Is My Calculation of Centripetal Force Correct?

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The discussion revolves around calculating the speed of a rock in outer space, attached to a spring and swung in a circular motion. The centripetal force is equated to the spring force, leading to the formula v = sqrt(F*r/m). The user initially calculates the speed as 41 m/s using the values provided. Other participants confirm the method is correct but suggest rechecking the calculation for accuracy. The conversation emphasizes the importance of verifying calculations in physics problems.
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In outer space a rock of mass 3 kg is attached to a long spring and swung at constant speed in a circle of radius 7.5 m. The spring exerts a force of constant magnitude 640 N. What is the speed of the rock?



I thought i was doing this right...but I guess not


Fspring = Fcent.

Fcent = m* v^2/r so... v = sqrt(F*r/m)

v = sqrt(640*7.5/3 ) = 41 m/s


If anyone could tell me what I'm doing wrong, that would be a lot of help! thanks! :-)
 
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quickclick330 said:
Fcent = m* v^2/r so... v = sqrt(F*r/m)

v = sqrt(640*7.5/3 ) = 41 m/s
Your method is fine. Just redo that calculation. (You're not off by much!)
 
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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