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**1. The problem statement, all variables and given/known data**

A 4 kg mass slides 2 m over a horizontal surface with force of kinetic friction of 2N, initial velocity is 5 m/s.

Find it's final velocity.

My problem... we've been asked to solve this problem using the Work-Energy theorem, and we've been given it in the form of:

W = ∆K + ∆U + ∆Einternal

I find I can make it work if only assume that the change in internal energy is zero, or the work done by friction is zero... and I think that they should equal to each other.

What is my error in understanding... or is the formula wrong

**2. Relevant equations**

W = ∆K + ∆U + ∆Einternal

**3. The attempt at a solution**

Here is one solution if the work done is 0....

0 = ∆K + ∆U + Einternal

0 = (Kf - Ki) + 0 + Fdcosθ

0 = ( 1/2 mvf^2 - 1/2 mvi^2) + 0 +Fkdcosθ

0 = (1/2 (4)(vf)^2 - (1/2 (4)(5)^2) + 0 + (-2)(2)(cos 180˚)

0 = 2vf^2 -50 +0 +4

vf^2 = 23

vf = √ 23 m/s