Finding the total mechanical energy

[Sophie Martinez]

Homework Statement

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?

Homework Equations

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

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.

 

[cnh1995]

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.

If you write the equation for conservation of energy, you'd see that the mass term is canceled 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?

 

[BvU]

Hello Sophie,

I tried equating the work and energy equations

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

Tip: in don't know situations just pick something (2 kg for example) and see if it divides out.

 

[Sophie Martinez]

If you write the equation for conservation of energy, you'd see that the mass term is canceled 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?

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

 

[cnh1995]

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

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.

 

[Sophie Martinez]

Hello Sophie,

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

Tip: in don't know situations just pick something (2 kg for example) and see if it divides out.

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

 

[Sophie Martinez]

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.

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

 

[cnh1995]

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

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.

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?

 

[haruspex]

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

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