Calculating the pilot's effective weight at the bottom and top of a circle

In summary: I allowed to answer this?:In summary, the problem involves a jet pilot taking his aircraft in a vertical loop with a speed of 1500 at the lowest point. The first part asks for the minimum radius of the circle to avoid exceeding 6.6's centripetal acceleration. The answer is 2.7 X 10^3. The second part involves calculating the pilot's effective weight at the bottom and top of the loop, assuming the same speed. To solve this, one must draw a free body diagram, determine the sum of all forces, and use the equation for the sum of all forces to find the magnitude of the normal force.
  • #1
bfpearce
1
0
Ok so there are two part to this problem:

Info: A jet pilot takes his aircraft in a vertical loop

Part 1: If the jet is moving at a speed of 1500 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 6.6 's.

I got the answer of this one to be 2.7 X 10^3

Part 2: Calculate the 68- pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed).

I honestly don't even know where to start with this one. Can somebody help??
 
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  • #2
bfpearce said:
Ok so there are two part to this problem:

Info: A jet pilot takes his aircraft in a vertical loop

Part 1: If the jet is moving at a speed of 1500 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 6.6 's.

I got the answer of this one to be 2.7 X 10^3

Part 2: Calculate the 68- pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed).
What are the forces acting on the pilot at the bottom? Draw a free body diagram. What must the sum of all forces be equal to in any free body diagram? What is the acceleration of the pilot at the bottom? Write out the equation for the sum of all forces. What must the magnitude of the normal force be in order for the forces to add up to the total net force?

Now do the same thing for pilot at the top of the loop.

AM
 

FAQ: Calculating the pilot's effective weight at the bottom and top of a circle

1. How do you calculate the pilot's effective weight at the bottom and top of a circle?

To calculate the pilot's effective weight at the bottom and top of a circle, you need to use the formula W = mg + mv²/r, where W is the effective weight, m is the mass of the pilot, g is the acceleration due to gravity, v is the velocity of the plane, and r is the radius of the circle.

2. What factors affect the pilot's effective weight at the bottom and top of a circle?

The pilot's effective weight at the bottom and top of a circle is affected by the mass of the pilot, the acceleration due to gravity, the velocity of the plane, and the radius of the circle. These factors all play a role in determining the centripetal force acting on the pilot.

3. Why is it important to calculate the pilot's effective weight at the bottom and top of a circle?

Calculating the pilot's effective weight at the bottom and top of a circle is important because it helps determine the amount of force the pilot experiences while flying in a circular path. This information is crucial for ensuring the safety and stability of the plane and the pilot.

4. Are there any safety considerations when calculating the pilot's effective weight at the bottom and top of a circle?

Yes, there are safety considerations when calculating the pilot's effective weight at the bottom and top of a circle. It is important to ensure that the centripetal force acting on the pilot does not exceed the limits of the plane and the pilot's body. Excessive forces can lead to loss of control and potential danger for the pilot.

5. How does the pilot's effective weight change as the plane travels in a circular path?

The pilot's effective weight changes as the plane travels in a circular path due to the changing velocity and radius of the circle. At the bottom of the circle, the effective weight is greater due to the added force of the plane's velocity. At the top of the circle, the effective weight is less due to the decreased force of the plane's velocity. The radius of the circle also affects the effective weight, with a smaller radius resulting in a greater effective weight.

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