Machine: Excavator

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William Haynes 5 years, 9 months ago

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Created this as a copy of Machine: lopping shears.

Name	Status	Author	Last Modified
Machine: lopping shears	Ready to use	William Haynes	10/12/2022 21:16
Evan Kurnia's copy of Machine: lopping shears	draft	Evan Kurnia Alim	22/11/2018 03:08
Machine: Excavator	Ready to use	William Haynes	10/12/2022 21:15

There are 2 other versions that do you not have access to.

Question statement

{geogebra_applet('cbh4g7zm', {map(dx(n),n,1..6)} + {map(dy(n),n,1..6)} )}

Diagram units are in: [{units[1]}]

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

L	quantity	quantity(1, "ft")
x1	quantity	quantity(1.8, "ft")
x2	quantity	quantity(3.9, "ft")
x3	quantity	quantity(2.6, "ft")
x4	quantity	quantity(7.2, "ft")
x5	quantity	quantity(0.9, "ft")
x6	quantity	quantity(5.45, "ft")
y1	quantity	quantity(1.1, "ft")
y2	quantity	quantity(4.6, "ft")
y3	quantity	quantity(1.15, "ft")
y4	quantity	quantity(1, "ft")
y5	quantity	quantity(2.3, "ft")
y6	quantity	quantity(9.85, "ft")
load	quantity	quantity(3600, "lbf")
units	list	[ "lbf", "ft", "0.05 ft" ]
x_t	quantity	quantity(21.85, "ft")
dperp_B	quantity	quantity(2.106705377401, "ft")
BC	quantity	quantity(37337.92149761408876845371549258169481924, "lbf")
dperp_D	quantity	quantity(2.4019437624560488, "ft")
DE	quantity	quantity(8168.384417101443397009137493921916085586, "lbf")

			Name	Type	Generated Value

			theta_b	number	55.6196552762
			theta_d	number	7.907162703

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
round(qty(random(12..24),'in') in units[1],units[2])

JME function reference

Description

scaling value for all lengths, which are also randomly perterbed actual value as scaled.

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

Can an exam override the value of this variable?

Generated value: `quantity`

quantity(1, "ft")

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill

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Ask the student a question, and give any hints about how they should answer this part.

The motion of the excavator is controled by three hydraulic cylinders. Determine the force exerted by cylinders $BC$ and $DE$ when supporting a {load} downward vertical load at $G$ . Neglect the weights of the parts.

$BC$ = BC T or C

$DE$ = DE T or C

Advice

Draw and number neat, labeled free body diagrams.

Given: $W$ = {load}

Find the necessarys angles.

Let $\theta_B$ and $\theta_D$ be the angles that BC and DE make with the horizontal.

$\theta_B = \tan^{-1} \left(\dfrac{\var{y1+y2}}{\var{x2}}\right) = \var{siground(theta_B,4)}° \qquad \theta_D = \tan^{-1} \left(\dfrac{\var{y4}}{\var{x4}} \right)= \var{siground(theta_D,4)}°$

Use Free Body Diagram I to solve for the force in cylinder $BC$.

$\begin{align} \textrm{I: } \Sigma M_A &= 0 \\ BC_x ( \var{y2}) - BC_y(\var{x1 + x2}) + W ( \var{x_t}) &= 0\\ BC ( -\var{scalar(y2)} \cos \theta_B + \var{scalar(x1+x2)} \sin \theta_B) &= \var{scalar(x_t)}\ W \\ BC &= W \left(\dfrac{\var{scalar(x_t)}}{-\var{scalar(y2)} \cos \var{siground(theta_B,4)}° + \var{scalar(x1+x2)} \sin \var{siground(theta_B,4)}°}\right) \\ &= \var{load} \left(\dfrac{\var{x_t}}{\var{siground(dperp_B,4)}}\right) \\ &= \var{siground(BC,4)} \textrm{ (compression)} \end{align}$

Use Free Body Diagram II to solve for the force in cylinder $DE$.

$\begin{align} \textrm{II: } \Sigma M_F &= 0 \\ -DE_x ( \var{y5}) - DE_y(\var{x5}) + W ( \var{x6}) &= 0\\ DE ( \var{scalar(y5)} \cos \theta_D + \var{scalar(x5)} \sin \theta_d) &= \var{scalar(x6)} W \\ DE &= W \left(\dfrac{\var{x6}}{\var{siground(dperp_D,4)}}\right) \\ &= \var{siground(DE,4)} \textrm{ (tension)} \end{align}$

Give a worked solution to the whole question.

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This question is used in the following exams:

33. Frames and Machines 3 by Michael Proudman in Engineering Statics.
Homework 19: Machines by Sarah Sojka in Statics at Randolph College.
33. Frames and Machines 3 by William Haynes in Engineering Statics.
Chapter 6 Exercises by William Haynes in Engineering Statics.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 3 months ago

William Haynes 6 years, 3 months ago

Error in variable testing condition

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Generated value: `quantity`

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Gap-fill

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Machine: Excavator

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 5 years, 9 months ago

William Haynes 5 years, 10 months ago

William Haynes 5 years, 10 months ago

William Haynes 6 years, 3 months ago

William Haynes 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: quantity

Parts

Gap-fill

Generated value: `quantity`