Consider a circular vertical loop-the-loop on a roller coaster. A car coasts without power around the loop. Determine the difference between

Question

Consider a circular vertical loop-the-loop on a roller coaster. A car coasts without power around the loop. Determine the difference between the normal force exerted by the car on a passenger with a mass of mm at the top of the loop and the normal force exerted by the car on her at the bottom of the loop. Express your answer in terms of mmm and the acceleration due to gravity ggg.

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Khánh Gia 3 years 2021-09-05T08:02:00+00:00 1 Answers 13 views 0

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    2021-09-05T08:03:45+00:00

    Answer:

    Explanation:

    Let v₁ and v₂ be velocities at lowest and topmost position . Let r be the radius of the circle .

    Let N₁ and N₂ be the normal reaction force .

    At the top position

    centripetal force = N₂ + mg ;  so

    N₂ + mg  = m v₂² / r

    At the bottom  position

    centripetal force = N₁ – mg ;  so

    N₁ – mg  = m v₁² / r

    subtracting these two equations

    N₁ – mg – N₂ – mg = m v₁² / r  – m v₂² / r

    N₁ – N₂ – 2mg = 1/r (m v₁²   – m v₂²  )

    N₁ – N₂ – 2mg = 1/r x mg x 2r  ( loss of potential energy = gain of kinetic energy )

    N₁ – N₂ =  2mg +  2mg

    = 4 mg .

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