# An object with a mass of 2 kg is on a surface with a kinetic friction coefficient of  9 . How much force is necessary to accelerate the object horizontally at 6 ms^-2?

Jan 25, 2016

If the object were on a frictionless surface the force required would be $12$ $N$, but including the frictional force it is $188.4$ $N$, but see the explanation: this is a silly answer because there is a problem with the question.

#### Explanation:

This is a very badly written question: the friction coefficient should have values between 0 and 1. Very rarely it can have values greater than one, and perhaps as high as 2, but 9 is a ridiculous and non-physical number. Are you sure it wasn't 0.9 and you missed something when writing down the question?

First we can calculate the required force due to the object's inertia:

$F = m a = 2 \cdot 6 = 12$ $N$

This is the force we'd need on a frictionless surface.

To calculate the frictional force, use:

${F}_{f} = \mu {F}_{N}$ where ${F}_{N}$ is the normal force acting - in this case the weight force of the object, $m g = 2 \cdot 9.8 = 19.6$ $N$.

${F}_{f} = \mu {F}_{N} = 9 \cdot 19.6 = 176.4$ $N$

To find the total force required we would add this to the $12$ $N$ above, but this is a silly number...