Machine: Pliers

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Question statement

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			Name	Type	Generated Value

d1	integer	53
d2	integer	180
theta	integer	50
P	integer	360
A	number	1479.9660152195
Q	vector	Vector with 2 components
Ax	number	936.5977342285
Ay	number	1145.8988133526

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Generated value: `integer`

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Parts

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1. Gap A Engineering Accuracy with units
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2. Gap Q Engineering Accuracy with units
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Determine the magnitudes of the force on pin $A$ and the gripping force $Q$ on the pipe when a $\var{qty(P,'N')}$ force $P$ is applied to the handles of the slip-joint pliers as shown.

$A =$ A

$Q =$ Q

Advice

Given $P = \var{qty(P,'N')}$ and the dimensions and angles on the diagram. Recognize that the pipe is a two-force body in compression, and that the force of the pipe on the pliers is perpendicular to the jaws

1. Draw a free body diagram of one of the handles.

2. Apply equilibrium equations.

$\begin{align}
\Sigma M_A &= 0\\
Q (\var{qty(d1,'mm')}) &= P (\var{qty(d2,'mm')})\\
Q & = (\var{qty(P,'N')}) (\var{siground(d2/d1,3)})= \var{siground(qty(abs(Q), 'N'),4)}\\\\
\Sigma F_x &= 0\\
A_x &= Q_x \\
&= Q \sin \var{theta}°= \var{siground(qty(Ax, 'N'),4)}\\\\
\Sigma F_y &= 0
\\A_y &= P + Q_y\\
&= P + Q \cos{\theta}= \var{siground(qty(Ay, 'N'),4) }\\\\
A&= \sqrt{A_x^2 + A_y^2} \\
&= \var{siground(qty(A,'N'),4)}
\end{align}$

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This question is used in the following exam:

Chapter 6 Exercises by William Haynes in Engineering Statics.

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William Haynes 2 years ago

William Haynes 2 years ago

William Haynes 2 years, 3 months ago

William Haynes 2 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Machine: Pliers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

William Haynes 2 years ago

William Haynes 2 years ago

William Haynes 2 years, 3 months ago

William Haynes 2 years, 3 months ago

Error in variable testing condition

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Generated value: integer

Parts

Gap-fill

Generated value: `integer`