Machine: lopping shears

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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('csq3j7yg', {map(dist(n),n,1..9)} )}

Determine

a) the mechanical advantage of the lopping shears shown, and

b) the {statement[version]}.

Note: The mechanical advantage of the shears is the ratio of the cutting force developed at $A$ to the force $P$ applied to the handles.

Give any introductory information the student needs.

			Name	Type	Generated Value

theta	number	71.0295921915
dp_1	quantity	quantity(153.5263088558995, "mm")
ma_1	decimal	dec("2.865958305641191600731106811544286244105")
dp_2	quantity	quantity(223.300248260861717, "mm")
ma_2	decimal	dec("2.23300248260861717")
ma_t	decimal	dec("6.399692011549566879187451592250233594615")
version	integer	1
given	list	List of 2 items
Statement	list	List of 2 items
answer	list	List of 2 items

			Name	Type	Generated Value

units	list	[ "N", "mm", "10 mm", "1 mm" ]
L	quantity	quantity(610, "mm")
d_1	quantity	quantity(100, "mm")
d_2	quantity	quantity(70, "mm")
d_3	quantity	quantity(140, "mm")
d_4	quantity	quantity(300, "mm")
d_5	quantity	quantity(11, "mm")
d_6	quantity	quantity(65, "mm")
d_7	quantity	quantity(32, "mm")
d_8	quantity	quantity(299, "mm")
d_9	quantity	quantity(311, "mm")
test	string	"$100 \textrm{ mm}$"

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Name

Data type

Value

xxxxxxxxxx
 
degrees(atan2(scalar(d_7),scalar(d_9-d_4)))

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Generated value: `number`

71.0295921915

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Parts

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1. Gap Advantage Engineering Accuracy with units
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2. Gap Force Engineering Accuracy with units
  Add

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

Mechanical advantage = Advantage $\var{if(version=0,latex('A'),latex('P'))}$ = Force

Advice

1. Draw and number a neat, consistent, labeled set of free body diagrams for the parts of the shears.

Note link DE is a two force member with a slope of $m = \dfrac{\var{d_7}} {\var{d_9 - d_4}}$, in tension. The free body diagrams must be consistent with each other and internal forces must occur in action-reaction pairs.

2. Find the necessary angle.

Let $\theta$ be the angle that DE makes with the horizontal.

$\theta = \tan^{-1} \dfrac{\var{d_7}}{\var{d_9-d_4}} = \var{siground(theta,4)}°$

3. Use FBD II and take moments about C to find the tension in DE.

$\begin{align}\textrm{II: }\Sigma M_C &= 0 \\ DE_x (\var{d_6}) + DE_y(\var{d_3}) &= P \,(\var{d_3 + d_4 })\\ DE &= \left ( \dfrac{\var{scalar(d_3 + d_4 )}}{\var{scalar(d_6)} \cos \theta + \var{scalar(d_3)}\sin \theta} \right) P \\&= \left(\dfrac{\var{d_3 + d_4 }}{\var{siground(dp_1,4)}} \right )P \\&= \var{siground(ma_1,4)} \,P \textrm{ (tension) } \end{align}$

4. FBD III and take moments about B to find the cutting force at A.

$\begin{align}\textrm{III: }\Sigma M_B &= 0 \\ A (\var{d_1}) &=DE_x (\var{d_5 +d_6 +d_7 }) + DE_y(\var{d_8-d_1}) \\ A &= \left ( \dfrac{\var{scalar(d_5 +d_6 +d_7 )}\cos \theta + \var{scalar(d_8-d_1)}\sin \theta}{\var{scalar(d_1 )}} \right) DE \\&= \left(\dfrac{\var{siground(dp_2,4)}}{\var{d_1 }} \right )DE \\&= \var{siground(ma_2,4)} \,DE \\ &= \var{siground(ma_2,4)}\, ( \var{siground(ma_1,4)} \,P )\\ &= \var{siground(ma_t,4)} P \end{align}$

5. Find the mechanical advantage

Mechanical Advantage = $\dfrac{A}{P} = \var{siground(ma_t,4)}$

6. Find the {statement[version]}.

$A = \var{siground(ma_t,4)} P$, so for $A$ $P$ = {given[version]}:

$A = \var{siground(ma_t,4)} (\var{given[0]}) = \var{siground(answer[0],4)}$

$P = \dfrac{\var{given[1]}}{\var{siground(ma_t,4)}} = \var{siground(answer[1],4)}$

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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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William Haynes 6 years ago

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Machine: lopping shears

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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William Haynes 5 years, 11 months ago

William Haynes 6 years ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

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Generated value: number

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Generated value: `number`