Question

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`?

Answer 1

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 = ma = 2*6 = 12` `N`

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

To calculate the frictional force, use:

`F_f = muF_N` where `F_N` is the normal force acting - in this case the weight force of the object, `mg = 2*9.8 = 19.6` `N`.

`F_f = muF_N = 9*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...