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yoslick11
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Homework Statement
Ok, I have attempted this problem, and believe I have the right answer. My work is not matching up though and I think I am missing something.
Question:
A hoop is rolling without slipping along a horizontal surface with a speed of 4.50 m/s when it starts up a ramp that makes and angle of 25.0° with the horizontal. What is the speed of the hoop after it has rolled 3.00m up the ramp?
Homework Equations
KE = 1/2*mv^2 + 1/2*I*w^2
I = mR^2
The Attempt at a Solution
This is what I got.
Total KE = 1/2*mv^2+1/2*Iw^2
substituting the I = mR^2 and w = v/R
Total KE = 1/2*m*v^2 + 1/2*(mR^2)*(v^2/R^2)
= 1/2*m*v^2 + 1/2*m*v^2
= mv^2
at 3m up on the incline
ke(bot) = pe(top)+ke(top)
m*v(initial)^2 = mgh + 1/2*m*v(final)^2
vi^2 = gh + 1/2*vf^2
vf = sqrt(2(vi^2-gh))
I believe at this point I am wanting vf = sqrt(vi^2-gh).. because the answer I believe is 2.80 m/s. sqrt(4.5^2 - (9.8*3sin25)) = 2.80 m/s
Am I looking at this correctly?
Any help would be appreciated.