# An object with a mass of 12 kg is on a surface with a kinetic friction coefficient of  2 . How much force is necessary to accelerate the object horizontally at  3 m/s^2?

Aug 12, 2018

The force is $= 271.2 N$

#### Explanation:

The coefficient of kinetic friction is

${\mu}_{k} = {F}_{r} / N$

The mass of the object is $m = 12 k g$

The acceleration due to gravity is $g = 9.8 m {s}^{-} 2$

The normal reaction is $N = 12 g$

The coefficient of kinetic friction is ${\mu}_{k} = 2$

Therefore,

${F}_{r} = {\mu}_{k} N = 2 \cdot 12 g = 24 g$

According to Newton's Second Law

$F - {F}_{r} = m a$

The acceleration is

$a = 3 m {s}^{-} 2$

Therefore,

$F = {F}_{r} + m a = 24 g + 12 \cdot 3 = 24 g + 36 = 271.2 N$