A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below.
A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle as shown in the figure below.
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter7: Dry Friction
Section: Chapter Questions
Problem 7.80P
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Question
Derive expressions for the initial accelerations of the plank and the roller. Your solution should include the following in a systematic way:
Statements of relevant kinematic and kinetic relationships with reference to your chosen global axes system
![12:33
and a direction, so you can only accelerate by
changing either the speed or the direction.
Step2
b)
Solution:
#
My sinu
To
since th rollers are identical, consider only one rollers.
free body diagram:
My caso
kinetic diagrams:
masing.
←
Suf+Jdx
IN Fr
R
ma
:
my case.
ap- absolute acceleration.
ar=ap+a F/p = actrd.
Map
rd=a²-ap
Plank [ {F₂2² = max] Mg sine - Fr = Map → 2.
Rollen [₁=Maz] rgsino - F₂ = Map &
[sing-Fr=
Mg sine-Fr = m (ar-an)
2MgSino-2F = m (ar-aa)
2 mgsint-2Fv+ar = aa. →.
Fr= (rd).
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Transcribed Image Text:12:33
and a direction, so you can only accelerate by
changing either the speed or the direction.
Step2
b)
Solution:
#
My sinu
To
since th rollers are identical, consider only one rollers.
free body diagram:
My caso
kinetic diagrams:
masing.
←
Suf+Jdx
IN Fr
R
ma
:
my case.
ap- absolute acceleration.
ar=ap+a F/p = actrd.
Map
rd=a²-ap
Plank [ {F₂2² = max] Mg sine - Fr = Map → 2.
Rollen [₁=Maz] rgsino - F₂ = Map &
[sing-Fr=
Mg sine-Fr = m (ar-an)
2MgSino-2F = m (ar-aa)
2 mgsint-2Fv+ar = aa. →.
Fr= (rd).
Was this solution helpful?
√x
Do
8
Transcribed Image Text:A thin plank of mass M is placed centrally across two solid cylindrical rollers each
of mass m, and the system is allowed to move freely from rest without slip down a
slope of angle as shown in the figure below.
in the initial colorations of the plank and the roller
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