In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H = 5.5 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor?
using conservation of energy
mgH = 1/2mv2 + 1/2Iw2 + mgh
where ,
I = 2/5 * m * r2
and
w = v/r
we have
mgH = 1/2mv2 + 1/2 * 2/5 * m * r2 * v2 / r2 + mgh
gH = 7/10 v2 + gh
v = sqrt ( 10 g (H -h) / 7 )
v = sqrt ( 10 ( 5.5 - 2) / 7)
v = 7 m/s
so,
now, we can find time in air
t = sqrt ( 2h / g)
t = sqrt ( 2 * 2 / 9.8)
t = 0.6388 sec
so,
horizontal distance
d = vt
d = 4.472 m
In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H...
In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H = 5.5 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor? Number Units
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