Calculating Force Components for U = 7x^2 + 9xy + 3(y^2)z

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The discussion focuses on calculating the components of the force vector F from the potential energy function U = 7x^2 + 9xy + 3(y^2)z. The user initially presents their calculated components as Fx = -14x - 9y, Fy = -9x - 6yz, and Fz = -3y^2, expressing uncertainty about the accuracy of Fx. Other participants confirm that Fx appears correct, providing reassurance. The conversation highlights the collaborative effort in verifying calculations related to force components in physics.
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Homework Statement



If U = 7x^2 + 9xy + 3(y^2)z, what are the components of the force vector F ?


The Attempt at a Solution


These are the answers I've come up with. I've gotten Fy and Fz correct, but the Fx is wrong and I'm pretty sure its actually right. However, I would love to be proven wrong lol.
Fx=-14x-9y
Fy=-9x-6yz
Fz=-3y^2
 
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Welcome to PF!

Hi Stryder_SW! Welcome to PF! :wink:
Stryder_SW said:
If U = 7x^2 + 9xy + 3(y^2)z, what are the components of the force vector F ?
…
Fx=-14x-9y
Fy=-9x-6yz
Fz=-3y^2

Well, your Fx looks right to me. :smile:
 
yeah, I'm about to message my professor lol.
 
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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