# Finding the total mechanical energy

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1. Dec 14, 2016

### Sophie Martinez

1. The problem statement, all variables and given/known data
A bead is sliding on a surface. At point A it is 80 cm above the ground, at point B it has just hit the ground and at point C it is 50 cm above the ground. At point A it has a speed of 200 m/s, so what will its speed be at point B and C?

2. Relevant equations
W=F.d
Kinetic Energy= (mv^2)/2
Gravitational potential energy= mass • 9.8 • height

3. The attempt at a solution
I tried to find the the total mechanical energy at one point by adding the GPE and KE. At point B the GPE is 0, so the kinetic energy will be the total mechanical energy due to the conservation of energy. The mass is not given in this question and without the mass I cannot figure it out. I tried equating the work and energy equatipns but o got the wrong answer.

2. Dec 14, 2016

### cnh1995

If you write the equation for conservation of energy, you'd see that the mass term is cancelled out.
At point A, the bead has both KE and PE and at point B, it has only KE. How would you write an equation describing this using the principle of conservation of energy?

3. Dec 14, 2016

### BvU

Hello Sophie,

Way to go. Why don't you post your working and we'll try to see what goes wrong.

Tip: in dunno situations just pick something (2 kg for example) and see if it divides out.

4. Dec 14, 2016

### Sophie Martinez

I think the equation would only be TME=(mv^2)/2 but because the mass is cancelled it would be (v^2)/2?

5. Dec 14, 2016

### cnh1995

Yes, but energy is not v2/2.
You need to write the complete equation.
Cancelling out the mass will only leave one unknown v in the equation.

6. Dec 14, 2016

### Sophie Martinez

I ended up with F•d=mgh and F•d=(mv^2)/2 because of the work-energy principle. I also tried to isolate m in each case and equated the two results and got (F•d)/gh=2(F•d)/v^2

7. Dec 14, 2016

### Sophie Martinez

So the complete one would be TME= v^2/2 + gh?

8. Dec 14, 2016

### cnh1995

Nope. Again, that's not an equation for energy because there's no mass term in it.
You need to use the "conservation" of energy equation.

9. Dec 15, 2016

### haruspex

If you say instead "TME per unit mass" that will work.