Linear Speed and Circular Motion Problem

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The problem involves an air puck revolving in a circle with a circumference of 2π, tied to a 1kg mass that remains in equilibrium. To find the force maintaining the circular path (Fc) and the linear speed of the puck (vt), the relevant equations include Fc = m*(vt^2) / r and vt = r*w. The user is struggling to determine the angular speed (w) and linear speed (vt) due to missing variables. Newton's third law is suggested as a principle to apply for calculating the force. Clarification on how to relate the variables is needed for a complete solution.
Cheapo2004
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Ok, I am having a hard time figuring this problem out for two reasons, the first is that my teacher is very tricky, 2nd is that I'm not sure how to work it out.

An air puck is tied to a string and allowed to revolve in a circle with circumference if 2pi. The other end of the string passes through a hole in the center of the surface and a mass of 1kg is tied to it. If the suspended mass remains in equilibrium..
A) What is the magnitude of the force that maintains the circular path
B) What is the linear speed of the puck

So, what I got out of this question is:
2pi*r = cir... so r=1
m = 1kg

So, with the information given, we need to find Fc (force that maintains circular path). The equations i have to find this are:

Fc = m*(vt^2) / r
Fc = m*r*(w^2)
(w meaning angular speed)

So, for either equation i need to find w, or vt. The equations i have for these are:

vt = r*w
w = Delta Theta / Delta T

So by moving from equation to equation I'm still missing 2 variables, I can't figure it out

Any help is appreciated!
 
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Use Newton III for A.
 
Päällikkö said:
Use Newton III for A.
...? Newton's 3rd law...?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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