Sigma FyB = MayB The roller -coaster car/rider of mass M shown in the figure at

Question

Sigma FyB = MayB The roller -coaster car/rider of mass M shown in the figure at right is released from rest from a height h and then moves freely with negligible friction, I he roller -coaster track includes a circular loop of radius R in a vertical plane. By working through different parts of this problem given below. yon will first derive an expression for the minimum height hmin from which the cart should be released if it is to barely complete the loop. Then you will derive an expression for the normal force exerted on the car/rider at the bottom of the loop (point B) for that starting height. Finally, you will compare magnitudes of this normal force and the weight of the car/rider and discuss implications of this comparison. If the cart started at height hmin, derive an expression for the magnitude of the normal force NBMin ex[erienced by the cart. Start with

Explanation / Answer

According to the conservation og energy , the speed of cart at point B is

M g h_min = ( 1/ 2) M v_Bmin ^2

v_Bmin = sqrt ( 2 g h _min)

Normal force on the cart is

N = M v_Bmin ^2 / R - M g

= M (2 g h_min ) ^2 / R - M g

= M g (4gh_min ^2 / R - 1 )

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