Loop the Loop rolter-coaster car may be represented by a block of mass 50.0 kg T

Question

Loop the Loop rolter-coaster car may be represented by a block of mass 50.0 kg The car is released from rest at a height h 57 0 m above the ground and slides along a frictionless track. The car encounters a loop of radius R·19 m at ground level, as shown. As you will learn in the course of this problem, the initial height 57.0 m is great enough so that the car never loses contact with the track Part A Find the kinetic energy K of the car at the top of the loop. Express your answer numerically, in joules Hints Submit My Answers Give Up Part B Find the minimum Initial height hmis at which the car can be released that stllalows the car to stay in contact with the track at the top of the loop Express your answer numerically, in meters Hints t1 My Answers Give Up Continue

Explanation / Answer

(A)Applying energy conservation,

PEi + KEi = PEf + KEf

m g h + 0 =m g (2R) + m v^2 /2

2 x 9.8 (57 - (2 x 19)) = v^2

v = 19.3 m/s

(B) at top of loop:

N + m g = m v^2 / R

N - > 0 for v_min

v = sqrt(R g) = 13.65 m/s

Applying energy conservation.

2 x 9.8 x h = (2 x 9.8 x 2 x 19) + (13.65^2)

h = 47.5 m

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