# 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.

Arun
25758 Points
4 years ago
n = mg - Fmax/2
n = Fmax/(1/$\small \sqrt$3)
n = $\small \sqrt$3 Fmax
Thus
mg - Fmax/2 = $\small \sqrt$3 Fmax
Knowing that
mg = 5*9.8 = 49

Hence Fmax = 22 N
Samar
13 Points
3 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