Where Is The Worst Place To Throw Up On A Rollercoaster?

Calculus Level 3

The above is an image of the Texas Giant wooden roller coaster located at Six Flags (an amusement park) in Texas.

From the top, the roller coaster is released and falls freely along the track. At which point would it experience the fastest acceleration ?

Image credit: Wikipedia
The acceleration is the same at all points C B A

Chung Gene Keun by Chung Gene Keun , 42, USA

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7 solutions

Võ Trọng
Mar 8, 2014

The slope at point B B has biggest value, so that B is correct answer.

12 Helpful 0 Interesting 0 Brilliant 0 Confused

a t o t a l = a t a n g e n t i a l 2 + a n o r m a l 2 a_{total} = \sqrt{a_{tangential}^2 + a_{normal}^2} ; though a t a n g e n t i a l a_{tangential} is highest at point B, since a n o r m a l = v 2 r a_{normal} = \frac{v^2}{r} and as the speed v v increases from A to C, we need to know the radius of curvature r r at each of the points to find the radial acceleration. a t a n g e n t i a l = 0 a_{tangential} = 0 at point B. so we have inadequate information to answer where the acceleration is the highest

Sreekar Guddeti - 7 years, 3 months ago

the answer is A because by the rule of oscillation the maximum accelertion take place at maximum extreme point

owesh ali - 7 years, 3 months ago

It is free falling.so,the governing parameter here is not the radial but the gravital acceleration which is maximum at point B as the track is almost vertical

islam abbady - 7 years, 3 months ago

may i be explained...

Sitaram Dash - 7 years, 3 months ago

B

Suraj Singh - 7 years, 3 months ago
Abhinav Jha
Mar 10, 2014

the roller coaster curve can be imagined as a function curve. The tangent at the points would give the weight component and the corresponding acceleration

4 Helpful 0 Interesting 0 Brilliant 0 Confused

but if u consider it as an SHM then

Deepanshu Dochaniya - 7 years, 3 months ago
Prakhar Gupta
Mar 10, 2014

There will be only two forces at any point on the roller coaster over the whole track.

Hence we have to look for a point where these two points cancel each other the least.

At point A and C the force of gravity is reduced greatly by the normal reaction by the track as the track is almost parallel to the earth.

At point B the track being almost vertical the two forces cancel each other by very small amount. Hence acceleration will be maximum at point B.

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Ayush Kumar
Mar 11, 2014

at point B the normal reaction changes its direction so centifugal force increase by double of normal reaction suddenly so roller coaster experince a very much force which is outward to to arc at point B.

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Ma Aditya
Mar 11, 2014

Component of gravity acting on the cart is highest at point B ( g sin ɵ is highest since ɵ is highest). Hence once you throw up, your resultant velocity increases at a higher rate than your vomit's. Hence, well you know what could happen after that.

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Jaseela Thasneem
Mar 9, 2014

acceleration is increasing upto middle of the way.. then it decrease

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Arijit Banerjee
Mar 8, 2014

at B slope is maximum ...so acc is max...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Why did u exclude radial accleration ?

Rohit Shah - 7 years, 2 months ago

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