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A body of mass 5kg is placed on rough horizontal surface. If coefficient of friction is 1/√3, find how much pulling force should act on the body at an angle 30° from horizontal so that the body just begins to move.

A body of mass 5kg is placed on rough horizontal surface. If coefficient of friction is 1/√3, find how much pulling force should act on the body at an angle 30° from horizontal so that the body just begins to move.

Grade:12th pass

2 Answers

Arun
25750 Points
6 years ago
n = mg - Fmax/2
n = Fmax/(1/\small \sqrt3)
n = \small \sqrt3 Fmax
Thus
mg - Fmax/2 = \small \sqrt3 Fmax
Knowing that
mg = 5*9.8 = 49
 
Hence Fmax = 22 N
Samar
13 Points
5 years ago
we can also find  
f
max
  directly by rearranging the two blue equations to solve for  
n
 , and then setting them equal to each other:
 
n
=
m
g
−
f
max
2
 
 
n
=
f
max
1
√
3
=
√
3
f
max
 
 
Thus,
 
m
g
−
f
max
2
=
√
3
f
max
 
 
Knowing that  
m
g
=
(
5
l
kg
)
(
9.81
l
m/s
2
)
 ,
 
f
max
=
22.0
   
N

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