Equilibrium of two particles: Cylinders in a trough

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Question statement

<p">{geogebra_applet('dmn6ddbb', [["width", width], ["r1",r1], ["r2",r2]] )}

Two cylinders are placed in a {width} {units[0]} wide container. The blue cylinder has a radius $r_1$ = {d1/2} {units[0]} and weighs {w1} {units[1]} and the yellow cylinder has a radius $r_2$ = {d2/2} {units[0] } and weighs {w2} {units[1]}.

Give any introductory information the student needs.

			Name	Type	Generated Value

base	rational	17/2
r1	rational	6
r2	rational	11/2
r	rational	23/2
theta	number	42.3426054522
A	number	2820.8228704877
B	number	4150
C	number	2084.9560347083

			Name	Type	Generated Value

width	integer	20
d1	integer	12
d2	integer	11
units	list	[ "ft", "lb" ]
w1	integer	2250
w2	number	1900

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
width - (d1+d2)/2
​

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `rational`

17/2

← Depends on:

d1
d2
width

→ Used by:

theta

Variable testing condition

Parts

Answers Gap-fill

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Assuming smooth contact surfaces, determine the magnitudes of Force A, where the two cylinders touch, Force B where the blue cylinder touches the bottom of the trough, and Force C where it touches the left wall.

$A$ = A $B$ = B $C$ = C

Advice

Given:

$d$ = {width} {units[0]} $\qquad r_1$ = {r1} {units[0]} $\qquad W_1 = $ {w1} {units[1]} $\qquad r_2$ = {r2} {units[0]} $\qquad W_2 = $ {w2} {units[1]}

Draw free body diagrams of the two cylinders.

{geogebra_applet('rchz6eew', [["width", width], ["r1",r1], ["r2",r2]] )}

Find angle $\theta$ from the geometry of the problem.

$\theta =cos^{-1} \left( \dfrac{d - r_1- r_2}{r_1+r_2} \right) = \var{siground(theta,4)}°$

Find force $A$ using equilibrium of the yellow cylinder

$\begin{align} \Sigma F_y &= 0\\A_y - W_2 &= 0\\ A \sin \theta &= W_2\\ A &= W_2\,/\,\sin \theta &=\var{show(A)}\end{align}$

Find forces $B$ and $C$ using equilibrium of the blue cylinder

$\begin{align} \Sigma F_y &= 0 & \Sigma F_x &=0\\ B - A_y - W_1 &= 0 & C-A_x &=0\\ B &= W_1 + A \sin \theta & C &= A \cos\theta \\&= \var{show(B)} & &=\var{show(C)} \end{align}$

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This question is used in the following exams:

Chapter 03 Exercises by Michael Proudman in Engineering Statics.
06. Multiparticle Equilibrium by Michael Proudman in Engineering Statics.
Statics - Chapter 3 Exercises by Jay McCormack in studio 4.
Chapter 3 Exercises by William Haynes in Engineering Statics.
06. Multiparticle Equilibrium by William Haynes in Engineering Statics.

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Equilibrium of two particles: Cylinders in a trough

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Generated value: `rational`

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Equilibrium of two particles: Cylinders in a trough

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 1 year, 1 month ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

William Haynes 5 years, 11 months ago

Error in variable testing condition

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Warning

Generated value: rational

Parts

Gap-fill

Generated value: `rational`