How to find the energy of an object that was at rest?

[haruspex]

E_k=mΔv²

Not quite... you forgot a factor.

 

[Davidllerenav]

Not quite... you forgot a factor.

Oh, yes the $\frac{1}{2}$, so it is $E_k=\frac{1}{2}m\Delta v$.

 

[haruspex]

Oh, yes the $\frac{1}{2}$, so it is $E_k=\frac{1}{2}m\Delta v$.

Now you forgot the square.

 

[Davidllerenav]

Now you forgot the square.

Sorry... $E_k=\frac{1}{2}m(\Delta v)^2= \frac{1}{2}m(0.02)^2v_0^2=\frac{1}{2}m(0.004)v_0^2$. It think it is correct know.

 

[haruspex]

Sorry... $E_k=\frac{1}{2}m(\Delta v)^2= \frac{1}{2}m(0.02)^2v_0^2=\frac{1}{2}m(0.004)v_0^2$. It think it is correct know.

I'm sorry to say that's another arithmetic error.

 

[Davidllerenav]

I'm sorry to say that's another arithmetic error.

I see, I made a mistake when I squared 0.02, it is 0.0004, not 0.004. so ##E_k=\frac{1}{2}m(0.0004)v_0^2.

 

[haruspex]

I see, I made a mistake when I squared 0.02, it is 0.0004, not 0.004. so $E_k=\frac{1}{2}m(0.0004)v_0^2$.

Right. And you can simplify slightly combining the 1/2 with the 4.

 

[Davidllerenav]

Right. And you can simplify slightly combining the 1/2 with the 4.

Yes, so simplifying I end up with $E_k=m(0.0002)v_0^2$. And that's all, right?

 

[haruspex]

Yes, so simplifying I end up with $E_k=m(0.0002)v_0^2$. And that's all, right?

Perfect.

 

[Davidllerenav]

Perfect.

Ok, thanks. I don't need to write the equations of the momentum of both rocket, do I?

 

[haruspex]

Ok, thanks. I don't need to write the equations of the momentum of both rocket, do I?

No, you already used that.

 

[Davidllerenav]

No, you already used that.

Ok, thank you so much for your help.

 

[jbriggs444]

Yes, so simplifying I end up with $E_k=m(0.0002)v_0^2$. And that's all, right?

There is a problem with this result. Neither $m$ nor $v_0$ are given in the problem description. Instead, what is given is $E_0$, the initial energy of the moving rocket.

Can you express the result you have in terms of $E_0$ rather than in terms of $m$ and $v_0$?

 

[Davidllerenav]

There is a problem with this result. Neither $m$ nor $v_0$ are given in the problem description. Instead, what is given is $E_0$, the initial energy of the moving rocket.

Can you express the result you have in terms of $E_0$ rather than in terms of $m$ and $v_0$?

Well, since $E_0=\frac{1}{2}m v_0^2$, I think I can express the result as $E_k=(0.0004)E_0$ right?

 

[jbriggs444]

Well, since $E_0=\frac{1}{2}m v_0^2$, I think I can express the result as $E_k=(0.0004)E_0$ right?

Yes, that is what I get as well.