Contact forces and Laws of Motion
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8/17/2019 Contact forces and Laws of Motion
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ω.
.
( ) ( )2
2
2
ˆˆ 2 ;
ˆ0, 0
( ) ;
a r r r r r
r r a r r
M dT r r dm dm dr dr
θ θ θ θ
θ ω
ω ρ
= − + +
= = = = −
= − = =
dm
dr r r̂
θ̂
T (r )
r
M ω 2 L/ 2
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:
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• µµµµ µµµµ
•
µµµµ
•
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8/17/2019 Contact forces and Laws of Motion
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() .
µ1s, µ1k respectively and those between
the surface of the two
blocks are µ2s, µ2k respectively. The
lower block is pulled by a force F which is
increased from zero till the blocks are in contact. Plot the
accelerations of both the
blocks as functions of F .
( )max 1 M
sF f M m g µ = = +
mµ2s, µ2k µ2s > µ1sµ2k >
µ1k
= −
No motion:
Starts sliding:
M F
µ1s, µ1k ( )
( )max
1 1 1, with M k s k f F
a g a g M m
µ µ µ = − = −+
( ) ( )
( ) ( )
max 2 2
2 1
2 1 1
2 2
For m: , or
The corresponding force is:
,
or
, or
m
s m s
s k
s k
m k m k
f mg a g
g M m F M m g
F M m g F
ma mg a g
µ
µ µ
µ µ
µ µ
= =
+ = − +
= + + =
= =
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( )
( )
( )1
1 2
1 2
, 2 2
For M:
or
with
M k k
M k k
M F s k
a M F M m g mg
F ga M m m M M
ga M m m
µ µ
µ µ
µ µ
= − + −
= − + +
= + −
