A uniform marble rolls down a symmetric bowl, starting from rest atthe top of the left side. The top of each side is a distanceh
above the bottom of the bowl. The left half of the bowlis rough enough to cause the marble to roll without slipping, butthe right half has no friction because it is coated with oil.
(a) How far up the smooth side will the marblego, measured vertically from the bottom? (Use the followingvariable as necessary: h.)
H = 1Click here to preview your answer.
(b) How high would the marble go if both sides were as rough as theleft side? (Use the following variable as necessary: h.)
H = 2Click here to preview your answer.
(c) How do you account for the fact that the marble goeshigher with friction on the right side than withoutfriction?
(a) How far up the smooth side will the marblego, measured vertically from the bottom? (Use the followingvariable as necessary: h.)
H = 1Click here to preview your answer.
(b) How high would the marble go if both sides were as rough as theleft side? (Use the following variable as necessary: h.)
H = 2Click here to preview your answer.
(c) How do you account for the fact that the marble goeshigher with friction on the right side than withoutfriction?
1 answer:
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Answer:
0.139 rad
Explanation:
We use Snell's law , where if
is the <em>refractive index</em> of the medium containing the <em>incident ray</em>,
would be the <em>incident angle</em>, and if
is the <em>refractive index</em> of the medium containing the <em>refracted ray</em>,
would be the <em>refraction angle</em>, which we want, so we do:
And finally:
We then insert our values: