M3 problems Watch

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Christophicus
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#1
Report Thread starter 13 years ago
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Okay, I just need to get started.

A uniform right circular cylinder of height h and radius r is placed on a plane face in contact with a rough horizontal plane, the coefficient of friction between the cylinder and the plane being mu. The plane is gradually tilted. Show that the cylinder will topple before it slides if mu > 2r/h

Okay, I know that on point of toppling reaction occurs at the point of toppling and on point of sliding F = mu*R

On point of sliding, F = mu*[email protected]
On point of toppling, :confused:
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yazan_l
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for minimum angle for slideing (@):
[email protected] = μ mg [email protected]
[email protected] = μ

for minimum angle for toppling ( α ) "see attachment" :
tan α = r / h/2 = 2r/h

now for toppling to occur bfore sliding , α should be less than @, i.e. tanα < [email protected]

now as μ>2r/h ==> [email protected] >2r/h ==> [email protected] > tan α ==> @ > α ==> toppling occurs first!
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Christophicus
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#3
Report Thread starter 13 years ago
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(Original post by yazan_l)
for minimum angle for slideing (@):
[email protected] = μ mg [email protected]
[email protected] = μ

for minimum angle for toppling (α) "see attachment" :
tan α = r / h/2 = 2r/h

now for toppling to occur bfore sliding , α should be less than @, i.e. tanα < [email protected]

now as μ>2r/h ==> [email protected] >2r/h ==> [email protected] > tan α ==> @ > α ==> toppling occurs first!
last exercise of m3.
Thanks for the help.
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