Finding the period of an object moving in horizontal circle

AI Thread Summary
The discussion focuses on calculating the speed and period of an object moving in a horizontal circle while suspended by a string. The correct velocity formula is debated, with one participant asserting it should be √(g*L*Cos(θ)) / tan(θ). Clarification is sought on the equivalence of this formula to the derived answer, which is confirmed to be correct if tan(θ) is properly included in the square root. The conversation emphasizes the importance of understanding trigonometric relationships in the context of circular motion. Overall, the discussion highlights the complexities of deriving motion equations in physics.
fontseeker

Homework Statement


A small mass m is suspended from a string of length L. The body revolves in a horizontal circle of radius R with a constant speed v. Find the speed of the body and the period of the revolution.

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Homework Equations



ΣFx = Tx = mV^2/r
Period = (2πr)/V

The Attempt at a Solution



IMG_4437.jpg


However, I was told that the velocity is actually √(g*L*Cos(θ)) / tan(θ). Why is my answer incorrect?
 
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fontseeker said:
However, I was told that the velocity is actually √(g*L*Cos(θ)) / tan(θ). Why is my answer incorrect?
Your answer looks correct. If ##\text{tan}(\theta)## is inside the square root, which I assume it should be, then the given answer is identical to yours.
 
NFuller said:
Your answer looks correct. If ##\text{tan}(\theta)## is inside the square root, which I assume it should be, then the given answer is identical to yours.
Could you please explain how the answer is identical?
 
Tan = sin/cos
 
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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