Centripetal Force Minimum Period Question

In summary, we discussed the problem of a boy spinning a 3.00kg rock on a 0.70 m string at a constant speed. We were asked to find the minimum period for the rock to spin in a circle without breaking the string, given that the maximum tension allowed is 80.0 N. Using the equation m4π^2r/T^2, we can determine that the minimum period is 1.02 seconds. This equation may look odd, but it is correct and shows that minimum period corresponds to maximum speed and thus, maximum tension.
  • #1
Lax0
2
0

Homework Statement


A boy ties a 3.00kg rock to a 0.70 m string and begins spinning it around in a horizontal circle at a constant speed. If the string will break if the tension is greater than 80.0 N, what is the minimum period for the rock to spinning in a circle. How do i solve this?


Homework Equations



m4∏^(2 ) r/T^2

The Attempt at a Solution


80.0= (3.00)4∏^(2)(0.70)/T^2
T= 1.02
 
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  • #2
Welcome to PF!
Looks good. I get a very slightly larger answer; might be worth running it through the calculator again.
 
  • #3
Your equations written as pie squared r instead of pie r squared, i think you did it right but it looks weird
 
  • #4
anaximenes said:
Your equations written as pie squared r instead of pie r squared, i think you did it right but it looks weird

its the equation in the textbook. So can you explain how max tension gets minimum period?
 
  • #5
Lax0 said:
its the equation in the textbook.
Yes, the equation is correct, though it does look odd at first sight.
So can you explain how max tension gets minimum period?
The stone has a certain distance to cover, 2πr, in one period. So minimum period means maximum speed, and that means maximum tension.
 
  • #6
Sorry your right, its so weird seeing pie digitally
 

Related to Centripetal Force Minimum Period Question

1. What is centripetal force?

Centripetal force is the force that is directed towards the center of a circular path. It is responsible for keeping an object moving in a circular motion.

2. How is centripetal force related to minimum period?

The minimum period of an object in circular motion is directly related to the centripetal force acting on it. The stronger the centripetal force, the shorter the period of the object's motion.

3. What factors affect the minimum period of an object in circular motion?

The minimum period of an object in circular motion is affected by the mass of the object, the speed of the object, and the radius of the circular path. A larger mass or faster speed will result in a longer period, while a smaller radius will result in a shorter period.

4. How is the minimum period of an object in circular motion calculated?

The minimum period of an object in circular motion can be calculated using the formula T = 2π√(r/g), where T is the period, r is the radius, and g is the acceleration due to gravity.

5. Can the minimum period of an object in circular motion ever be equal to zero?

No, the minimum period of an object in circular motion cannot be equal to zero. This would mean that the centripetal force is also zero, and the object would no longer be in circular motion. The minimum period can approach zero, but it can never be exactly zero.

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