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 320 m/s at this time, find the
radius of the loop.
Answer in units of km.

Answer 1

10·45 km

Explanation:

Given acceleration due to gravity = 9·8 m/s²

At the top of the loop-the-loop maneuver, her speed = 320 m/s

As she experiences weightlessness, at the top of the loop-the-loop maneuver, therefore the weight must be balanced by another force which is in this case is the centrifugal force

This centrifugal force is a pseudo force which will acting when we take the reference with respect to that circular motion which means we are working in that frame of reference

Since she is experiencing weightlessness, therefore the weight must be balanced by centrifugal force

Let the pilot mass be m kg

Weight = m × g

Centrifugal force = (m × v²) ÷ r

where m is the mass of the pilot

v is velocity

r is the radius of the circle

∴ m × g = (m × v²) ÷ r

∴ r = v² ÷ g = 320² ÷ 9·8 = 10448·98 m =10·45 km

∴ radius of the circle = r = 10·45 km

Answer 2

10·45 km

Step-by-step explanation:

Given acceleration due to gravity = 9·8 m/s²

At the top of the loop-the-loop maneuver, her speed = 320 m/s

As she experiences weightlessness, at the top of the loop-the-loop maneuver, therefore the weight must be balanced by another force which is in this case is the centrifugal force

This centrifugal force is a pseudo force which will acting when we take the reference with respect to that circular motion which means we are working in that frame of reference

Since she is experiencing weightlessness, therefore the weight must be balanced by centrifugal force

Let the pilot mass be m kg

Weight = m × g

Centrifugal force = (m × v²) ÷ r

where m is the mass of the pilot

v is velocity

r is the radius of the circle

∴ m × g = (m × v²) ÷ r

∴ r = v² ÷ g = 320² ÷ 9·8 = 10448·98 m =10·45 km

∴ radius of the circle = r = 10·45 km