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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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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). Was this solution helpful? √x Do 8
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
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
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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