- #1
Shuo Xue
- 5
- 0
Homework Statement
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A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2)
Homework Equations
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Find the speed of the wheel when it is 10m below the top.
The Attempt at a Solution
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mgh = 1/2mv^2 + 1/2IW^2
W= v/r
mgh = 1/2mv^2 + 1/2(1/2mr^2)(v/r)^2
mgh = 1/2mv^2 + 1/4mv^2
gh = 3/4mv^2
v^2 = 4gh/3
v^2 = 4(9.81)(10)/3
v = 11.4m/s
I got v = 11.4 m/s
but my answer is incorrect as it is different from the answer given which is 23m/s.
I want to know the correct solution.
I've also tried searching for the height first.
h = (3/4v^2)/g
h = 30.58m
and then 10m below from the top
h = 20.58m
v^2 = 4gh/3
v^2 = 4(9.81)(20.58)/3
v = 16.41m/s
Which is still far from the answer also.