High School

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Calculate the normal force with which the seat acts on the 83 kg pilot at the top of the circle (assume the same speed).

A. [tex]F = mg[/tex]
B. [tex]F = 83 \, \text{kg}[/tex]
C. [tex]F = g[/tex]
D. [tex]F = 0 \, \text{N}[/tex]

Answer :

Final answer:

The normal force experienced by a pilot at the top of a circle can be calculated based on the difference between the centripetal force required for circular motion and the gravitational force. Without specific values for speed or centripetal force, we can't determine an exact value for the normal force, and the options provided are either incorrect representations of force or conditionally correct.

Explanation:

To calculate the normal force with which the seat acts on an 83 kg pilot at the top of the circle, we assume the pilot is in circular motion. At the top of the circle, the normal force (N) and the gravitational force (mg) act in opposite directions, and the pilot feels lighter. If the pilot's speed is such that the centripetal force required for circular motion is equal to the gravitational force (mg), then the normal force would be zero, since there would be no need for the seat to exert any additional force to maintain the circular path.

However, if the centripetal force required is greater than mg, then the normal force would be the difference between the centripetal force and gravitational force. This can be represented by the equation: N = ma_c - mg, where a_c is the centripetal acceleration. Conversely, if the centripetal force required is less than mg, the normal force would be adding to the gravitational force to provide the necessary centripetal force.

Without the specific value of the centripetal force or the speed of the pilot, we cannot calculate an exact value for the normal force. Nonetheless, theoretically, options (a) F = mg, (b) F = 83 kg, (c) F = g are incorrect for they do not represent forces, and (d) F = 0 N could be correct only under the special circumstance mentioned above where centripetal force equals the gravitational force.

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