Equilibrium of a particle: ball in a trough

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William Haynes

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Question statement

{geogebra_applet('dsdqn4dr',[['α', alpha+'°'],['β', beta+'°']])}

A: {A} B: {B}

Give any introductory information the student needs.

			Name	Type	Generated Value

alpha	integer	50
beta	integer	45
A	quantity	quantity(4.968654699515353263812735337226066363367, "N")
W	quantity	quantity(7, "N")
B	quantity	quantity(5.382794259098736657586238832959135067024, "N")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(20..70#5)

JME function reference

Description

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

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Generated value: `integer`

→ Used by:

Statement

Parts

Gap-fill
1. Gap Force A Engineering Accuracy with units
  Add
2. Gap Force B Engineering Accuracy with units
  Add

Gap-fill

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

A {w} cylinder rests in the trough shown. Assume that the contact surfaces are smooth (frictionless).

Determine the reactions at $A$ and $B$ .

$A$ = Force A $B$ = Force B

Advice

There are two ways to solve this problem

1. Equilibrium Equation Method

Draw a free body diagram of the cylinder.
Set up and simplify the equlibrium equations:

$\qquad\Sigma F_x = 0$ and $\Sigma F_y = 0$
Use algebra to solve simultaneously for the unknown forces $A$ and $B$.

2. Force Triangle Method

Draw a free body diagram of the cylinder.
Arrange forces acting on the cylinder into a force triangle.
Use trig to solve for the unknown reaction forces.

Answers

$A$ = {siground(A,4)} $B$={siground(B,4)}

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Part	Test	Passed?
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Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
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This question is used in the following exams:

Chapter 03 Exercises by Michael Proudman in Engineering Statics.
05. Equilibrium of a Particle by Michael Proudman in Engineering Statics.
Statics - Equilibrium by Robert Birch in Robert's workspace.
Statics - Chapter 3 Exercises by Jay McCormack in studio 4.
Chapter 3 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
Chapter 3 Exercises by William Haynes in Engineering Statics.
05. Equilibrium of a Particle by William Haynes in Engineering Statics.

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William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 7 months ago

Error in variable testing condition

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Generated value: `integer`

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Equilibrium of a particle: ball in a trough

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 6 years, 5 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`