Circular motion-find the minimum speed

AI Thread Summary
To maintain a circular path, the minimum speed of the ball is determined by the gravitational force acting on it at the top of the circle. At this point, the tension in the string becomes zero, meaning the centripetal force required for circular motion is provided solely by gravity. The formula for minimum speed (v) can be derived from the equation v = √(g * r), where g is the acceleration due to gravity and r is the radius of the circle. For a 1.2m string, the minimum speed is approximately 3.43 m/s. Understanding these principles clarifies the relationship between speed, tension, and gravitational force in circular motion.
Shad94
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The question is:

A ball of a mass 4kg is attached to the end of a 1.2m long string and whirled around in a circle that describes a vertical plane..what is the minimum speed that the ball can be moving at and still maintain a circular path?

i try solve it by use T+mg=mv*2/r.But i can't find the tension...
 
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Shad94 said:
The question is:

A ball of a mass 4kg is attached to the end of a 1.2m long string and whirled around in a circle that describes a vertical plane..what is the minimum speed that the ball can be moving at and still maintain a circular path?

i try solve it by use T+mg=mv*2/r.But i can't find the tension...

You don't need to calculate the tension. What is the condition for the "minimum speed"?
Or what happens with T when v is less than that minimum?
 
Can you give me the answer...because i still don't understand it..
 
nasu said:
You don't need to calculate the tension. What is the condition for the "minimum speed"?
Or what happens with T when v is less than that minimum?

Can you give me the answer...because i still don't understand it..
 
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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