Machine: Vice grips

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Name	Status	Author	Last Modified
Machine: Vice grips	Ready to use	William Haynes	28/02/2023 23:25
Ian's copy of Machine: vice grips	draft	Ian Loasby	03/06/2019 11:51
Heather's copy of Machine: vice grips	draft	Heather Driscoll	03/06/2019 14:52

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Question statement

{applet}

Give any introductory information the student needs.

			Name	Type	Generated Value

theta	number	67.1263348094
dperp	number	4.5348392297
CE	number	26.4617980751
Bx	number	24.380952381
A	number	20.4119601329

			Name	Type	Generated Value

X1	integer	43
X2	integer	33
X3	integer	64
X4	integer	23
Y1	integer	27
Y2	integer	9
params	list	Nested 6×2 list
applet	ggbapplet	HTML node

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Name

Data type

Value

xxxxxxxxxx
 
degrees(arctan(x3/y1))

JME function reference

Description

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Generated value: `number`

67.1263348094

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Parts

Gap-fill
1. Gap A Mathematical expression
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Gap-fill

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Determine the compressive force on object $A$ in terms of squeezing forces $P$ when the vice grip pliers are in the position shown. (Assume that the forces acting on $A$ are vertical.)

$A$ = A

Advice

Start by drawing neat, correct, labeled free body diagrams for the lower handle and the lower jaw. Recognize that piece $CE$ is a two force member in compression so the force on pin $E$ acts down and left along a line passing through $C$ and $E$.

Geometry

Determine angle $\theta$ from the geometry of the pliers.

\[\theta = \tan^{-1}\left( \dfrac{\var{q(x3)}}{\var{q(y1)}}\right) = \var{d(theta)}°\]

FBD II

\[\begin{align}\text{II: } \Sigma M_B &= 0\\ CE_x \,(\var{q(y2)}) -CE_y\,(\var{q(x2)}) + P \,( \var{q(x2+x3+x4)})& = 0 \\ CE\left( \var{y2} \sin \theta - \var{x2} \cos \theta \right) &= -P \,( \var{q(x2)}+\var{q(x3)}+\var{q(x4)})\\CE &=-P \,\left( \dfrac{\var{q(x2+x3+x4)}}{\var{-q(dperp)}} \right)\\ &= \var{d(ce)} P \\ \\ \text{II: }\Sigma F_x &= 0\\ B_x &= CE_x\\ &= CE \sin{\theta}\\ &= ( \var{d(ce)} P )\,(\sin \var{d(theta)}°)\\&= \var{d(bx)} P\end{align}\]

FBD I

\[\begin{align} \text{I: }\Sigma M_D &=0\\ A\,(\var{q(x1)}) &= B_x\,(\var{q(y1)} + \var{q(y2)})\\ A &= (\var{d(bx)} P) \, \left(\dfrac{\var{q(y1+y2)}}{\var{q(x1)}}\right)\\ &= \var{d(A)} P\end{align}\]

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This question is used in the following exams:

32. Frames and Machines 2 by Michael Proudman in Engineering Statics.
Homework 19: Machines by Sarah Sojka in Statics at Randolph College.
32. Frames and Machines 2 by William Haynes in Engineering Statics.
Chapter 6 Exercises by William Haynes in Engineering Statics.

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William Haynes 4 years, 8 months 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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Generated value: `number`

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Machine: Vice grips

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 4 years, 8 months 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

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`