Vertical circle, miminum radius

In summary, the question involves finding the maximum radius of a vertical circle for a fighter pilot diving at a supersonic speed, where her apparent weight is never more than six times her weight. To solve this, the equation for apparent weight is used, along with the equation for centripetal acceleration, which can be rearranged to solve for acceleration. The resulting value can then be substituted into the first equation and set equal to six times the weight to find the maximum radius.
  • #1
sunnyorange
7
0
This is my question
A fighter pilot dives her fighter plane toward the ground at maximum supersonic speed of 2170 km/hr. She pulls out of the dive on a vertical circle. What is the maximum radius of the circle, so that her apparent weight is never more than six times her weight?

I have no idea how to approach this. However, I know apparent weight= mg+ma, and a_c= V^2/r

Help needed!:eek:
 
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  • #2
well solve your second eq for a then sub it into your first and have it equal to 6*w
 
  • #3
mathmike said:
well solve your second eq for a then sub it into your first and have it equal to 6*w

How do I find the centripetal acceleration? radius?
 

1. What is a vertical circle and minimum radius?

A vertical circle is a circular motion performed by an object in a vertical plane, while a minimum radius refers to the smallest distance from the center of the circle to its edge.

2. How is the minimum radius of a vertical circle calculated?

The minimum radius of a vertical circle can be calculated using the equation R = v^2 / g, where R is the minimum radius, v is the velocity, and g is the acceleration due to gravity.

3. What factors affect the minimum radius of a vertical circle?

The minimum radius of a vertical circle is affected by the velocity of the object, the acceleration due to gravity, and the mass of the object. A higher velocity and lower acceleration or mass will result in a smaller minimum radius.

4. Why is the minimum radius important in vertical circle motion?

The minimum radius is important in vertical circle motion because it determines the tightness of the circle and the amount of force needed to keep the object moving in that circular path. A smaller minimum radius requires a greater centripetal force to keep the object from flying off the circle.

5. Can the minimum radius of a vertical circle ever be zero?

No, the minimum radius of a vertical circle can never be zero. This would mean that the object is not moving in a circular path, but rather in a straight line, which is not considered vertical circle motion.

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