// Numbas version: exam_results_page_options {"name": "Moment of a force about a point", "extensions": ["geogebra", "quantities", "weh"], "custom_part_types": [{"source": {"pk": 19, "author": {"name": "William Haynes", "pk": 2530}, "edit_page": "/part_type/19/edit"}, "name": "Engineering Accuracy with units", "short_name": "engineering-answer", "description": "

A value with units marked right if within an adjustable % error of the correct value.  Marked close if within a wider margin of error.

Does clumsy substitution to

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1. replace '-' with ' '

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2. replace '°' with ' deg'

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to allow answers like 10 ft-lb and 30°

", "name": "student_units"}, {"definition": "try(\ncompatible(quantity(1, student_units),correct_units),\nmsg,\nfeedback(msg);false)\n", "description": "", "name": "good_units"}, {"definition": "switch(not good_units, \n student_scalar * correct_units, \n not right_sign,\n -quantity(student_scalar, student_units),\n quantity(student_scalar,student_units)\n)\n \n", "description": "

This fixes the student answer for two common errors.

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If student_units are wrong  - replace with correct units

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If student_scalar has the wrong sign - replace with right sign

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If student makes both errors, only one gets fixed.

", "name": "student_quantity"}, {"definition": "try(\nscalar(abs((correct_quantity - student_quantity)/correct_quantity))*100 \n,msg,\nif(student_quantity=correct_quantity,0,100))\n ", "description": "", "name": "percent_error"}, {"definition": "percent_error <= settings['right']\n", "description": "", "name": "right"}, {"definition": "right_sign and percent_error <= settings['close']", "description": "

Only marked close if the student actually has the right sign.

", "name": "close"}, {"definition": "sign(student_scalar) = sign(correct_quantity) ", "description": "", "name": "right_sign"}], "settings": [{"input_type": "code", "evaluate": true, "hint": "The correct answer given as a JME quantity.", "default_value": "", "label": "Correct Quantity.", "help_url": "", "name": "correctAnswer"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered correct if the scalar part of the student's answer is within this % of correct value.", "default_value": "0.2", "label": "% Accuracy for right.", "help_url": "", "name": "right"}, {"input_type": "code", "evaluate": true, "hint": "Question will be considered close if the scalar part of the student's answer is within this % of correct value.", "default_value": "1.0", "label": "% Accuracy for close.", "help_url": "", "name": "close"}, {"input_type": "percent", "hint": "Partial Credit for close value with appropriate units.  if correct answer is 100 N and close is ±1%,
99  N is accepted.", "default_value": "75", "label": "Close with units.", "help_url": "", "name": "C1"}, {"input_type": "percent", "hint": "Partial credit for forgetting units or using wrong sign.
If the correct answer is 100 N, both 100 and -100 N are accepted.", "default_value": "50", "label": "No units or wrong sign", "help_url": "", "name": "C2"}, {"input_type": "percent", "hint": "Partial Credit for close value but forgotten units.
This value would be close if the expected units were provided.  If the correct answer is 100 N, and close is ±1%,
99 is accepted.", "default_value": "25", "label": "Close, no units.", "help_url": "", "name": "C3"}], "public_availability": "restricted", "published": false, "extensions": ["quantities"]}], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"alpha'": {"group": "Inputs", "definition": "random(-150..150#5 except [0,5,10,90,-5,-10,-90])", "name": "alpha'", "templateType": "anything", "description": "

angle of force with respect to the bar.

"}, "Fperp": {"group": "results", "definition": "M/D", "name": "Fperp", "templateType": "anything", "description": "

The perpendicular component of the force.

"}, "version": {"group": "display", "definition": "random(0..4)", "name": "version", "templateType": "anything", "description": "

which question version?

"}, "direction": {"group": "results", "definition": "if(alpha'<180,'clockwise','counterclockwise')", "name": "direction", "templateType": "anything", "description": ""}, "Dperp": {"group": "results", "definition": "M/F", "name": "Dperp", "templateType": "anything", "description": "

The perpendicular distance.

