A car in an amusement park ride rolls without friction around a track (Fi point

Question

A car in an amusement park ride rolls without friction around a track (Fi point A at a height h above the bottom of the loop. Treat the car as a particle. What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B Express your answer in terms of R. 1). The car starts from rest at of 1 Submit Part B rthe car starts at heighth=3.70 R and the radius is R1·140 m.compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter. Express your answer with the appropriate units. te= Value Units

Explanation / Answer

(a)
Conserving the energies at all level

Ka + Ua = Kb + Ub

So at point B let the velocity be Vb where Vb = (gR)^(1/2)

Ka = 0
Hence,
Ua - Ub = Kb
Ua = mgh
Ub = mg*(2R)

Hence,
mg(h - 2R) > 1/2mVb^2
or
mg(h - 2R) > 1/2mgR
h > 5R/2

(b)
h = 3.7R m
R = 14 m

Ka + Ua = Kc + Uc
Ka = 0
hence ,
Ua - Uc = Kc
mgh - mg*R = Kc
mgR(3.7 - 1) = Kc
2.7mgR = Kc
2.7mgR = (1/2)mVc^2
(5.4gR)^(1/2) = Vc
(5.4*9.8*14)^(1/2) = Vc
Vc = 27.22 m/s

(c)
Radial Acceleration = Vc^2/R = 27.22^2/14 = 52.923 m/s^2

(d)
At point C tangential direction will be down, the normal force at point C is horizontal, there is no friction, so the only downward force is
gravity,
a = 9.8 m/s^2

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