How much work would it take to horizontally accelerate an object with a mass of 4 kg to 3 ms^-1 on a surface with a kinetic friction coefficient of 6?

Jun 14, 2017

The weight force of a $4$ $k g$ mass is given by:

${F}_{w} = m g = 4 \times 9.8 = 39.2$ $N$

The frictional force will be given by:

${F}_{\text{frict}} = \setminus \mu {F}_{w} = 6 \times 39.2 = 235.2$ $N$

Work will be done doing two things: overcoming friction and increasing the kinetic energy of the object. Let's take the kinetic energy first:

${E}_{k} = \frac{1}{2} m {v}^{2} = \frac{1}{2} \times 4 \times {3}^{2} = 18$ $J$

Now the work done in overcoming the friction will be given by:

$W = {F}_{\text{frict}} s$ where s is the distance traveled.

We don't know the distance it takes to accelerate the object from rest to $3$ $m {s}^{-} 1$.

And I'm stuck here. If we assume something we may be able to get it, but I'll have to leave that to some of my smarter colleagues.