"}, "F": {"group": "Inputs", "definition": "qty(random(10..150)*random(0.1,0.5,1),'lb')", "name": "F", "templateType": "anything", "description": "

Magnitude of the force.

"}, "debug": {"group": "display", "definition": "false", "name": "debug", "templateType": "anything", "description": ""}, "beta": {"group": "display", "definition": "if(beta'>90,180-beta',beta')", "name": "beta", "templateType": "anything", "description": ""}, "alpha": {"group": "display", "definition": "if(abs(alpha')>90,(180-abs(alpha')),abs(alpha'))", "name": "alpha", "templateType": "anything", "description": "

Angle alpha as shown on the diagram, always less than 90°.

"}, "answers": {"group": "display", "definition": "[['$F_\\\\perp$', Fperp , '$M$', M],\n\n['$d_\\\\perp$', Dperp, '$M$', M ],\n\n['$d_\\\\perp$',Dperp, '$F$', F],\n\n['$\\\\ell$', D, '$F_\\\\perp$', Fperp],\n\n['$\\\\alpha$',qty(alpha,'deg'), '$d_\\\\perp$',Dperp]]\n", "name": "answers", "templateType": "anything", "description": "

"}, "beta'": {"group": "Inputs", "definition": "random(20..160#10 except 90)", "name": "beta'", "templateType": "anything", "description": "

angle of bar from positive x axis

"}, "M": {"group": "results", "definition": "siground(sin(radians(alpha)),5) * ( F * D )", "name": "M", "templateType": "anything", "description": "

The magnitude of the moment

"}, "D": {"group": "Inputs", "definition": "qty(random(6..30#2),'in')", "name": "D", "templateType": "anything", "description": "

Length of the bar AB.

"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "
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1. Draw the line of action of the force.
2. \n
3. Make a triangle including the perpendicular distance $d_\\perp.$
4. \n
5. Use geometry to find an angle in this triangle.
6. \n
7. Use trig to find the value of the perpendicular distance.
8. \n
9. Apply equation $M=F d_\\perp$  to find the moment.
10. \n
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Alternate method

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1. Identify and solve for the component of force $F$ perpendicular to the control rod, $F_\\perp d$  .
2. \n
3. Find the moment using $M = F_\\perp d$
4. \n

Determine the moment of a force about a point by using $M= F d_\\perp$ or $M = F_\\perp d$.

"}, "tags": ["2-d", "2-D", "Mechanics", "mechanics", "Moment", "Perpendicular distance", "perpendicular distance", "statics", "Statics"], "functions": {}, "statement": "

A {scalar(f)} lb force F is applied to the control rod AB as shown. Knowing that the length of the rod is {scalar(d)} inches and that $\\alpha$ is {alpha}°, determine the component of F perpendicular to rod AB and the magnitude of the moment produced.

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A {scalar(f)} lb force F is applied to the control rod AB as shown. Knowing that the length of the rod is {scalar(d)} inches and that $\\alpha$ is {alpha}°, determine the perpendicular distance from the line of action of force F to point B, and the magnitude of the moment produced.

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Force F is applied to the {scalar(d)} inch long control rod AB at angle $\\alpha$ = {alpha}° as shown.  Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point B, determine the perpendicular distance from the line of action of force F to point B, and the magnitude of force F.

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A {scalar(f)} lb force F is applied to control rod AB at angle $\\alpha$ = {alpha}° as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point B, determine the length of the control rod, and the component of F in a direction perpendicular to AB.

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A {scalar(f)} lb force F is applied to the {scalar(d)} inch long control rod AB as shown. Knowing that it creates a {siground(scalar(M),4)} in lb {direction} moment about point B, determine angle $\\alpha$ and the perpendicular distance between the line of action of force F and point B.

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F: {F} D:{D} $\\alpha$: {alpha} $F_\\perp$: {fperp} $d_\\perp$: {dperp} M: {M}

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", "preamble": {"css": "", "js": ""}, "parts": [{"customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "prompt": "

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