You have been tasked with designing a roller coaster track for an amusement park

Question

You have been tasked with designing a roller coaster track for an amusement park client. The major design constraint of the ride is that the passengers cannot experience a normal force equal to zero or more than 4 times their weight. Given the design constraint, determine the limiting heights hA and hC of the two hills A and C shown in the drawing below. The roller coaster starts at point A. Also, the radius of the curve at point B is 15 m and at point C is 20 m. Neglect friction.

You have been tasked with designing a roller coaster track for an amusement park client. The major design constraint of the ride is that the passengers cannot experience a normal force equal to zero or more than 4 times their weight. Given the design constraint, determine the limiting heights hA and hC of the two hills A and C shown in the drawing below. The roller coaster starts at point A. Also, the radius of the curve at point B is 15 m and at point C is 20 m. Neglect friction.

Explanation / Answer

speed at b, vB = sqrt(2g*hA) at b, force equlibrium Nb-mg = mvB^2/RB Nb - mg = m*(2g*hA)/15 Nb = mg(1+ 2hA/15) Nb 1 + 2*hA/15 or = 12.5 m limiting value of hC = 12.5 m ANSWER : hA = 22.5 m , hC = 12.5 m

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