First slide

Friction on horizontal surface

Question

A body of mass m is kept on a rough horizontal surface (coefficient of friction = $μ$ ). A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by F, where F is,

Moderate

A

$| \vec{F} | = mg$
B

$| \vec{F} | = mg + μmg$
C

$| \vec{F} | = μmg$
D

$| \vec{F} | \leq mg \sqrt{1 + μ^{2}}$

Solution

Since body does not move hence it is in equilibrium.
$f_{r}$ = frictional force which is less than or equal to limiting friction.
Now N = mg
$Hence \vec{F} = \vec{N} + {\vec{f}}_{r} | \vec{F} | \leq (mg)^{2} + (μmg)^{2} | \vec{F} | \leq mg \sqrt{1 + μ^{2}}$

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