A roller coaster cart and passengers has a capacity of 2,000kg. The roller coast

Question

A roller coaster cart and passengers has a capacity of 2,000kg. The roller coaster needs to be designed such that the cart and passengers can make it around a loop that has a radius of 20m. At the top f the loop draw the Free Body Diagramed for the cart. Write Newton's 2^nd Law equations (s) at the top of the loop. What condition is required for the cart to remain in contact with the track at the top of the loop? (An equation or explanation will be acceptable for this part). What is the minimum speed required for the cart to make it around the loop?

Explanation / Answer

a) At the top of the loop draw the free body diagram , Draw two forces dowanwards ,Normal Reaction and and Weight ! Both arrows dowanward

b) N+mg= ma ( N= normal force, mg= weight, m, mass, a= acceleration)

c) N+mg= ma

N+mg= mv^2/r

v= speed at the top , It has to be in contact then lets take the limiting condition, Say just about to loose , Lets take N=0

so mg= mv^2/r

v^2/r=g

v= Sqrt(rg) That should be the minimum speed at the top most point

d) Use energy conservation lets say it just reaches at the top

so 0.5 mv^2 = mgh (h=2r)

v= sqrt(2gh)

v= sqrt(2*9.8*40) = 28 m/s

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