Uploaded by Bahul Raina

Friction Notes

advertisement
2.1 INTRODUCTION
R
N
G
Force of
friction
f
W
f
W
P Direction of
impending motion
N
Fig. 2.1  
  
 
   2.1.1 Engineering Applications of Friction
 ­ € ‚
f
Impending motion
Static
fricton
fm
Dynamic friction
P
It is the angle made by the resultant () of the normal reaction () and
limiting force of friction ( ) and made with the direction of normal reaction.
is the resultant of normal reaction and force of friction .
=
2 2
is the angle of friction
tan =
or
= tan –1
N
R
P
f
W
It is ratio of limiting frictional force and the normal reaction.
The coefficient of friction,
=
= tan =     
N
f = N
Y
X
W cos Motion
W sin W
    
 







­

   
­
€
‚
‚
€
­     ­ €
‚    ‚ ƒ „
†‡†ˆ‰  Š‹
20 N
N
P sin 25°
25°
f
W
 
­
 Œ
Œ

 ­ŽŠ

ŽŠ
Œ
ƒ   
 ­€‚
ƒ„
ƒ„ † ‡
‡
‡
‡ˆ
ƒ„ † ‡‡ ­‰‡ ­‰
‡ €Š‹
‡
ƒ „
ƒ­„‡‰
‡‡ €Š‹‡ Œ Ž † ‘ ƒ„
ƒ„ † N
P
P sin P cos f
W

        ­­ n
N si
N
f
N cos Y
X
W

P
N
Y
X
W cos f
W sin W
 
 
s
N
P
co
Y
P sin X
P
W cos f
W sin W
P
P sin Y
N
P cos X
W cos f
W sin W
  P f
N
Y
X
W cos W sin W
    
P
Y
N
X
W cos f
W sin W
 
 ­    €‚
ƒ„ † „ ­­‡ €ˆ‰Š
P
N
Y
X
W cos f
W sin W


 €
ˆ ˆ  ‰ ‹


 
 
­€€
‚‚ ƒ „ „ † ‡

† s
co
N
P
in
Ps
Y
P
X
W cos f
W sin W

 


     
 
­   €
  5m
0.2
RR
fR
X
RF
fF
mg cos mg sin W = mg
m
0.5
0.5
m
‚  Y
ƒ ƒ„ †
†„‡
      
     
 ­  €  
   ­   ­
   € ‚ ƒ €  ‚ „ € ‚
fB
B
B
L/2
L
W
fA
A
O
RA
RB
      ­€­­‚ ƒ„ ƒ†
‡ˆ ˆ ‰ Š
B
RB
300 N
fA
A
60°
RA
„ ƒ ‹ ­ Š
Œ ‡ Ž
‘ ’ “ ‘ ’    ­‚ ƒ” •†
B
RB
10 m
5m
6m
20 N
fA
A
RA
O
8m
   
 ­
   
€ 

‚ƒ„ ‚ † ‚ ‚ ‚ ‚
‚ ‚ ‚ ‚ ‚‡ ‚ ‚‚ ‚ ‚‚ ‚
‚ ˆ
‰Š‹ŒŠ†Ž  ‘’
fB
B
RB
l
x
1.5W
W
l/2
fA
45°
A
O
RA



   
  
  
  ­
­
€

‚ €ƒ    
 
B
RB
3.5
m
3m
7m
800 N
600 N
fA
60°
A
O
RA
­€
‚
‚
­€
‚
‚ ƒ ‚„ ‚‚‚ ‚„
­€
‚
‚ ƒ † ƒ „ ‚„
‚
„
‡
‚
ƒ­ †ƒ €  „ ˆ

‚
   ‰ Š   
    
   ­
€‚ ­

‚€ ‚ ­

 ­
ƒ  
Y
R1
f1
N1
W
X
R2
N2
R2 cos ( + )
f2
R2 sin ( + )
R2 sin ( + )
f2
Y
R2 cos ( + )
R2
N2
P
X
R3
N3
Motion
f3



­
€
‚ ‚€
€
‚ €
ƒ„  ­ †€€‡ˆ„ €‰
Š„ˆŠ
­
€ˆŠ
 ‹ ˆ
€
 ‚ €
†€€‡
€‰
€
‹‰
‹‰ €‰‚ ‹‰
€
  ­€ €‚
ƒ
„
„
ƒƒƒ†ƒƒƒ†ƒƒƒ† ƒ
ƒ†€ ††ƒ ‡†ˆ€ € ƒ† ƒ
 ˆƒ†ƒƒ†ƒ† ‡†ƒƒ†ƒƒ† ‰

Š ‡ ƒƒ†ƒ‹ŒŽ
‡ ƒ ‰‹ŒŽ
‘ ƒƒ† ƒ‹Œ’Ž
€ƒ†€ ‹ŒŽ
Driver
Slack side
Follower
T2
r2
r1
Tight side
T1
 ­
€‚
 ‚
‚
ƒ ­‚
 ­­‚ ‚„‚­
€­‚
d
r
T1
T2
†
ƒ­ ‡€­ ‡ €­‚
ˆ  ‚
 ­ ‚ ‚ ‰‚
 
Š 
­‚
‡ ‚

ˆ ­‚
0.9155 N-m
Ans.
Example 2.14:
 
  ­€ 
€‚ ƒ„  
Solution: € ‚ † ‰„
‚
‡ˆ
‚ ‡
25 kW Ans.
Example 2.15:
„‡  „
 ˆ   Š‹
 €  Œˆ
 ˆƒ„ 
 Solution: Ž
 
‡ ‡
ˆ
Š
‘ˆ
‡‡
‡
ˆ
1.054 kN.m
Ans.
Example 2.17:        
  ­ € 
‚‚ ­
    €  ‚ƒ 
  €ƒ   „ 
‚„      
†‡ˆ ‡­‰ ƒ‚‚‚Š
0.5
m
T2
T1
‹„ Solution:
‚
‚
‚‚ ‚
Œ
Ž   „‘‘‘Œ‘‚Œ
1562.2 N
Ans.
Example 2.18: ‚‚ € „   „  „ €€  ­ 
’  “€ „€     € ’  ’ “ƒ €   ‚”   € „’  €€ ‚‚“
†‡ˆ ‡­‰ ƒ‚‚‚Š

    
­€  €‚ ƒ„   
­  ƒ„„ 
  ƒ„  ­†
­ ­    †‡ ­ ‡
 ˆ
   ‰
‚  
R
W
P
p
dm


 


­€ ‚ƒ ­ ­ ‚ƒ
‚ƒ ‚ƒ ‚ƒ ‚ƒ ‚ƒ „
„
‚ƒ „
„
‚ƒ „
„
‚ƒ „
„
  
    ­  € ­ ‚ ƒ „
† ‡  † €ˆ ‰Š
‹
Œ Ž‘Œ’
‡
‹­
“ 
‰ ‰ ‘”
–Ž”
•Œ–ŽŽ–
Download