Minimum speed to maintain a circular trajectory

[xxgaxx]

Homework Statement

a rock of mass 0.500 kg is tied to a string of radius 75 cm and is revolving in a vertical circle at a uniform speed. determine the minimum speed for the rock to maintain a circular trajectory without the string collapsing (not staying taut). (Hint: where would that occur in the trajectory?)

m=0.500 kg
r=.75 m

Homework Equations

mg=(mv^2)/r

The Attempt at a Solution

v=(gr)^(1/2) (square root of g*r)
v=2.7 m/s
i don't know where i use the mass of 0.500 kg

 

[Hootenanny]

Homework Statement

a rock of mass 0.500 kg is tied to a string of radius 75 cm and is revolving in a vertical circle at a uniform speed. determine the minimum speed for the rock to maintain a circular trajectory without the string collapsing (not staying taut). (Hint: where would that occur in the trajectory?)

<snip>

mg=(mv^2)/r

Are you sure that the weight of the rock is the only force acting? Furthermore, are you sure that the weight of the rock always acts radially?

 

[baba89]

I can confirm that your solution for the minimum speed to maintain a circular trajectory is correct. The equation you used, mg=(mv^2)/r, is the centripetal force equation and can be used to solve for the minimum speed required for the rock to stay in circular motion without the string collapsing. The mass of 0.500 kg is used in this equation to represent the weight of the rock, or the force of gravity acting on it. This force must be balanced by the centripetal force in order for the rock to maintain its circular trajectory. Your solution demonstrates a clear understanding of the concept of centripetal force and its role in circular motion. Good job!