# Homework Help: Work Done Incline

1. Jul 11, 2015

### Sarah00

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

2. Relevant equations
W = F d
F = ma

3. The attempt at a solution
Constant Speed ==> a = 0 ==> Net Force = 0 ==> F cos 37 = mg sin 37 ==> F = 37.6 N
sin 37 = h/d ==> 6/10 = 0.5/d ==> d = 5/6
W = F d = 5/6 * 37.6 = 31.3 N [Not In Choices] - Any Help?

2. Jul 11, 2015

### Dr. Courtney

Perhaps it would be better to consider the work done as the change in potential energy and approach it that way.

3. Jul 11, 2015

### Sarah00

yup! W = mgh = 5 * 10 * 0.5 = 25 J
In my previous attempt, my mistake was not writing cos 37 in finding the work

4. Jul 11, 2015

### Sarah00

Sir,
I applied the method you mentioned on this questions but it does not work with me!

Confused now on when to use that method

That method find work done by gravity, is it same as work done by F ? Why?

5. Jul 12, 2015

### SammyS

Staff Emeritus
The original problem had constant speed. I think you will find that this one doesn't.

Your initial method (after correcting by including cos(37°) in that case) should work here.

6. Jul 12, 2015

### Sarah00

How "constant speed" differ?

7. Jul 12, 2015

### CWatters

KE is constant.

8. Jul 12, 2015

### Sarah00

Sorry, but how is that relevant?
The way I think of the work done is final energy - initial energy
In final energy I have potential energy (mgh) only
In initial energy there is nothing in this case
So,
W = mgh

Where is my point of confusion?

9. Jul 12, 2015

### Ellispson

The final energy will not be only in the form of potential energy.

10. Jul 12, 2015

### Avaron Cooper

Without thinking too much, why don't you attempt this question using your previous knowledge on basics...

11. Jul 12, 2015

### Sarah00

ok, let say the speed is not constant..
E initial is zero because potential is zero and it is at rest at the begining
E final is potential and kinetic energy will be ..

That also the same with if speed is constant.

So, why it differ

12. Jul 12, 2015

### Sarah00

I did attempt the question and got the answer of 52 J but I am asking why I can't use that method

13. Jul 12, 2015

### Avaron Cooper

If the speed is constant to a direction, it means it has no external unbalancrd force towards that direction..

14. Jul 12, 2015

### Avaron Cooper

When there's an unbalanced force and the object shows a displacement, there's a work done.

15. Jul 12, 2015

### Sarah00

That's right, but it does not answer my question in that why I can't use the concept of conservation of energy

16. Jul 12, 2015

### Avaron Cooper

We don't know the final kinetic energy. Since there is an external unbalanced force there is an acceleration so the initial KE cannot be taken as the final KE. So to apply conservation of energy, we don't have enough data.

17. Jul 12, 2015

### Sarah00

OK Thanks, what about if it is constant speed. Initially velocity = 0 but final is not 0. So how we only used W = change in potential energy, without considering hte KE

18. Jul 12, 2015

### Avaron Cooper

If there is a motion I think there should be a velocity.;)

19. Jul 12, 2015

### CWatters

That is correct for #1 (constant velocity) but not #4 (constant force)

In #4 the block is accelerating so the final KE is not the same as the initial KE.

You can use conservation of energy to solve this but you would need to calculate the final velocity.

It is easier to use work = force * displacement.

20. Jul 12, 2015

### Sarah00

Thanks, but why you said it is correct for #1 ?
It is constant velocity so we still have velocity in Ef but we don't have it in Ei (before applying the force)

21. Jul 12, 2015

### Sarah00

Guys, I understand that in [constant force] we can't use principle of energy without find final KE.
But my problem is why we could use it in [constant speed], as we still have final KE

22. Jul 12, 2015

### SammyS

Staff Emeritus
W = ΔE :
(Work done by an external force) = Change in total mechanical energy.
also E = KE + PE
So W = ΔKE + ΔPE​

In the first problem:
The velocity was constant, so the Kinetic Energy didn't change. Therefore, the work done by force, F, was equal to the change in Potential Energy.

When you did the problem using the definition of Work, you had to find the amount of force which produced zero acceleration. -- It was just enough to counteract gravity.​

In the second problem:
You are given the force. It's unlikely that it's the exact amount to counteract gravity, so the acceleration will not be zero. There will be a change in kinetic energy as well as in potential energy. You can still get an answer from energy considerations, but it will be quite a bit more involved than simply calculating the Work directly.​

23. Jul 12, 2015

### Sarah00

But isn't the speed constant DURING the action of the force NOT before? So before (E initial) there was no movement i.e. KEi = 0 ?

24. Jul 12, 2015

### SammyS

Staff Emeritus
That issue is not addressed in the problem. (You're referring to the first problem, right?)

It simply says that the block is moving up the incline at a constant speed.

25. Jul 12, 2015

### Sarah00

Aha now I am happy enough..

Same kinetic energy before and after so they cancel each other

Thanks guys !
You were so kind !