A roller coaster cart and passengers has a capacity of 2.000 kg. The roller coas

Question

A roller coaster cart and passengers has a capacity of 2.000 kg. 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 Diagram for the cart Write Newton's 2^nd Law equation(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 I be acceptable for this part). What is the minimum speed required for the cart to make it around the loop?

Explanation / Answer

b) Fnet at the top of loop = mg- 2mv^2/ h2

c) we will use conservation of energy to calculate the minimum height from which the cart should be released to stay in touch with loop,

Initial pE = KE at the top of loop + PE at the top of loop

mg (H1) = 1/2mv^2 + mg(h2)--------eq(1)

minimum force required for cart to stay in touch with loop wll happen when, mg =2mv^2/ h2

v^2 = h2g/ 2

plugging value of v^2 in eq(1),

mgH1= 1/2m (h2g/ 2 )+ mg(h2)

H1 = h2/ 4 + h2 = 5/4( h2)----------condition for cart to stay in touch with loop at top

d)minimum speed

v= sqroot ( h2g/ 2)

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