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

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

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Answer 1 · 2016-03-25T02:45:24

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

Explanation:

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

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

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:

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

So net force will be:

$F_{net} = F_{applied} - F_{friction} = 28 N$ $F_"net" = F_"applied" - F_"friction" = 28 " N"$

We can see next picture to understand it better:

enter image source here

Now, having $F_{net}$ $F_"net"$ and $F_{friction}$ $F_"friction"$ , let us find $F_{applied}$ $F_"applied"$ :

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

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

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An object with a mass of 7kg7 kg is on a surface with a kinetic friction coefficient of 8 8 . How much force is necessary to accelerate the object horizontally at 4ms2 4 m/s^2?

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Explanation:

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