Page 94 - Mechanical Engineer's Data Handbook

APPLIED MECHANICS 83

2.4.5 Three mass vibration system

Natural frequency on = (two values)
A2 - k,k, (- + - -)]
1
1
1
+
m1m2 m2m3 mlm3
If m, is infinite it is equivalent to a wall, hence:

2.7 Friction

2.7. I Friction laws
For clean dry surfaces the following laws apply
approximately. The friction force is proportional to
the perpendicular force between contacting surfaces
and is independent of the surface area or rubbing
speed. This only applies for low preqym and speeds.
There are two values of friction coefficient, the ‘static’ Angle of repose 4 = tan-’fi; or when fi= tan 4
value when motion is about to commence, and the If the angle of the plane is greater than the angle of
‘dynamic’ value, which is smaller, when there is repose, the body will slide down the plane.
motion.
Force horizontal
I
F= Wtan(0+4) (up plane)
t
F= Wtan(0-4) (down plane)

F
Coefficient of friction p = -
N

2.7.2 Friction on an inclined plane
2.7.3 Rolling friction
Force parallel to plane :
The force to move a wheeled vehicle F,=prN
F = W@ cos 0 +sin 0) (up plane) where: pr = rolling coefficient of resistance, N =wheel
F = W(p cos 0 -sin 0) (down plane) reaction.