Machinery's Handbook, 31st Edition
174 Friction Rolling Friction.— When a body rolls on a surface, the force resisting the motion is termed rolling friction or rolling resistance . Let W = total weight of rolling body or load on wheel, in pounds (newtons); r = radius of wheel, in inches (centimeters); f = coefficient of rolling re- sistance, in inches (centimeters). Then, resistance to rolling, in pounds (newtons) is given as: F r = W f / r Coefficient of rolling resistance varies with conditions. For wood on wood, f = 0.06 inch (0.152 cm) may be used; for iron on iron, 0.02 inch (0.051 cm); iron on granite, 0.085 inch (0.216 cm); iron on asphalt, 0.15 inch (0.381 cm); and iron on wood, 0.22 inch (0.559 cm). The coefficient of rolling resistance f is given in inches (or centimeters) and is not the same as the sliding or static coefficient of friction given in Table 1 and Table 2, in which m is a dimensionless ratio between frictional resistance and normal load. Various investiga- tors are not in close agreement on the true values for these coefficients and the foregoing values should only be used for the approximate calculation of rolling resistance. Simple Mechanisms Levers Types of Levers Examples
a
W l F L # = A pull of 80 pounds is exerted at the end of the lever, at W ; l = 12 inches and L = 32 inches. Find the value of force F required to balance the lever. F 32 80 12 32 960 30 pounds # = = = If F = 20; W = 180; and l = 3; how long must L be made to secure equilibrium? L 20 180 3 27 # = = W F L # Total length L of a lever is 25 cm. A weight of 400 N, supported at W ; l is 10 cm. Find the value of F . F 400 ( ) 10 ( ) 25 = ------------- = 160 N If F = 400 N, W = 900 lbs, and a = 1.5 m, what should L equal to secure equilibrium?
l
L
W
F
: : FW l L =
: : FW l L =
F L W l # # =
F L W l # # =
F L W l L W F W a # # =
F L W l L W F W a # # F W l = #
l W F F a W l F L W F L # =
F W l #
l W F F a
# #
# #
= + =
= + =
= + =
= + =
L
a
l
W
F
: : FW l L =
: : FW l L =
F L W l # # =
F L W l W l F L # # = = #
F L W l L W F W a # # =
F L W l L W F W a # # F W l =
l W F F a W l F L W F L =
F W l #
W F L
l W F F a
900 ( ) 1.5 ( ) 900– 400 = ------------- = 2.7 m
# #
# #
L
= − =
= − =
= − =
= − =
c
x
b
Let W = 20, P = 30, and Q = 15 lbs; a = 4, b = 7, and c = 10 in. If x = 6 in., find F . F 6 2043071510 73 3 1 lb s # # # = + + = Assuming F = 20 lbs in the example above, how long must lever arm x be made? x 20 2043071510 22 inches # # # = + + =
a
Q P
W
F
When three or more forces act on lever: F x W a P b Q c x F W a P b Q c F x W a P b Q c # # # # # # # # # # = + + = + + = + +
The above formulas are valid using metric SI units, with forces expressed in newtons, and lengths in meters. However, it should be noted that the weight of a mass W kilograms
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