F = m * (0.85 Hz)^2 * 2πm = F / (0.85 Hz)^2 * 2π Calculate Mass of Skaters

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The discussion revolves around calculating the mass of two identical ice skaters using the spring constant and frequency of their circular motion. The spring constant is given as 650 N/m, and the frequency of revolution is 0.85 Hz. The relevant equation for frequency in terms of mass and spring constant is f = (1/2π)√(k/m), which leads to the conclusion that the mass must be adjusted for both skaters. Clarification is provided that the mass should not be considered as double that of one skater, as they are both spinning around a common center. The conversation emphasizes understanding the dynamics of the system and the effective spring constant when considering both skaters.
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Homework Statement


Two identical ice skaters are holding onto opposite ends of a very long spring with a spring constant of 650 N/m. While spinning in a circle, the skaters frequency of revolution is measured to be 0.85 Hz. What is the mass of the skaters?


Homework Equations


F = kx


The Attempt at a Solution


F = (650 N/m)x ?
 
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Remember, circular motion is the resultant of two perpendicular SHM with the same frequency and amplitude and phase difference of pi/2. ehild
 
Oh so then u use the equation
f=(1/2∏)√(k/m)
And the m needs to be 2m...ok got it!

Thank you!
 
No, m is not twice that of one skater-just the opposite.

Both skaters spin along the same circle. The situation is the same for each of them as if there was a pole at the centre, and half of the spring connected to the pole with one end and the other end to the skater. What is the spring constant of a halved spring?

ehild
 
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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