question archive A roller coaster is being designed on a parabolic track: that rotates at a constant speed as seen in the figure above
A roller coaster is being designed on a parabolic track: that rotates at a constant speed as seen in the figure above
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A roller coaster is being designed on a parabolic track: that rotates at a constant speed as seen in the figure above. Assume the cart rolls on the track as a frictionless point-rnass of 'l CID-kg. Determine the equations of motion in terms of the distance from the lowest point, q1 = $2. a. What is the lcinetic energy of the cart? b. What is the potential energy of the cart? c. What is the equation of motion for the cart?
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Solution 2 2 = 0:5 K2 Z m = 100 kq let at height to from orformed live - Rafoence velocity of mars is v such that V=Wr where Is as the radial distance at weight z Balancing energy - 2 I mv 2 = maz Im wigz = my z 2 = W29 2 For 91 = X2 putting 2 , = W2 x 2 comparing, with given equation (1) W 2 - 29 2 05 $0, w = Jo so, kinetic energy of the cant = 1 my 2 = 1 m (AL)2 = 1 X100x (59 ) 2 ,2 2 = 490 92 = 490 xx (6 ) potential energy of the cart = maz = 100 X 9. 80 * 2 2 980 2 2 equation of motion of cart is - where 10 = 19 & is radial distance of cast at height I I is acceleration due to gravity
