Centripetal force ball on a string lab

AI Thread Summary
The discussion focuses on deriving an expression for centripetal force (Fc) in a lab scenario involving a mass spinning on a string. The relationship between centripetal force, tension (FT), and gravitational force (FG) is established, noting that FT equals FG for the mass at the bottom of the string. The angle (theta) of the string affects the horizontal plane in which the mass circles, indicating that the horizontal component of tension (FTx) provides the necessary centripetal force. A diagram is suggested to clarify the forces at play. The conversation emphasizes understanding the dynamics of the system to formulate the correct expression for Fc.
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Homework Statement


So referring to this lab , http://static3.mbtfiles.co.uk/media...ureate/physics/824297/html/images/image12.pngIn this lab you are holding the plastic tube and twirling it to make the small mass spin in a circle. Keep in mind there is a mass on the bottom.

I have to create an expression for Fc with theta and radius.

Homework Equations



Fc = 4pi^2rf^2 * m

The Attempt at a Solution


Well from the FBD of the small mass, we know that FC = FT

and from the FBD of the mass at the bottom we know that FT=FG.

Therefore for the system, wouldn't FC = FG of the mass on the bottom?

As for the equation i am not really sure were to start, could someone help me out please.
 
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The string attached tot the mass going in a circle is angled downwards a bit, that is the horizontal plane in which the mass is circling is a bit below the top of the tube. That is the theta that is mentioned. Best to draw a diagram and post it.
 
so i know the lab looks something like this, and the Fg of the small mass will cancel out the fty in the tension, therefore ftx controlling the motion.
 

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Yes, the x component provides the centripetal force.
 
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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