# Change in Kinetic energy and final speed

1. Sep 28, 2006

### bearhug

A 41 kg box initially at rest is pushed 4 m along a rough, horizontal floor with a constant applied force of 121 N. If the coefficient of kinetic friction between the box and the floor is 0.29, find (a) the work done by the applied force
4.84×102 J
b) the increase in internal energy of the box + floor system due to friction 4.67×102 J
c) the work done by the normal force on the block due to the floor
0.00 J
d) the work done by the gravitation force on the block due to the earth 0.00 J
e) the change in kinetic energy of the box
I have everything else figured out here I'm stuck. The change of kinetic energy I used the equation ΔK= -fk(d) which would equal -4.66e2 J but I'm not sure if there's another force that I need to add on. If there is where?

f) the final speed of the box: for this I orignally used W=1/2mvf^2- 1/2mvi^2 making it 484=1/2(41)vf^2 which would give a final velocity of 4.86m/s is this right?

2. Sep 28, 2006

### andrevdh

b) 0 J - The floor experiences a similar friction force, but in the opposite direction. Although we know that both will heat up so this one I am not sure about.

e) The change in kinetic energy of the box is given by the work done by the resultant force acting on the box.

Last edited: Sep 28, 2006
3. Sep 28, 2006

### bearhug

For e) can you explain a little more than that? I'm not sure if I'm going in the right direction in solving that problem.

4. Sep 29, 2006

### andrevdh

Lets come back to b) first. The work done by friction changes the internal energy of a system (the object heats up and therefore stores energy that could under certain circumstances do work). So the change in internal energy of a system due to a frictional force f acting on it over a distance d is given by

$$\Delta I = -fd$$

This means that the internal energy change is positive due to a frictional force acing on the object. In this case the increase in the internal energy of the floor and the box comes from a decrease in in internal energy of whoever is pushing the box along the floor.