# An object with a mass of 5 kg is on a surface with a kinetic friction coefficient of  3 . How much force is necessary to accelerate the object horizontally at 7 m/s^2?

Jul 11, 2017

The force is $= 182 N$

#### Explanation:

The coefficient of friction is

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

The frictional force is ${F}_{r}$

The normal force is $N = m g$

The net force on the object is $= F$

According to Newton's Second Law

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

$F - {\mu}_{k} N = m a$

$F = {\mu}_{k} m g + m a = m \left({\mu}_{k} g + a\right)$

${\mu}_{k} = 3$

$a = 7 m {s}^{-} 2$

$m = 5 k g$

Therefore,

$F = 5 \left(3 \cdot 9.8 + 7\right) = 182 N$