Uniform circular motion - plane in a circular arc

To find the radius of the plane's arc, you can use the equation ac = v^2/r where ac is the centripetal acceleration, v is the speed of the plane, and r is the radius of the arc. You can rearrange this equation to solve for r, which will give you the radius of the plane's arc. The mass of the plane is not needed for this calculation. In summary, to find the radius of the plane's arc, use the equation ac = v^2/r where ac is the centripetal acceleration, v is the speed of the plane, and r is the radius of the arc.
  • #1
Sean1218
86
0

Homework Statement



As a pilot comes out of a dive in a circular arc she experiences an upward acceleration of 9.0 gs (i.e. 9 x 9.8).

a) Mentions that the Pilot's mass is 60 kg, already solved this

b) If the speed of the plane is 330 km/h, what is the radius of the plane's arc?

Homework Equations



ac = v2/r
Fnet = [tex]\Sigma[/tex]F

The Attempt at a Solution



No idea what to do because I can't figure out what is causing the centripetal acceleration.

mv2/r = - mg

I don't know the mass of the plane, and if I add another force which I assume would cause the centripetal acceleration then I have no way of calculating that either.
 
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  • #2
The upward acceleration the pilot experiences is directed towards the center of rotation, so you are given the centripetal acceleration.
 

1. What is uniform circular motion?

Uniform circular motion is the motion of an object along a circular path at a constant speed. This means that the object is moving with the same speed and direction at every point along the path.

2. What is the difference between uniform circular motion and non-uniform circular motion?

The main difference between uniform circular motion and non-uniform circular motion is that in uniform circular motion, the speed of the object remains constant, while in non-uniform circular motion, the speed changes at different points along the path.

3. How does the centripetal force affect an object in uniform circular motion?

The centripetal force is the force that keeps an object moving in a circular path. In uniform circular motion, the centripetal force acts towards the center of the circle and is responsible for changing the direction of the object’s velocity, but not its speed.

4. Can an object in uniform circular motion have a changing velocity?

Yes, an object in uniform circular motion can have a changing velocity. While the speed remains constant, the velocity changes because its direction is constantly changing due to the centripetal force.

5. How is the acceleration of an object in uniform circular motion calculated?

The acceleration of an object in uniform circular motion can be calculated using the formula a = v²/r, where a is the acceleration, v is the speed, and r is the radius of the circular path. This means that the acceleration is directly proportional to the square of the speed and inversely proportional to the radius of the path.

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