4. A loop-the-loop roller coaster has a 12.0m radius. A car is moving at 25m/s a

Question

4. A loop-the-loop roller coaster has a 12.0m radius. A car is moving at 25m/s at the bottom of the loop.

A) What forces are doing work on the car as it goes through the loop? Explain.

B) Determine the velocity of the car at the top of the loop. Show your work and explain your reasoning.

C) Determine the force exerted by the seat of the car on a 75kg passenger when passing inverted at the top of the loop. Include a force diagram in your answer. Show your work.

D) What concepts did you apply in part (c) in order to work this problem? In which Units did you learn these concepts? List the concepts and the Units in which you learned them.

Explanation / Answer

a) there are primarily two forces, centripetal force which is always directed towards the center of loop and gravitational force always directed towards the earth.

b) we will use conservation of energy,

1/2 ( m) 25^2 = m(9.8)( 24) + 1/2 mv^2

312.5- 235.2 = 1/2 v^2

v at top = 12.43 m/s apprx

c) mv^2 / r = N + mg

where N is the force exerted by the seat on the passenger

N = m ( v^2/ r - g) = 75 ( 12.43^2/ 12- 9,.8) = 231.25 N

d) craeted conditions for forces equilbrium

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