# An object with a mass of 5 kg is on a surface with a kinetic friction coefficient of  4 . How much force is necessary to accelerate the object horizontally at  17 m/s^2?

Apr 9, 2017

The force is $= 281 N$

#### Explanation:

The frictional force is

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

The normal force is $N = m g$

So,

${F}_{r} = {\mu}_{k} \cdot m g$

Resolving in the horizontal direction ${\rightarrow}^{+}$

We apply Newton's second Law

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

So,

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

$F = {\mu}_{k} m g + m a$

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

$= 5 \left(4 \cdot 9.8 + 17\right)$

$= 5 \cdot 56.2 = 281 N$