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 m 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 m and the acceleration due to gravity g.

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Thu Thảo 5 years 2021-08-28T16:50:45+00:00 1 Answers 256 views 0

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  1. thienthi
    -1
    2021-08-28T16:52:19+00:00
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    Answer:

      N₁ -N₂ = mg [(v₁²-v₂²) / rg + 2]

       N₁- N₂ = 2mg

    Explanation:

    For this problem we apply Newton’s second law at the two points

    Bottom of the circle

    Y   Axis  

                  N₁ – W = m a

                  N₁ = m (a₁ + g)

                  N₁ = mg (a₁ / g + 1)

    Acceleration is centripetal

                 a₁ = v₁² / r

                  N₁ = mg (v₁² / rg + 1)

    Top of the circle

    Y Axis

                -N₂ – W = m (-a₂)

                  N₂ = m (a₂- g)

                  N₂ = m g (a₂ / g – 1)

                  a₂ = v₂² / r

                  N₂ = mg (v₂² / rg -1)

    The difference between this normal force is

                N₁ -N₂ = mg [v₁² / rg +1 – v₂² / rg +1]

                N₁ -N₂ = mg [(v₁²-v₂²) / rg + 2]

    In general the speed at the top of the circle is less than the speed at the bottom, as long as you have a system to keep this speed constant, if you keep it constant the result is reduced to

                 N₁- N₂ = 2mg

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