#1
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An Interesting Physics Problem
What is the maximum slope that a solid sphere of uniform density can roll down without slipping, if the coefficient of static friction between the sphere and the incline is 1/2?
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#2
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Re: An Interesting Physics Problem
26.6 degrees (from the horizontal)?
That can't be it or else this wouldn't be interesting...I give up. Edit - Can I have multiple answers? I want to add an answer of 63.4 degrees from the horizontal. |
#3
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Re: An Interesting Physics Problem
Neither of those two answers appear to be correct.
Perhaps if you provided a worked out solution. Edit: Ah, never mind. I see how you got that. Definitely not. |
#4
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Re: An Interesting Physics Problem
Vertical. (you didn't say I couldnt add some, uuummmm.... prespin [img]/images/graemlins/smile.gif[/img] ) |
#5
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Re: An Interesting Physics Problem
[ QUOTE ]
Vertical. [/ QUOTE ] Wrong. [ QUOTE ] (you didn't say I couldnt add some, uuummmm.... prespin [img]/images/graemlins/smile.gif[/img] ) [/ QUOTE ] Prespin all you want. It will still slip. Do you see why? |
#6
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Re: An Interesting Physics Problem
I think it's atan(2*mu), which here is 45deg. Post a solution in a bit.
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#7
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Re: An Interesting Physics Problem
[ QUOTE ]
Neither of those two answers appear to be correct. Perhaps if you provided a worked out solution. Edit: Ah, never mind. I see how you got that. Definitely not. [/ QUOTE ] Ya, the first one I was sure was wrong and I just realized I did the second one wrong, so here is a reworked solution. x direction parallel to slope, y direction perpendicular, angle is theta Sum moments bout point of contact, P: mgrsin(theta)=Ip*alpha Ip=2/5mr²+mr² d²x/dt² = a_x = r/2*alpha solveing for acceleartion in x direction a_x a_x = (5/14)*g*sin(theta) Now summing forces in x direction: -Ff + mgsin(theta) = m*a_x = m*(5/14)*g*sin(theta) where Ff = mu*N = 0.5*N = 0.5mg*cos(theta) -0.5mgcos(theta)+mgsin(theta)=5/14*mg*sin(theta) solving for theta: theta = 37.9 degrees from the horizontal. |
#8
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Re: An Interesting Physics Problem
Solid attempt, but no.
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#9
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Re: An Interesting Physics Problem
[ QUOTE ]
I think it's atan(2*mu), which here is 45deg. Post a solution in a bit. [/ QUOTE ] Nope. Let me just give the numerical answer so you'll know when you've gotten it. The slope is 7/4. |
#10
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Re: An Interesting Physics Problem
[ QUOTE ]
[ QUOTE ] I think it's atan(2*mu), which here is 45deg. Post a solution in a bit. [/ QUOTE ] Nope. Let me just give the numerical answer so you'll know when you've gotten it. The slope is 7/4. [/ QUOTE ] Oops I think I made one other silly mistake. I get this if I modify one line in my solution: Instead of: d²x/dt² = a_x = r/2*alpha If I use: d²x/dt² = a_x = r*alpha I get a slope of 7/4 or angle of 60.3 deg. |
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