Rate of change in temperature. Another way to do this?

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The discussion centers on solving a physics problem related to temperature change and energy transfer. The user has successfully calculated the rate of change in temperature using basic equations but is inquiring about a potential calculus-based approach. However, it is noted that the rate of change is constant, and the method used is deemed sufficient. The response confirms that no advanced calculus is necessary for this problem. Overall, the original solution is validated as effective.
navm1
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Homework Statement


[/B]
My question is regarding Part B of this problem, I have solved it but I'm wondering if there is another way to solve it since it says dtheta/dt and one of the hints I found online suggested that I use the chain rule.

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Homework Equations


Q = mc(deltaT)
Q/t = P

The Attempt at a Solution



For the first part, i just did theta/time to find angular velocity, then multiplied by radius to find the tangential velocity, then just multiplied by the force of 520N by pi/9, the tangential velocity to get 180 Watts.

For the second part I just divided the equation for Q by t to make deltaT/t=P/mc and got 0.064 C/s.

If there was a calculus way to solve this I'd appreciate some help. Thanks
 
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navm1 said:
For the second part I just divided the equation for Q by t to make deltaT/t=P/mc and got 0.064 C/s.

If there was a calculus way to solve this I'd appreciate some help. Thanks
There's no calculus of any interest here, the rate is constant. Your method is as good as any.
 
makes sense. thanks haruspex
 
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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