Riding a Loop-the-Loop. A car in an amusement parkride rolls without friction ar

Question

Riding a Loop-the-Loop. A car in an amusement parkride rolls without friction around the track shown in the figurebelow. It starts from rest at point A at a heighth above the bottom of the loop. Treat the car as aparticle. (a) What is the minimum value of h (interms of R) such that the car moves around the loopwithout falling off at the top (point B)?
1R

(b) If h = 4.40R andR = 22.0 m, compute the speed,radial acceleration, and tangential acceleration of the passengerswhen the car is at point C, which is at the end of ahorizontal diameter.
2 m/s (speed)
3 m/s2 (radial acceleration --toward center of circle)
4 m/s2 (tangential acceleration --downward)
(a) What is the minimum value of h (interms of R) such that the car moves around the loopwithout falling off at the top (point B)?
1R

(b) If h = 4.40R andR = 22.0 m, compute the speed,radial acceleration, and tangential acceleration of the passengerswhen the car is at point C, which is at the end of ahorizontal diameter.
2 m/s (speed)
3 m/s2 (radial acceleration --toward center of circle)
4 m/s2 (tangential acceleration --downward)

Explanation / Answer

   at the top if the block is to be on verge offalling off the track then we getthat        FN = 0    the resultant will be     FR = FN + mg            = m v2 / r    m g = m vtop2 /r    vtop = (g r)    if 1 represent the  block at therelease point and 2 represent the block at the top of the loop andgroud is at the zero    location for PE, then we get that    v1 =0              y1 = h    v2 = (g r)    y2 = 2 r       as both the energies are equal we getthat    E1 = E2    (1 / 2) m v12 + m gy1 = (1 / 2) m v22 + m gy2    solve for h    h = 2.5 R

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