Contact with friction

Transcription

1 Body of known weight is maintained in equilibrium by two squeezing fingers as shown Draw the free body diagram:

2 Body of known weight is maintained in equilibrium by two squeezing fingers as shown N F F N hich forces if any can be determined from equilibrium? Gr Pi Bl Ye Normal forces Friction forces Normal and friction forces No forces

3 It is possible to support the member in a horizontal position with fingers on top and bottom sides as shown. True Pi False Gr

4 Consider supporting the member in a horizontal position with fingers on top and bottom sides as shown Draw the free body diagram:

5 hich one is the correct FBD? F 2 N 2 F 2 N 2 Pi N 1 F 1 Gr N 1 F 1 N 2 F 2 N 2 Ye N 1 F 1 Bl N 1 F 1

6 hich one is the correct FBD? Pi N 2 F 2 x d L N 1 F 1 ΣF x = 0: F 2 = F 1 ΣF y = 0: +N 2 -N 1 = 0 ΣM c = 0 : -Fd N 2 (L-x) + N 1 L = 0 x = (Fd L)/N 2 x > 0 for Fd >L On a verge of slipping F= µ s N 2 and µ s >L / N 2 d

7 Consider supporting the member in horizontal position with fingers on both sides as shown N N F F forces distributed over the area of contact produce net vertical force F

8 Consider supporting the member in horizontal position with palms at the ends against a couple that twist the member hat do palms acting at the ends of the member exert on it? Draw the free body diagram:

9 Consider supporting the member in horizontal position with palms at the ends against a couple that twist the member N N M F F F M F Sketch forces distributed over the area of contact that produce the net force F and couple M F end face

10 N N M F forces distributed over the area of contact producing net vertical force F F F M F forces distributed over the area of contact producing net couple M F or or

11 P B It is possible to support the member in a horizontal position with fingers on front and back sides as shown: True Pi False Gr

12 Consider supporting the member in horizontal position with fingers on front and back sides in two different ways P P B hich of the two grips allows for the larger transverse force P to be balanced assuming same normal force exerted by fingers? A Gr Pi Bl Grip A can support more transverse load than Grip B Grip B can support more transverse load than Grip A The two grips can support the same transverse load

13 Try supporting the member in horizontal position with fingers on front and back sides in two different ways hy can you balance it with grip B, but not with grip A? B A

14 Consider supporting the member in horizontal position with fingers on front and back sides in two different ways B A Draw the free body diagrams:

15 +-N 2F 2M F

16 +-N 2M F 2F Sketch forces distributed over the area of contact that could produce F and M F : net frictional force F net frictional couple M F

17 +-N 2M F 2F Distribution of forces producing net force and couple: net frictional force F net frictional couple M F

18 Consider supporting the member in horizontal position with fingers on front and back sides as shown +-N 2F 2 M F Sketch forces distributed over the area of contact that could produce F and M F : net frictional force F net frictional couple M F

19 Consider supporting the member in horizontal position with fingers on front and back sides as shown Distribution of forces producing net force and couple: +-N 2F 2 M F net frictional force F net frictional couple M F

20 B A 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

21 Ballerina wears point shoes while executing a pirouette (to decrease frictional moment by making the area of contact smaller)

22 P Contact with friction Consider supporting the member in horizontal position with two fingers at the end as shown How can fingers apply a balancing couple? Gr Pi Bl Ye friction forces can create a couple; normal forces cannot normal forces can create a couple; friction forces cannot both normal and friction forces can create a couple either normal or friction forces can create a couple, but not both

23 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

24 If friction forces are neglected, do both fingers exert identical normal forces to keep the member in equilibrium? P True False Gr Pi

25 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 P P N 1 N 2

26 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

27 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

28 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

29 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

30 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

31 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

32 Rod can be completely supported with respect to all possible loads by hand exerting normal and friction forces V P Transverse Force Axial Force M T Bending Couple Twisting Couple

33 hat 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 M T Bending Couple Twisting Couple

34 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 M T Bending Couple Twisting Couple