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What are the laws of Physics involved in the design of the roller coaster?

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Introduction

Physics Project – The working of a roller coaster

Research Question 1 – What are the laws of Physics involved in the                                                             design of the roller coaster?

Ans. The following laws apply to all roller coasters –

  1. Potential and kinetic energy conversions – The roller coaster is pulled up the initial hill by a chain lift and gains potential energy. As it moves down the hill this converts into kinetic energy. This process continues throughout the ride.  
  1. Law of Conservation of Energy – Energy can't be lost or created, only transferred or converted. Therefore, the total mechanical energy of the train is constant throughout the ride. The total mechanical energy E = k.e. + p.e. .
  1. Friction – In real life energy is not conserved. Friction opposes motion and acts backwards. It is a non – conservative force. Thus, any one component in the ride must be lower than the previous one as energy is lost all the time.
  1. Centripetal Acceleration – The formula for centripetal acceleration is – ar = v^2 / r where ar – acceleration, v – velocity and r – radius. This acceleration is caused by the centripetal force which act towards the centre of the loop.
  1. 'G' – forces
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Middle

  1. The g – forces felt by riders : Both normal and lateral (sideways). If the downward forces experienced by riders’ are too strong, the ride can be uncomfortable and at times even fatal.
  1. Centripetal acceleration during the loop : If the acceleration is too high during the loop riders' will feel 'sucked' towards the centre at the top at times resulting in fatal neck injuries.
  1. Riders need to be healthy : Riders' with brain problems, heart problems, high blood pressure should not ride on the coasters. One has to also meet certain height and weight restrictions.

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Physics Project – The working of a roller coaster

Research Question 3 – Why are the loops clothoid and not circular?

Ans. The reason for loops being clothoid and not circular is –

A larger radius means a lower centripetal acceleration. A clothoid shape is like a teardrop. If the loop is circular the centripetal acceleration is constant throughout as the radius is constant.

However, a teardrop shape has a sharper turn at the top which makes the radius smaller. This ensures that the centripetal acceleration is higher at the top.

The coaster can be then

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Conclusion

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Physics Project – The working of a roller coaster

Research Question 5 – When at the top of the loop a rider will feel partially weightless. Why?

Ans. The reasons for weightlessness are –

  1. At the top of the loop gravity is pulling you downwards and the centrifugal (upward) force is also present. The resultant force is near zero and this is why you feel almost completely weightless.
  1. When a rider is at the top of the loop he applies a force on the floor of the coaster which can be termed as the riders' 'apparent' weight. The apparent weight acts upwards and adds to the centrifugal force.
  1. Our body is made up of different organs suspended in a fluid, blood. When we accelerate normally our body parts push each other. However, in a roller coaster as there is hardly any net force acting on the rider so the organs don't push each other as much as they do normally and thus they feel weightless (ex :- Stomach).

Note:- At times the centrifugal (acceleration) forces are so high that the rider feels negative 'g' – forces and feels as though he is being pulled upwards (net force is upwards).

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