# Work on an incline

1. Feb 27, 2005

### Jayhawk1

I am having a lot of trouble with this problem:

What is the minimum work needed to push a 1147 kg car 376 m up a 15.1o incline if the effective coefficient of friction is 0.23?

I thought that it was (m)(.23)(sin 15.1)(376) but that isn't right. Any help would be appreciated.

2. Feb 27, 2005

### dextercioby

Nope,my guess is that it should encompass a "cosine".So what is the force up against whom u have to do work...?

Daniel.

3. Feb 27, 2005

### Jayhawk1

So it should be (m)(.23)(cos15.1)(376)? ...for some reason I though the coeff. of friction incorporated the angle... am I wrong in assuming this?

4. Feb 27, 2005

Just use the work energy theorem.
$$\Delta W = \Delta E_g + \Delta E_f + \Delta E_s$$

Draw a free body diagram first, it will help you.

Regards,

5. Feb 27, 2005

### dextercioby

There are 2 forces agains which work needs to be performed:gravity & friction force...
You have found the one for gravity (it should be with a minus) and u need to add to it the work performed by friction force.

Daniel.

6. Feb 27, 2005

### marlon

Suppose the x-axis is along the incline and y-axis is perpendicular to this surface...

We have 3 fources on the object : gravity, friction$${\mu}{\vec N}$$
, normal force N

So along the x-axis we have :

$$F_x = -mgsin(\theta) - {\mu}N$$

Along the y-axis we have :

$$F_y = 0 = -mgcos(\theta) + N$$

Now, you can calculate N from the second equation and then plug it into the first one. Now you know everything along the incline (x-axis). So just fill in the numbers and multiply this by the distance that is travelled.

regards
marlon

7. Feb 27, 2005

### Jayhawk1

So for the component of force due to friction it is (coeff. friction)(mass)(376)?

Last edited: Feb 27, 2005
8. Feb 27, 2005

### marlon

Wrong, besides you confused the OP, when you started about "encompassing" a cosine...his formula was initially correct for the gravity-part.

marlon

9. Feb 27, 2005

### marlon

Nope, read my post...

it is (coeff friction)(NORMAL FORCE) for the formula of the friction force along the incline. Beware of the minus-sign. Then multiply this by 376 to get the work done...

I showed you how to calculate the normal force N

marlon

10. Feb 27, 2005

### dextercioby

What's wrong in my statement that u quoted...?:surprised:

Daniel.

11. Feb 27, 2005

### marlon

Look at post number 3 !!!

marlon

12. Feb 27, 2005

### dextercioby

You said "wrong" when u quoted something right,isn't that so...?:tongue2:

Marlon,what can i say more...?:yuck:

Daniel.

13. Feb 27, 2005

### marlon

Please, stop being such a big baby about this. You know very well you are wrong. Now, you don't have to admit it to me, but just stop posting useless answers just to have the last word.

marlon

Stick to the facts

14. Feb 27, 2005

### marlon

$$F_x = -mgsin(\theta) - {\mu}mgcos(\theta)$$

I just replaced N with the second equation. Now for the work, you can omit the minus-signs

Fill in the numbers and multiply by the travelled distance and you are done. ps disregard dexter's posts because they are erronuous...

marlon

Last edited: Feb 27, 2005