Circular motion- radius of the plane's vertical loop

In summary, the pilot's mass is 80kg and the airspeed indicator reads 110m/s at the top of the vertical loop. Using the equation Fc=mV2/R, we can calculate the radius of the loop to be 1,235m. This is confirmed by the fact that at this point, the pilot experiences weightlessness.
  • #1
dani123
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0

Homework Statement



An 80-kg pilot flies a plane in a vertical loop. At the top of the loop, where the plane is completely upside-down for an instant, the pilot hangs freely in the seat and does not push against the seat belt. The airspeed indicator reads the 110 m/s. What is the radius of the plane's vertical loop?

Homework Equations



Fc=Fg
Fc=mV2/R

The Attempt at a Solution



So we know that m= 80kg v=110m/s and we are looking for R.
In order to do this, I simply rearranged the Fc=mV2/R equation and solved for R. And this turned out to give me R=1 235m.

I would like if someone could verify that my work here is done correctly and that the significant figures are being respected. Thank you so much for your time and help :)
 
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  • #2
That is correct. You could also say that centripetal acceleration = v^2/R = g if there is no force on the pilot due to the seat or his seat belt. The pilot at this instant is effectively in 'free fall'
 

Related to Circular motion- radius of the plane's vertical loop

1. What is circular motion and how is it related to the radius of a plane's vertical loop?

Circular motion is the movement of an object along a circular path. In the case of a plane's vertical loop, the circular motion refers to the path the plane takes as it travels through the loop. The radius of the loop is the distance from the center of the loop to the outer edge.

2. How does the radius of a plane's vertical loop affect the speed and acceleration of the plane?

The radius of the loop directly impacts the speed and acceleration of the plane. A larger radius will result in a higher speed and lower acceleration, while a smaller radius will result in a lower speed and higher acceleration. This is because the larger the radius, the longer the distance the plane has to travel, while the smaller the radius, the shorter the distance.

3. What happens to the forces on the plane as it travels through a vertical loop?

As the plane travels through the loop, it will experience both centrifugal force and centripetal force. The centrifugal force, which is caused by the inertia of the plane wanting to continue in a straight line, will push the plane towards the outside of the loop. The centripetal force, which is provided by the track of the loop, will keep the plane moving in a circular path.

4. How does the angle of the plane's path affect the radius of the loop?

The angle of the plane's path does not directly affect the radius of the loop. However, it does impact the speed and acceleration of the plane, which in turn can affect the radius. A steeper angle of approach will result in a smaller radius and a faster speed, while a shallower angle will result in a larger radius and a slower speed.

5. What factors can influence the radius of a plane's vertical loop?

The main factor that can influence the radius of a plane's vertical loop is the initial speed of the plane. A higher initial speed will result in a larger radius, while a lower initial speed will result in a smaller radius. Additionally, the angle of approach, the mass of the plane, and external forces such as wind resistance can also play a role in determining the radius of the loop.

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