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opeth_35
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Problem about boundries in this solve of quantum problem
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The discussion centers on the boundaries in a quantum problem integral, specifically in spherical coordinates. The integral's limits are defined as r from 0 to infinity, θ from 0 to π, and φ from 0 to 2π. There is confusion regarding the origin of these boundaries, with a suggestion to clarify the use of trigonometric identities in the problem. The conversation emphasizes the distinction between "limit" or "bound" for numbers and "boundary" for curves or surfaces. Understanding these boundaries is crucial for solving the quantum problem effectively.
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tiny-tim
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hey opeth_35! 
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)
the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)
(btw, we say "limit" or "bound" for a number … "boundary" is for a curve or a surface
)the integral is over the whole of space, and it's in spherical coordinates,
so the limits are: r from 0 to ∞, θ from 0 to π, and φ from 0 to 2π
(i don't understand your second question, but maybe the answer is that they used one of the standard trigonometric identities … sin2θ = (1 - cos2θ)/2)
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
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}...
I was told forces are vectors so they can be divided into x and y components, but what about the normal force or the force of static friction? do you divide those into x and y components if say you had a block that was lying on an angled surface?
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