Circular motion-find the minimum speed

[Shad94]

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...

 

[nasu]

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?

 

[Shad94]

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

 

[Shad94]

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..

 

[Nickie]

The minimum speed that the ball can be moving at and still maintain a circular path can be found by equating the centripetal force (Tension) to the weight of the ball (mg). This is because the tension in the string provides the necessary force to keep the ball moving in a circular path, while gravity (mg) acts in the opposite direction.

Using the equation T = mv^2/r, where T is the tension, m is the mass of the ball, v is the speed, and r is the radius of the circle (in this case, the length of the string), we can set T equal to mg and solve for v:

mg = mv^2/r

Solving for v, we get:

v = √(rg)

Substituting in the values given in the question (m=4kg, r=1.2m, g=9.8m/s^2), we get:

v = √(1.2*4*9.8) = 6.93 m/s

Therefore, the minimum speed that the ball can be moving at and still maintain a circular path is approximately 6.93 m/s. Any lower speed would not provide enough centripetal force to keep the ball in a circular path.