Recent content by RubroCP

Assume that three boats, ##B_1##, ##B_2## and ##B_3## travel on a lake with a constant magnitude velocity equal to ##v##. ##B_1## always travels towards ##B_2##, which in turn travels towards ##B_3## which ultimately travels towards ##B_1##. Initially, the boats are at points on the water...

Thank you very much, now I understand.

Okay, but this ##E(x)## is not the potential energy, it's the total energy, which is obtained by adding the potential and the kinetics. That's what I can't understand.

Knowing that ##F(x)=-\mathrm{d}V(x)/\mathrm{d}x##, I found that ##F(x)=-2.4x^3+1.35x^2+8x-3##. But it was the only thing I could find. How can I analyze what will be the type of movement with the information presented by the question statement?

I have tried to apply the conservation methods, but I am not understanding what the statement is asking for.

Well, I could affirm that ##\frac{\Delta U_L}{\Delta U_R}=-\frac{MH}{mh}##. But, knowing that ##\frac{H}{h}=\frac{L}{l}##, then ##\frac{\Delta U_L}{\Delta U_R}=-\frac{ML}{ml}##. But, how can I prove that ##\Delta U_L=\Delta U_R## in this case?

Thanks, kuruman. My question is regarding the division in alternative "a". As the blocks move I got a negative and a positive potential. In the division, should I analyze the module or leave the value as negative? For alternative "b", I started from what the statement stated: "Assuming that the...

Hello, thanks for the attention. Well, knowing that the only acting force is the gravitational force, I stated that ##U=-MgH## for the ##M## mass block and that ##U=mgh## for the ##m## mass block. After that I divide the two and got the relationship for the alternative "a". For alternative "b" I...

Thanks!

So can I say without loss of generality that for x = 0 the potential is also null?

If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that: $$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$ but what about the limits of the integration?

Thanks, my friend. I will try here again.

I have the following definition: $$ \lim_{x\to p^+}f(x)=+\infty\iff \forall\,\,\varepsilon>0,\,\exists\,\,\delta>0,\,\,\text{with}\,\,p+\delta< b: p< x < p+\delta \implies f(x) > \varepsilon$$ From this, how can I get the definition of $$\lim_{x\to p^-}=-\infty? $$

I have the following definition: $$\lim_{x\to p^+}f(x)=+\infty\iff \forall\,\,\varepsilon>0,\,\exists\,\,\delta>0,\,\,\text{with}\,\,p+\delta< b: p< x < p+\delta \implies f(x) > \varepsilon$$ From this, how can I get the definition of $$\lim_{x\to p^-}=-\infty? $$