Contact with friction
Body of known weight W is maintained in equilibrium by
two squeezing fingers as shown
Draw the free body diagram:
Contact with friction
Body of known weight W is maintained in equilibrium by
two squeezing fingers as shown
N
F
W
F
N
Which forces if any can be determined
from equilibrium?
Gr Normal forces
Pi
Friction forces
Bl
Ye
Normal and friction forces
No forces
Contact with friction
It is possible to support the member in a horizontal position with
fingers on top and bottom sides as shown.
True
False
Pi
Gr
Contact with friction
Consider supporting the member in a horizontal position with
fingers on top and bottom sides as shown
Draw the free body diagram:
Contact with friction
Which one is the correct FBD?
F2
W
Pi
N2
F2
N1
F1
W
Gr
N2
Ye
W
F2
N1F1
W
Bl
N2
N1
F1
N2
N1
F1
Contact with friction
Which one is the correct FBD?
Pi
N2
x
F2
d
W
ΣFx = 0:
L
N1
F1
F2 = F1
ΣFy = 0: W+N2-N1= 0
ΣMc = 0 : -Fd –N2(L-x) + N1L = 0
x = (Fd –WL)/N2 ⇒ x > 0 for Fd >WL
On a verge of slipping F= µsN2 and µs >WL / N2 d
Contact with friction
Consider supporting the member in horizontal position with
fingers on both sides as shown
N
N
F
W
F
forces distributed over the area of
contact produce net vertical force F
Contact with friction
Consider supporting the member in horizontal position with
palms at the ends against a couple that twist the member
What do palms acting at the ends of the member exert on it?
Draw the free body diagram:
Contact with friction
Consider supporting the member in horizontal position with
palms at the ends against a couple that twist the member
N
MF
F
F
W
Sketch forces distributed over the area of contact
that produce the net force F and couple MF
N
MF
end face
Contact with friction
N
MF
F
F
forces distributed over the area of
contact producing net vertical force F
W
N
MF
forces distributed over the area of
contact producing net couple MF
or
or
Contact with friction
P
B
It is possible to support the member in a horizontal position with
fingers on front and back sides as shown:
True
False
Pi
Gr
Contact with friction
Consider supporting the member in horizontal position with
fingers on front and back sides in two different ways
P
P
B
Which of the two grips allows for the larger transverse force P to be
balanced assuming same normal force exerted by fingers?
Gr Grip A can support more transverse load than Grip B
Pi
Grip B can support more transverse load than Grip A
Bl
The two grips can support the same transverse load
A
Contact with friction
Try supporting the member in horizontal position with
fingers on front and back sides in two different ways
Why can you balance it with grip B, but not with grip A?
W
W
B
A
Contact with friction
Consider supporting the member in horizontal position with
fingers on front and back sides in two different ways
W
W
B
Draw the free body diagrams:
A
Contact with friction
W
+-N
W
2F
2MF
Contact with friction
+-N
W
W
2MF
2F
Sketch forces distributed over the area of contact that could produce F and MF :
net frictional force F
net frictional couple MF
Contact with friction
+-N
W
W
2MF
2F
Distribution of forces producing net force and couple:
net frictional force F
net frictional couple MF
Contact with friction
Consider supporting the member in horizontal position with
fingers on front and back sides as shown
W
+-N
W
2 MF
2F
Sketch forces distributed over the area of contact that could produce F and MF :
net frictional force F
net frictional couple MF
Contact with friction
Consider supporting the member in horizontal position with
fingers on front and back sides as shown
W
+-N
W
2F
Distribution of forces producing net force and couple:
net frictional force F
net frictional couple MF
2 MF
Contact with friction
W
W
B
• contact areas A and B have the same vertical dimension
• contact area B has larger horizontal dimension that A
Vertical forces in grip B are farther apart – create larger couple for
same normal force exerted by fingers
A
Contact with friction
Ballerina wears point shoes while executing a pirouette
(to decrease frictional moment by making the area of contact smaller)
Contact with friction
Consider supporting the member in horizontal position with
two fingers at the end as shown
P
How can fingers apply a balancing couple?
Gr friction forces can create a couple; normal forces cannot
Pi
normal forces can create a couple; friction forces cannot
Bl
Ye
both normal and friction forces can create a couple
either normal or friction forces can create a couple, but not both
Contact with friction
Consider supporting the member in horizontal position with
two fingers at the end as shown
P
FBD if only friction forces were to provide a couple:
P
Contact with friction
If friction forces are neglected, do both fingers exert identical
normal forces to keep the member in equilibrium?
P
True Gr
False Pi
Contact with friction
If friction forces are neglected, to produce a couple, net forces from above and below
must have different magnitudes and must not act on the same line of action
P
P
P
W
W
P
P
W
N1
W
N2
Contact with friction
Hand wrapped around the member keeps it in equilibrium against the
twisting couple applied at its end
Sketch forces distributed over the area of contact
that keep the member in equilibrium
=
T
Contact with friction
Hand wrapped around the member keeps it in equilibrium against the
twisting couple applied at its end
T
frictional forces distributed over the area of contact
are producing a resultant couple equal to that twisting the member
T
resultant
Contact with friction
Hand wrapped around the member keeps it in equilibrium against
an axial force applied at its end
Sketch forces distributed over the area of contact
that keep the member in equilibrium
P
Contact with friction
Hand wrapped around the member keeps it in equilibrium against
an axial force applied at its end
P
frictional forces distributed over the area of contact
are producing a resultant force equal to that applied to the member
P
resultant
Contact with friction
Hand wrapped around the member keeps it in equilibrium against an
bending couple applied at its end
Sketch forces distributed over the area of contact
that keep the member in equilibrium
=
M
Contact with friction
Hand wrapped around the member keeps it in equilibrium against an
bending couple applied at its end
M
forces distributed over the area of contact are producing a resultant
couple equal to that applied to the member
M
resultant
Contact with friction
Rod can be completely supported with respect to all possible loads by
hand exerting normal and friction forces
V
P
Transverse Force
Axial Force
T
M
Bending Couple
Twisting Couple
Contact with friction
What if very little friction forces can be exerted on surface:
what forces or couples cannot be provided by the support?
V
P
Transverse Force
Axial Force
T
M
Bending Couple
Twisting Couple
Contact with friction
If very little friction forces can be exerted on surface,
no axial force and no twisting couple could be supported
V
P
Transverse Force
Axial Force
T
M
Bending Couple
Twisting Couple