# Work done by kinetic friction force without coefficient?

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1. Oct 8, 2014

### Jessica Sweet

1. The problem statement, all variables and given/known data
A person pulls a box (m=10 kg) horizontally with +2m/s2 acceleration by applying 45 N force. The displacement of the box is 8 meters from initial position.
a) How much work is done by applied force?
b) How much work is done by kinetic frictional force?

2. Relevant equations
Wf = Fcosθs
F=ma
Wfk = -Fks ???
Fk = μN ???

3. The attempt at a solution
I solved for part a, which was 360J.
I don't know how to solve for part b, which it seems like I would need the friction coefficient?
I tried Wfk = -(10)(2)(8) = -160 J, but that is incorrect.
How do I find Fk to solve for the work done by friction?

Last edited: Oct 8, 2014
2. Oct 8, 2014

### jack action

Answer this question: How much of the applied force is used to accelerate the box?

3. Oct 8, 2014

### Jessica Sweet

Um, 45 N of force was applied to it. Would force of kinetic friction be -45 N then? Or am I just getting myself confused?

4. Oct 8, 2014

### Entanglement

Jack has a point.
Yes, you applied 45 N,
but apparently that's not the force used to accelerate the box since its mass is 10 Kg and its accelerations is 2 m / s / s. The net force is what you should be looking at. Rethink. :):)

Last edited: Oct 8, 2014
5. Oct 8, 2014

### jack action

$$\sum F = ma$$
$$F_{total} - F_{friction} = ma$$

6. Oct 8, 2014

### nasu

Write Newton's second law for the box.

7. Oct 8, 2014

### Jessica Sweet

Alright, so Ftotal = 45 N, I am looking for frictional force, and ma = 20.
45-Ffk = 20
Ffk=25
Then I have Wfk = -(25)(8) = -200 J?

8. Oct 8, 2014

### jack action

Look again at your OP and you already found 360 J and 160 J. How does your 200 J fits in there?

Just for the fun of it, can you find the coefficient of friction?

9. Oct 8, 2014

### Jessica Sweet

Are you saying I could have subtracted the 160 from 360? What value does the 160 J represent that I solved for? Gosh, I feel stupid.

10. Oct 8, 2014

### Jessica Sweet

Never mind, I got it all covered. My brain is working again. It's amazing what stress can do to the brain. Thanks for the help everybody.
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