles per hour? Draw for 
a complete revolution of the wheel a diagram to show the variation of pS 
pressure of the wheel on the rail. At what speed, in miles per hour, would the 
locomotive have to run to make the minimum pressure on the rail zero? iy 
5, A wheel weighing 2100 lbs. has its centre of gravity0°4 inch from its axis. The — 
wheel is mounted on a shaft which runs in two bearings 5 feet apart on opposite 
sides of the wheel, one bearing being 2 feet from the plane of revolution of the 
wheel. What are the forces on the bearings due to the centrifugal force or oj 
unbalanced wheel when the latter is making 200 revolutions per minute ? 
weight placed at a radius of 3 feet 6 inches in the plane of revolution of the 
wheel will balance it ? re 
6. The crank shaft of a gas-engine carries two fly-wheels A and B, the planes — 
of revolution of which are 3 feet 6 inches apart. The plane of revolution of the 
crank is between the wheels, and 1 foot 7 inches from the plane of revolution of 
A. The crank arms and crank pin are equivalent to a weight of 108 lbs. at a © 
radius of 10 inches in the plane of revolution of the crank. What weights 
at a radius of 2 feet, one on each wheel,-will balance the. crank? a 
7. The centrifugal force of an overhung crank is equal to that of a weight 
644 Ibs. at a radius of 1 foot. The crank shaft is supported on two bearings 
5 feet apart, the one nearest to the crank being at a distance of 1 foot 6 inches — 
from the plane of revolution of the crank. Find the forces on the bearings due 
to the centrifugal force of the crank when the speed of the shaft is 150 revolu- 
tions per minute. What weights placed at 2 feet 6 inches radius, one in each 
of two planes 2 feet 6 inches apart, between the bearings, and equally distant 
from them, will balance the crank? 
8. The following particulars relate to an ordinary inside cylinder locomotive. 
There are two cranks at right angles, the left-hand crank leading. Distance — 
between centre lines of cylinders, 25 inches. Stroke of pistons, 24 inches, 
Distance between planes of revolution of balance masses in wheels, 60 inches. 
The revolving parts which have to be balanced are equivalent to 700 Ibs. at the — 
centre of each crank pin. Find the weights of the masses and their angular — 
positions in relation to the cranks to balance the revolving parts, the centres of © 
gravity of the balance masses being at a radius of 32 inches. . 
9. A shaft, 10 feet span between the bearings, carries two weights of 10 lbs. 
and 20 lbs. acting at the extremities of arms 14 feet and 2 feet long respectively, 
the planes in which the weights rotate being 4 feet and 8 feet respectively fre 
the left-hand bearing, and the angle between the arms 60°. If the speed of 
rotation be 100 revolutions per minute, find the displacing forces on the two 
bearings of the machine. Moreover, if the weights are balanced by two addi- 
tional rotating weights, each acting at a radius of 1 foot, and placed in planes 
1 foot from each ‘bearing respectively, estimate the magnitude of the two. 
balance weights and the angles at which they must be set relative to the two 
arms. [Inst.C.E.] 
10. A, B, C, and D are the planes of revolution, taken in order, of four 
masses connected to a shaft. The weights of the masses are 10, 16, 12, and 20. 
Ibs. respectively, and the distances of their centres of gravity from the axis 
‘the shaft are 2, 1-5, 1, and 1:25 inches respectively. The angular positions of 
the radii from the axis to the centres of gravity of the masses with respect to 
reference radius OX are 0°, 90°, 150°, and 240° respectively. The distances of 
the planes B, C, and D from the plane A are 10, 18, and 32 inches respectively. 
The given masses are to be balanced by masses at 1 inch radius, one in a plan 
