A race car driving on a banked track that makes an angle θ with the horizontal rounds a curve for which the radius of curvature is R.

Part A

There is one speed vcritical at which friction is not needed to keep the car on the track. What is that speed in terms of θ and R? Express your answer in terms of the variables R, θ, and the acceleration due to gravity g. vcritical =

Part B

If the coefficient of friction between tires and road is μ, what maximum speed can the car have without going into a skid when taking the curve? Express your answer in terms of the variables R, θ, μ and the acceleration due to gravity g. vmax =

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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