![](\"resources/question-resources/vicegrips2FBD_VTYoSKJ.png\")
Determine the compressive force on object $A$ due to squeezing forces $P$ when the vice grip pliers are in the position shown. (Assume that the forces acting on $A$ are vertical.)
\n$A$ = [[0]]
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\n", "rulesets": {}, "extensions": ["geogebra", "quantities", "weh"], "variables": {"Bx": {"group": "solution", "name": "Bx", "templateType": "anything", "description": "", "definition": "ce sin(radians(theta))"}, "CE": {"group": "solution", "name": "CE", "templateType": "anything", "description": "\\dfrac{\\var{q(x2+x3+x4)}}{\\var{q(dperp)}}
", "definition": "(x2+x3+x4)/dperp"}, "X1": {"group": "Ungrouped variables", "name": "X1", "templateType": "anything", "description": "x
", "definition": "43 + random(-5..5)\n"}, "Y1": {"group": "Ungrouped variables", "name": "Y1", "templateType": "anything", "description": "", "definition": "24+random(-3..3)"}, "X4": {"group": "Ungrouped variables", "name": "X4", "templateType": "anything", "description": "", "definition": "20 + random(-3..3)"}, "dperp": {"group": "solution", "name": "dperp", "templateType": "anything", "description": "\\var{x2} \\cos \\theta - \\var{y2} \\sin \\theta
", "definition": "x2 cos(radians(theta)) - y2 sin(radians(theta))"}, "X3": {"group": "Ungrouped variables", "name": "X3", "templateType": "anything", "description": "", "definition": "61 + random(-6..6)"}, "Y2": {"group": "Ungrouped variables", "name": "Y2", "templateType": "anything", "description": "", "definition": "9 + random(-2..2)"}, "X2": {"group": "Ungrouped variables", "name": "X2", "templateType": "anything", "description": "", "definition": "35 + random(-5..5)"}, "ggb_vars": {"group": "Ungrouped variables", "name": "ggb_vars", "templateType": "anything", "description": "", "definition": "[['x1',x1],['x2',x2],['x3',x3],['x4',x4],['y1',y1],['y2',y2]]"}, "A": {"group": "solution", "name": "A", "templateType": "anything", "description": "(\\var{d(bx)} P) \\left(dfrac{\\var{q(y1+y2)}}{\\var{q(x1)}}
", "definition": "bx * (y1+y2)/x1"}, "theta": {"group": "solution", "name": "theta", "templateType": "anything", "description": "", "definition": "degrees(arctan(x3/y1))"}}, "tags": [], "name": "Heather's copy of Machine: vice grips", "preamble": {"js": "", "css": ""}, "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 $E$.
\n
Geometry
\nDetermine angle $\\theta$ from the geometry of the pliers.
\n\\[\\theta = \\tan^{-1}\\left( \\dfrac{\\var{q(x3)}}{\\var{q(y1)}}\\right) = \\var{d(theta)}°\\]
\nFBD II
\n\\[\\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}\\]
\nFBD I
\n\\[\\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}\\]
\n", "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "Find the mechanical advantage of a pair of 'vice-grip' pliers."}, "type": "question", "contributors": [{"name": "Heather Driscoll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1703/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}]}], "contributors": [{"name": "Heather Driscoll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1703/"}, {"name": "William Haynes", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2530/"}]}