Spiraling up/uniform circular motion, combined with constant velocity (Help)

In summary, the conversation is about a problem involving birds of prey rising on thermals and modeling their spiral motion as uniform circular motion with a constant upward velocity. The question asks for the bird's speed relative to the ground, magnitude and direction of acceleration, and the angle between its velocity vector and the horizontal. The equations used include a = v^2/R for finding acceleration and simple geometry for finding the angle. The student is seeking help and advice on how to approach the problem.
  • #1
cassandralynn
1
0

Homework Statement


Please help! This is my question!

It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 8.00m every 5.00s and rises vertically at a rate of 3.00m/s .
a)Find the speed of the bird relative to the ground.
b)Find the magnitude of the bird's acceleration.
c)Find the direction of the bird's acceleration.
d)Find the angle between the bird's velocity vector and the horizontal.

Homework Equations


I'm not to sure of the equations that I should really use as I am trying to re-learn all the math behind it! My guesses are:
a) a(rad) = v^2/R and stops from there...

The Attempt at a Solution


I have made a diagram of what I think it should look like but that's about as far as my attempt goes... I am in need of some help and advice, My main problem is looking at the question and trying to decide what equation will give me the right answer. Please help!
 
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  • #2
(a) you can find the linear distance the bird travels in one revolution and then divide by the time it takes to get the velocity.

(b) Use the formula you gave as a relevant equation.

(c) In circular motion, where does the acceleration vector point?

(d) You know the linear velocity (vx) and the vertical velocity (vy). If you draw a diagram, it should be apparent that you can find the angle with some simple geometry.

edit: for (b) and (c) you might need to take into account gravity. This means you'll need to do a bit of geometry as well.
 

FAQ: Spiraling up/uniform circular motion, combined with constant velocity (Help)

What is spiraling up/uniform circular motion?

Spiraling up/uniform circular motion refers to the motion of an object moving in a circular path with a constant speed. This motion is characterized by a continuous change in direction, resulting in the object moving in a spiral-like pattern.

How is spiraling up/uniform circular motion different from regular circular motion?

Spiraling up/uniform circular motion is different from regular circular motion because it involves a simultaneous combination of two types of motion: circular motion and constant velocity. In regular circular motion, the speed of the object may vary, while in spiraling up/uniform circular motion, the speed remains constant.

What causes an object to spiral up in uniform circular motion?

In uniform circular motion, an object spirals up due to the combination of its constant velocity and the centripetal force acting on it. The centripetal force, which is directed towards the center of the circular path, continuously changes the direction of the object's motion, causing it to spiral up.

How does the radius of the circular path affect the object's spiraling up motion?

The radius of the circular path affects the object's spiraling up motion by determining the amount of centripetal force acting on the object. A smaller radius will result in a larger centripetal force, causing the object to spiral up at a faster rate. On the other hand, a larger radius will result in a smaller centripetal force, causing the object to spiral up at a slower rate.

What is the relationship between the speed and acceleration in spiraling up/uniform circular motion?

In spiraling up/uniform circular motion, the object's speed remains constant, but its acceleration is constantly changing. This is because the object is changing direction at each point along its circular path, resulting in a continuous change in its acceleration. However, the magnitude of the acceleration remains constant, as it is determined by the object's speed and the radius of the circular path.

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