Centrip Force and Coef. of Friction

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To determine the maximum velocity of a yoyo being whirled in a circle before the string breaks, the centripetal force formula can be applied, considering the mass of the yoyo and the breaking force limit. For a yoyo with a mass of 200 g and a breaking force of 10 N, the maximum velocity can be calculated using the equation F = mv²/r. In the case of a car navigating a curve with a radius of 100 m and a coefficient of friction of 0.5, the maximum velocity can also be derived from the centripetal force equation. The discussion emphasizes the importance of applying the correct formulas to solve these physics problems. Understanding these concepts is essential for solving similar centripetal force and friction-related questions.
Dunience
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Can someone help me on these problems?

Centrip Force prob.
A yoyo is whirled around in a circle over some yoyo’s head. The string will break if the force is greater than 10 N. If the mass of the yoyo is 200 g and the length of the string is 0.5 m, what is the maximum velocity of the yoyo?

The Coeffient/Centrip Force prob.
A car is going around a curve with a radius of 100 m. That is the maximum velocity of the car if the coefficient of friction is 0.5?
 
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What have you done so far?
 
how about using F_{centripetal} = \frac{mv^2}{r}

marlon
 
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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