# How much work would it take to horizontally accelerate an object with a mass of 8 kg to 9 m/s on a surface with a kinetic friction coefficient of 3 ?

Dec 31, 2016

This problem lacks enough information to complete the work done against friction. See the discussion below.

#### Explanation:

There are two sources of energy involved here.

First, because the mass increases in velocity, there is an increase in its kinetic energy. Starting from rest ($v = 0$), it gains kinetic energy equal to

$K E = \frac{1}{2} m {v}^{2} = \frac{1}{2} \left(8\right) {\left(9\right)}^{2} = 324 J$

At the same time, we must do work against the force of friction. This will appear in the form of heat:

W = F_f Deltad)=mu_kmgDeltad

Before we can complete this, we need to find the distance the object travels. Unfortunately, we lack enough information to do this! We need either the acceleration of the body or the time taken to reach the final speed.

Check the problem and repost the question once you have one of these values.