# Help with Kinetic/Potential Energy problem

1. Dec 19, 2006

### apollo11cdr

Help with Kinetic/Potential Energy problem !!

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

Can anyone help me solve a problem. ??

A stone weighing 0.62 kg is fired from point a at 5.5 m s-1 , at point b mid range (Maximum height) it has 2.3 joules kinetc energy.. what is the height of the stone at point b ????

b]2. Relevant equations[/b]

mg h = half mv squared

h = v2/2g

3. The attempt at a solution

h = 30.25 m s -1 / 2 x 9.8 ms -2

That is the only solution I can think of !!!!

anyone suggest another way to solve this ???

Thanks

A11cdr

2. Dec 19, 2006

### neutrino

How did you come to that "solution"?

Forget the formulae for a moment. How would you apply the conservation of energy to this problem?

3. Dec 19, 2006

### apollo11cdr

Looking thru the problem that was the only equation that came to mind...

With the stone at its maximum height I dont understand why it has a KE of 2.3 joules !! unless perhaps that is proportional to its initial KE.

Baffled....

4. Dec 19, 2006

### neutrino

I'm the one baffled at the moment.

Conservation of (mechanical) energy: In the absence of dissipative forces, the sum of kinetic and potential energies of a system is always a constant. Here your "system" is the stone.

Apply this principle to the problem.

5. Dec 19, 2006

### apollo11cdr

Thank you.. I will read up on that topic !!

Im sorry to have confused you !!

6. Dec 19, 2006

### apollo11cdr

How about initial kinetic energy / 9.8 n

9.4 J / 9.8 n = 0.959m or 1m

I think the 2.3 joules at the point B (maximum height) is just a decrease of KE before it becomes PE.. cant understand why it quoted really other than KE can never be negative it is a product of definite quantities or something ?

Am I getting warm ???

7. Dec 19, 2006

### neutrino

Take the point from which the stone was fired as zero P.E (well, this could be anything, but we choose zero for convenience). At the same point the stone also has some K.E. Now, the sum P.E + K.E is a constant, say C.

PE + KE = C, and in whatever way the KE and PE change, their sum remains C, at all times (this is assuming that there is no air resistance or friction involved). You can find what this C is when the stone is fired. Now when it is at the top, the KE has changed, and so has the PE, but as stated earlier, their sum remains what it was when the stone was fired.

Can you do the problem now?

8. Dec 19, 2006

### neutrino

Generally, it is not necessary that the energy should be completely PE (or completely KE) at some point. What you have is projectile motion; unless the stone was shot straight up, the KE at the top will not be zero. Remember, there is still the horizontal component of the initial velocity at the top.

9. Dec 19, 2006

### apollo11cdr

Still trying :-)

I have used equation for Initial KE which gives me a total of 9.4 Joules.
So I presume that is the figure that will be the total KE + PE... the constant

I am lost when it comes to the object having 2.3 joules at the middle of the curve.... as it is not zero.. I am puzzled ...

KE = 2.3 J at point B , so PE must equal 7.1 Joules if energy is constant... but I cant seem to find the right equation to establish the height of the stone mid range... could be 7.1 J / gravity 9.8 N ???

I must thank you for your help !!!

10. Dec 19, 2006

### neutrino

That's right.

Why should it be zero? Did you read my last post?

Right again.

I think you've mixed up numbers and units somehow. The PE (at a height h, which is small compared to the radius of the earth) is mgh.

11. Dec 19, 2006