Machinery's Handbook, 31st Edition
176
Simple Mechanisms Inclined Plane—Wedge
W = weight of body
If friction is taken into account, then Force P to pull body up is:
l
P
h
cos sin P W = µ α+ α ^ h
W Q
Force P 1 to pull body down is:
b
cos sin P W 1 = µ α− α ^ h
Neglecting friction:
Force P 2 to hold body stationary: sin P W 2 = ^ h in which μ is the coefficient of friction. cos α−µ α
sin P W l h W W P h l Q W l b W # = = = = = =
sin
α
# #
P P
cosec
=
α
#
α
cos
α
# #
W = weight of body
W = weight of body
P
P
h
W Q
b
W Q
Neglecting friction: cos sin sin cos cos cos P W W P Q W # # # β α α β = = =
With friction: tan z =
Neglecting friction:
With friction:
Coefficient of friction
P W b h W W P h b P Q W W # # # = = = = = =
tan Coefficient of friction µ z =
tan
α
# #
µ
cot sec
α
cos sin P W # =
h
− + ^ ^
β z α z
β α β + ^ h
tan P W =
α
α z + ^ h
cos
α
h
P
b
P
b
h
Q
Q
Q
Q
l
Neglecting friction:
Neglecting friction:
P Q l b Q Q P b l P 2 2 2 2 1 # # # # = = =
tan cot P Q h b Q Q P b h P 2 2 2 2 1 # # # # = = = = With friction: Coefficient of friction = μ = tan φ . tan P Q 2 α z = + ^ h α α
sin
α
csc
α = With friction: Coefficient of friction = μ . cos sin P Q 2 = µ α+ α ^ h
F
Force Moving Body on Horizontal Plane. — F tends to move B along line CD ; Q is the component which actually moves B ; P is the pressure, due to F , of the body on CD . cos Q F P F Q 2 2 # α = = −
P
Q B
C
D
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