Question

An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. the acceleration of gravity is 9.8 m/s 2 . if her speed is 210 m/s at this time, find the radius of the loop. answer in units of km.

Answer 1

Answer:

the radius of the loop is 4.5km

Explanation:

An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop-the-loop maneuver. the acceleration of gravity is 9.8 m/s 2 . if her speed is 210 m/s at this time, find the radius of the loop. answer in units of km.

using the formula

F=mv^2/r

f=centripetal force(N)

v=velocity

r=radius of the loop

m=mass of the aerobatic airplane

a= centripetal acceleration

NOte that the force needed to keep an object in a circular path is called centripetal force.

The centripetal force produces a centripetal acceleration

centripetal acceleration can be simpliifed with the following formular

a=$v^{2} /r$

9.8=$210^{2} /r$

r=44100/9.8

r=4500m

r=4.5km

the radius of the loop is 4.5km

Answer 2

 For "weightlessness," gravity = centripetal acceleration 
 g = v² / r 
 r = v² / g = (210m/s)² / 9.8m/s² = 4500 m = 4.5 km 
 The answer is 4.5 Km (radius of the loop)