A marble rolls without slipping on a track shown below. It starts out at a heigh

Question

A marble rolls without slipping on a track shown below. It starts out at a height of 2 m above the level where the marble rolls off the track at an angle of 37 degree. Neglect air resistance. Find the expression for the kinetic energy of the marble just before it leaves the track? Determine the linear and angular speeds of the marble before it levels the track Determine the highest vertical level above the take-off point reached by the marble in the air. Determine the range of the marble after leaving the track. If the marble had been a disk instead, would the height and range be more or less?

Explanation / Answer

a)

KE = (0.5) I w2 + (0.5) m v2

b)

h = height of initial point = 2

PE at initial point = KE at point where it leaves the track

mgh = (0.5) I w2 + (0.5) m v2

mgh = (0.5) (0.4) (m r2) (v/r)2 + (0.5) m v2

mgh = (0.7) m v2

v = sqrt(gh/0.7)

v = sqrt(9.8 x 2 / 0.7 )

v = 5.3 m/s

c)

maximum height reached = h = v2 Sin237 / (2g) = (5.3)2 (Sin37)2 / (2 x 9.8) = 0.52

d)

range = v2 sin2(37) /g = (5.3)2 sin74 / (2 x 9.8) = 1.4 m

e)

for the disk the value of "v" will be smaller so it would reach less height and range .

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