For full points I would like to see the correct answer and a brief explanation.

Question

For full points I would like to see the correct answer and a brief explanation.

Thank you.

You ride a roller coaster car of mass 1500 kg (including passengers) from rest down a frictionless track a vertical distance H = 42 meters above the bottom of a vertical loop as shown. The (circular) vertical loop is 30 m in diameter. When the roller coast car is upside down at the top of the vertical loop, the magnitude of contact force between the car and the track is F Newtons. assume the entire track is frictionless. Which of the following is closest to the speed in m/s of the roller coast car when it is upside down at the top of the vertical loop? If = 10 meters, which of the following is closest to the speed in m/s of the roller coast car when it is on the horizontal part of the track? Which of the following is closest to the value of F?

Explanation / Answer

1) conservation of energy

m g H = m g d + 1/2 mv^2

v = sqrt(2 g (H-d)) = sqrt(2*9.81*12)=15.34 m/s

2) m g H = m g h + 1/2 mv^2

v = sqrt(2 g (H-d))=sqrt(2*9.81*32)=25.06 m

3) F + mg = mv^2/r

F = 1500*15.34^2/15 - 1500*9.81=8817 N

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