# An object with a mass of 12 kg is on a surface with a kinetic friction coefficient of  1 . How much force is necessary to accelerate the object horizontally at 7  ms^-2?

Feb 13, 2016

The total force is composed of two pieces: the force required to accelerate the mass and the force required to overcome friction. $F = m a + \mu m g = 12 \cdot 7 + 1 \cdot 12 \cdot 9.8 = 201.6$ $N$.

#### Explanation:

The total force is made up of two different forces.

If there were no friction, the force required to accelerate a mass of $12$ $k g$ at an acceleration of $7$ $m {s}^{-} 2$ is given by Newton's Second Law :

$F = m a = 12 \cdot 7 = 84$ $N$

The second part is the frictional force:

${F}_{f} = \mu {F}_{N}$ where $\mu$ is the frictional coefficient and ${F}_{N}$ is the normal force, which in turn is $m g$, the mass times the acceleration due to gravity.

${F}_{f} = \mu m g = 1 \cdot 12 \cdot 9.8 = 117.6$ $N$

To find the total force, just add these two forces:

$F = m a + \mu m g = 12 \cdot 7 + 1 \cdot 12 \cdot 9.8 = 201.6$ $N$.