Evan Kurnia's copy of Machine: lopping shears

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Evan Kurnia Alim 6 years, 4 months ago

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('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		Error evaluating variable theta: Variable `d_7` is not defined.
dp_1		Error evaluating variable dp_1: Variable `theta` is not defined.
ma_1		Error evaluating variable ma_1: Variable `d_3` is not defined.
dp_2		Error evaluating variable dp_2: Variable `d_5` is not defined.
ma_2		Error evaluating variable ma_2: Variable `dp_2` is not defined.
ma_t		Error evaluating variable ma_t: Variable `ma_1` is not defined.
version	integer	0
given	list	List of 2 items
Statement	list	List of 2 items
answer		Error evaluating variable answer: Variable `ma_t` is not defined.

			Name	Type	Generated Value

units	list	[ "N", "mm", "10 mm", "1 mm" ]
L		Error evaluating variable l: Can't automatically convert from quantity to mm.
d_1		Error evaluating variable d_1: Variable `L` is not defined.
d_2		Error evaluating variable d_2: Variable `L` is not defined.
d_3		Error evaluating variable d_3: Variable `L` is not defined.
d_4		Error evaluating variable d_4: Variable `d_1` is not defined.
d_5		Error evaluating variable d_5: Variable `L` is not defined.
d_6		Error evaluating variable d_6: Variable `L` is not defined.
d_7		Error evaluating variable d_7: Variable `L` is not defined.
d_8		Error evaluating variable d_8: Variable `L` is not defined.
d_9		Error evaluating variable d_9: Variable `L` is not defined.

Automatically regenerate variables?

Name

Data type

Value

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

JME function reference

Error

Error evaluating variable theta: Variable d_7 is not defined.

Description

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

Can an exam override the value of this variable?

← Depends on:

→ Used by:

dp_1
dp_2

Advice

Parts

Gap-fill
1. Gap Gap 0. Engineering Accuracy with units
  Add
2. Gap Gap 1. Engineering Accuracy with units
  Add

Gap-fill

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

Mechanical advantage = Gap 0. $\var{if(version=0,latex('A'),latex('P'))}$ = Gap 1.

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.

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

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]}:

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

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

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
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Evan Kurnia's copy of Machine: lopping shears

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Evan Kurnia Alim 6 years, 4 months ago

Error in variable testing condition

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Parts

Gap-fill