Find Minimum Radius for Safe Vertical Looping | Jet Pilot in 1400 km/h Loop

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In summary, the conversation is about determining the minimum radius of a vertical loop for a jet pilot flying at a speed of 1400 km/h, so that the centripetal acceleration at the lowest point does not exceed 6.0 g's. The equation F=m(v^2/r) is used to calculate the centripetal acceleration, but since the mass is unknown, the normal force minus the weight of the jet cannot be used. Instead, only the acceleration needs to be calculated by using the formula v^2/r.
  • #1
justinbaker
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A jet pilot takes his aircraft in a vertical loop

(a) If the jet is moving at a speed of 1400 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g's.


I am having some trouble here. I converted the speed to be 389 m/s. I thought i would use the equation F=m(v^2/r) Then F would equal the normal force minus mg. But this does not seem to work out since we do not know the mass. I am a little confused. So any help would be great. Thanks
 
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  • #2
F = ma.. Fcent = m*Acent
 
  • #3
vsage said:
F = ma.. Fcent = m*Acent

i don't understand what you are saying
 
  • #4
I'm saying the question is asking for centripetal acceleration which is given by v^2/r. You don't need to sum the forces just the accelerations.
 

1. What is the radius of a circle?

The radius of a circle is the distance from the center of the circle to any point on the circle's circumference. It is represented by the letter "r" and is usually measured in units such as inches, centimeters, or meters.

2. How do I find the radius of a circle?

To find the radius of a circle, you can use the formula: r = C/2π, where C is the circumference of the circle and π is the mathematical constant pi (approximately 3.14). You can also measure the distance from the center of the circle to any point on the circumference using a ruler or measuring tape.

3. Can I find the radius of a circle if I only know its diameter?

Yes, you can find the radius of a circle if you know its diameter. The diameter is the distance across the circle passing through the center, and it is equal to twice the radius. Therefore, you can find the radius by dividing the diameter by 2.

4. How do I find the radius of a circle if I only know its area?

To find the radius of a circle if you know its area, you can use the formula: r = √(A/π), where A is the area of the circle and π is the mathematical constant pi. You can also rearrange the formula for area (A = πr²) to solve for the radius.

5. Can the radius of a circle be negative?

No, the radius of a circle cannot be negative. It is a measure of distance and, therefore, is always positive. If you are working with equations that involve the radius, it is important to remember to use the absolute value to ensure a positive value is obtained.

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