Finding friction from tangential acceleration

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A car accelerates uniformly on a flat circular track with a tangential acceleration of 2.25 m/s² and skids off after traveling a quarter of the way around. To find the coefficient of static friction, the relevant equation incorporates both tangential and radial acceleration. The user initially struggled to calculate the radial acceleration but later resolved the issue independently. The discussion highlights the importance of understanding the relationship between tangential acceleration, radial acceleration, and friction in circular motion. The problem is ultimately solved, demonstrating the application of physics principles in real-world scenarios.
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[SOLVED] Finding friction from tangential acceleration

Homework Statement



A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 2.25 m/s^2. The car makes it one quarter of the way around the circle before it skids off the track. Determine the coefficient of static friction between the car and track from these data.

Homework Equations



\thetafinal = 90
\thetainitial = 0

friction = mass(net acceleration)

\mu = (sqrt((tan accel.)^2) + ((radial accel.)^2))) / g

The Attempt at a Solution



I know the above equation is used to find the coefficient of friction but I do know how to find the radial acceleration from what is given. Any help would be greatly appreciated. Thanks.
 
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Nevermind...I figured it out.
 
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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