Potential energy algebra problem

AI Thread Summary
To solve for height h in the potential energy equation PE = mgh, isolate h by dividing both sides by mg. If the object is moving, equate gravitational potential energy (GPE) to kinetic energy (KE) to find h. For a stationary object, the simplified approach directly leads to h = PE/(mg). The discussion emphasizes understanding the algebraic manipulation rather than just obtaining the answer. Mastery of these concepts is essential for learning physics effectively.
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Homework Statement



The equation for potential energy, PE, of a mass m and at height h, where the acceleration due to gravity is g, is PE =m*g*h. Solve for h.

* = multiply

Homework Equations


If someone could please tell me how to work it out and not tell me the answer i'd be very appreciative as i joined this forum to learn and not to get answers.

The Attempt at a Solution


Have no idea how to answer.

Homework Statement


Homework Equations


The Attempt at a Solution

 
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There's a couple ways you could do this. Is the object moving at all or is it standing still?


IF:

It is moving, set GPE equal to KE and isolate h.

It is stationary, just isolate h in the equation PE = mgh
 
To solve for h, you can divide both sides of the equation by mg, which will cancel out the mg on the right side and leave you with h.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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