Car Crash on Inclined Circular Racetrack

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A car is navigating an inclined circular racetrack at a 40-degree angle, with the center of rotation located 45 meters from the car and 5 meters above ground level. The car maintains maximum speed due to a coefficient of kinetic friction of 0.35. Upon hitting an oil slick, the friction coefficient drops to zero, leading to a loss of control. The discussion clarifies that the center of rotation is effectively the center of the track. Understanding these parameters is crucial for visualizing the car's trajectory and crash point.
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"A car is driving on a circular racetrack, which is inclined at an angle of 40 degrees to the horizontal. The centre of rotation for the track lies in the horizontal plane, and is 45 m from the centre fo the racetrack and 5.0 m above ground level. The car's tires have a coefficient of kinetic friction of 0.35. The car is driving at the maximum possible speed to stay in its position on the narrow track. All of a sudden, the car hits an oil slick and the coefficient of friction is reduced to 0. Where, relative to the centre of the track, does the car crash into the ground?"

I need help visualizing this problem. Where exactly is this "centre of rotation for the track"?
Thank you! :)
 
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Hi sparkle123! :smile:

Your problem appears to be badly formulated.
It should say:
"The centre of rotation for the track lies in the horizontal plane, and is 45 m from the car and 5.0 m above ground level."
 
Thanks I like Serena! :)

so centre of rotation for the track = centre of track?
 
Yep! :)
 
Thanks! :)
 
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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