# An object with a mass of 2 kg is on a surface with a kinetic friction coefficient of  7 . How much force is necessary to accelerate the object horizontally at 6 m/s^2?

Dec 20, 2015

I found: $F = 149.2 N$

#### Explanation:

Kinetic Friction is given as:
${f}_{k} = {\mu}_{k} \cdot N$
Where:
${\mu}_{k} =$kinetic friction coefficient$= 7$
$N =$Normal Reaction (in this case of horizontal movement)$= \text{weight} = m g$
with:
$m = 2 k g$
$g = 9.8 \frac{m}{s} ^ 2$

To produce an acceleration $a = 6 \frac{m}{s} ^ 2$ we need a force $F$ to overcome friction that, according to Newton's Second Law, will be given as:
$F - {f}_{k} = m a$
$F = {f}_{k} + m a$
$F = {\mu}_{k} \cdot m g + m a$
$F = \left(7 \cdot 2 \cdot 9.8\right) + \left(2 \cdot 6\right) = 149.2 N$