# An object with a mass of 7 kg is on a surface with a kinetic friction coefficient of  8 . How much force is necessary to accelerate the object horizontally at  4 m/s^2?

Mar 25, 2016

Let us apply Newton's Laws to solve this problem.

#### Explanation:

According to Newton's 2nd Law of Motion ($F = m a$), to get an acceleration of 4 ${\text{m/s}}^{2}$, we need a force:

$F = m \cdot a = 7 \text{ kg" cdot 4 " m/s"^2 = 28 " N}$

This would be the force necessary to move the body if there were not any other forces (as friction). However, in our case, a stronger force is required to compensate friction.
So, let us take 28 N as net force.

Now, we are going to find friction force. This equals to:

${F}_{\text{friction" = mu cdot N = mu cdot m g = 8 cdot 7 " kg" cdot 9,8 " m/s}}^{2} =$
$= 548 , 8 \text{ N}$

So net force will be:

${F}_{\text{net" = F_"applied" - F_"friction" = 28 " N}}$

We can see next picture to understand it better:

Now, having ${F}_{\text{net}}$ and ${F}_{\text{friction}}$, let us find ${F}_{\text{applied}}$:

${F}_{\text{applied" = F_"net" + F_"friction" = 28 " N" + 548,8 " N" = 576,8 " N}}$