How Is Centripetal Force Calculated for a Bird Pulling Out of a Dive?

[Fractal314]

1. A bird of mass 0.211kg pulls out of a dive, the bottom of which can be considered to be a circular arc with a radius of 25.6m. At the bottom of the arc, the bird's speed is a constant 21.7m/s. Determine the magnitude of the upward lift on the bird's wings at the bottom of the arc.

I am pretty sure that Fc= -4(pi squared)(r)(m)(f) / Tsquared

and... Fc= -mv squared / r

r= radius, m= mass, Fc = centripetal force

3. Ok so I don't understand what it means by "pulling out of a dive", I mean is that supposed to be part of the arc? This question is put under the heading centripetal force in my textbook but I don't understand how it is centripetal. Furthermore, if all is well, does it come down to the question being as simple as subbing in the values to the equation I have here.


Also, can anybody tell me how the centripetal force equation is derived from F=MA? I am lost on that too.

 

[Epsillon]

On the bottom of the dive there is the upward lift force pulling it up and also gravity pulling the bird down. so Fc= Upward lift force - Fg

 

[thomate1]

Firstly, let's define centripetal force. It is the force that keeps an object moving in a circular path, directed towards the center of the circle. In this case, the bird is moving in a circular path at a constant speed, so there must be a force acting on it to keep it moving in that path. This force is the upward lift on the bird's wings.

Now, let's look at the equations you have mentioned. The first equation is the formula for centripetal force, where r is the radius of the circle, m is the mass of the object, and T is the time it takes to complete one full revolution. The second equation is the simplified version, where v is the speed of the object and r is the radius.

In this scenario, the bird is pulling out of a dive, which means it is changing its direction from being downward to being horizontal. This change in direction requires a force to counteract the downward force of gravity and keep the bird moving in a circular path. This force is the upward lift on the bird's wings.

To calculate the magnitude of this upward lift, we can use the second equation you provided, Fc= -mv squared / r. Substituting the given values, we get Fc= -(0.211kg)(21.7m/s)^2 / 25.6m = -40.2N. However, since the question asks for the magnitude of the lift, we take the absolute value and get 40.2N as the answer.

Now, to answer your question about how the centripetal force equation is derived from F=MA, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F=ma). In circular motion, the acceleration is directed towards the center of the circle, and its magnitude is given by a=v^2/r. So, substituting this into the equation, we get F=mv^2/r, which is the same as the second equation you provided.

I hope this helps clarify your doubts. Remember, it is important to understand the concepts behind the equations rather than just memorizing them. Keep practicing and you will get the hang of it!