Question

A roller coaster starts from rest at A, rolls down the track to B, describes a circular loop of 12-m diameter, and travels up and down past point E. Assume that there is no energy loss due to friction. Given: h = 20 m. Shoe the free body diagrams at points B,D, and E. Determine the force exerted by his seat by a 80 kg rider at B and D and the minimum value of the radius of curvature at E if the roller coaster is not to leave the track at that point.

Answer 1

Free Body Diagrams at B, D and E;

By work energy theorem, speed of a body moving between 2 elevated points;

If body starts from rest;

For A and B,

For A and D,

For A and E,

Diameter is;

d = 12 m

Radius will be;

r = d/2 = 6 m

Taking the FBD of point-B;

...(Answer)

Taking the FBD of point-D;

...(Answer)

For minimum value of radius at E,

N_E = 0

Taking the FBD of point-E;

...(Answer)