Finding friction from tangential acceleration

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SUMMARY

The discussion addresses the calculation of the coefficient of static friction for a car accelerating uniformly on a flat circular track with a tangential acceleration of 2.25 m/s². The car travels one quarter of the way around the circle before skidding off, prompting the need to determine the friction coefficient using the equation μ = (sqrt((tan accel.)² + (radial accel.)²)) / g. The user initially struggled to find the radial acceleration but later resolved the issue independently.

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  • Understanding of circular motion dynamics
  • Familiarity with tangential and radial acceleration concepts
  • Knowledge of static friction and its coefficient
  • Basic algebra for solving equations
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  • Study the derivation of radial acceleration in circular motion
  • Learn about the relationship between tangential and radial accelerations
  • Explore the application of Newton's laws in circular motion scenarios
  • Investigate real-world examples of friction in automotive dynamics
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Physics students, automotive engineers, and anyone interested in the dynamics of motion and friction in circular paths.

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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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