A 75 kg pilot flies in her plane in a loop and notices that at the top of the loop, where the plane is completely uspside down for an instant, she hangs freely in her seat. the airspeed indecator reads 120m/sec.
(a)what is the radius of the planes loop?
(b) What is the centripetal acceleration?
To find the radius of the plane's loop, we can use the centripetal force formula:
Centripetal Force = (mass) x (centripetal acceleration)
In this case, the pilot experiences a sensation of weightlessness at the top of the loop, which means the net force acting on her is zero. Therefore, the centripetal force acting on her must be equal to her weight:
Centripetal Force = Weight = (mass) x (gravity)
Substituting values:
(mass) x (centripetal acceleration) = (mass) x (gravity)
Since the mass cancels out, we can use the following equation to find the centripetal acceleration:
Centripetal acceleration = gravity
(a) Now, we can find the radius of the plane's loop using the formula for centripetal acceleration:
Centripetal acceleration = (velocity²) / (radius)
Since the velocity is given as 120 m/s and the centripetal acceleration is equal to gravity, we can rewrite the equation as:
gravity = (120 m/s)² / (radius)
To find the radius, rearrange the equation:
radius = (120 m/s)² / gravity
To solve the problem, we need to know the value of gravity. Assuming we are on Earth, the value of gravity is approximately 9.8 m/s².
Substituting the value of gravity:
radius = (120 m/s)² / 9.8 m/s²
Simplifying the equation, we have:
radius = 146.939 m
So, the radius of the plane's loop is approximately 146.939 meters.
(b) Since the centripetal acceleration is equal to gravity, the centripetal acceleration is 9.8 m/s².