Engineering Mechanics Quiz

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Questions and Answers

What would be the magnitude of each force P if the couple is replaced by two forces P and -P, each with a magnitude of 400 N?

  • 200 N
  • 400 N (correct)
  • 600 N
  • 800 N

What will happen to the lever if the horizontal 80-lb force is replaced with a force at O and a couple?

  • The lever will experience both translation and rotation. (correct)
  • The lever will undergo translational motion only.
  • The lever will experience no changes.
  • The lever will remain static.

How is the moment associated with a couple applied to a rectangular plate determined?

  • By the product of force and distance from the point of application.
  • By the average of the forces in the couple.
  • By the sum of individual forces acting on the plate.
  • By the product of the magnitudes of the two forces in the couple. (correct)

What is the necessary condition for two forces P and -P to be considered an equivalent couple?

<p>They must be of equal magnitude and act in opposite directions. (D)</p> Signup and view all the answers

In the scenario involving the couple of two 100-N forces, what angle θ would be required to maintain equilibrium when replaced by forces P and -P?

<p>90 degrees (D)</p> Signup and view all the answers

What is a truss?

<p>A framework composed of members joined at their ends to form a rigid structure (B)</p> Signup and view all the answers

All members of a truss are assumed to be two-force members.

<p>True (A)</p> Signup and view all the answers

What assumption is made regarding the weight of the truss members?

<p>The weight of the member is small compared to the force it supports.</p> Signup and view all the answers

The method for finding the forces in the members of a truss is called the __________.

<p>Method of Joints</p> Signup and view all the answers

Which of the following is NOT a common application of trusses?

<p>Electric circuits (A)</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Plane Truss = Truss where members lie in a single plane Equilibrium = State where net forces and moments are zero Two-force member = Member with forces applied at two points only Pin Joint = Connection assuming rotation without friction</p> Signup and view all the answers

The method of sections can analyze forces in any member of a truss directly.

<p>True (A)</p> Signup and view all the answers

How many unknown members should not exceed when using the method of sections?

<p>Three</p> Signup and view all the answers

What is the definition of moment in the context of force?

<p>The tendency to rotate a body about an axis (D)</p> Signup and view all the answers

According to Varignon’s theorem, the moment of a force about any point is equal to the sum of the forces acting on it.

<p>False (B)</p> Signup and view all the answers

What is the term for the moment produced by two equal and opposite forces?

<p>couple</p> Signup and view all the answers

The formula for calculating moment is given by M = r × F, where M represents moment, r is the __________, and F is the __________.

<p>distance, force</p> Signup and view all the answers

Match the components with their respective definitions:

<p>Moment = Tendency to rotate a body Torque = Another term for moment Couple = Two equal and opposite forces Varignon’s Theorem = Moment equals sum of moments of components</p> Signup and view all the answers

In the given example problem, if a couple consists of two 100-N forces, what is the resultant effect of these forces?

<p>No net force, produces rotation (A)</p> Signup and view all the answers

The sum of the moments of two forces forming a couple is zero.

<p>True (A)</p> Signup and view all the answers

What does the variable 'd' represent in the context of a couple?

<p>The distance between the two forces</p> Signup and view all the answers

Flashcards

Couple

A pair of forces with equal magnitudes, opposite directions, and different lines of action.

Equivalent couple

A couple that produces the same moment as another couple.

Magnitude of force

The size or strength of a force.

Angle θ

The angle between the forces in a couple.

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Moment

Tendency of a force to cause rotation.

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Moment of a force

Rotational tendency of a force

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Varignon's Theorem

Moment of a force about a point equals the sum of moments of components about the same point

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Couple

Two equal, opposite forces creating rotation

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Couple Moment

Combined rotational effect of a couple

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Equivalent Couple

Couple with same rotational effect

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Force Components

Individual parts of a force

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Moment calculation

Moment (M) = Force (F) × Distance (r)

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Rotation

Turning action of force

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Plane Truss

A rigid structure made of interconnected members lying in a single plane.

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Two-Force Member

A structural member subjected to only two forces acting at its ends. These forces must be equal, opposite, and collinear.

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Method of Joints

An equilibrium method to find member forces in a truss by analyzing the forces at each joint.

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Method of Sections

A shortcut equilibrium method to find member forces directly by analyzing a cut section of the truss.

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Pin Joint

A connection between two truss members that allows rotation but no translational movement.

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Equilibrium

A state where the net force and moment acting on an object are zero.

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Truss Assumptions

Simplified assumptions (like two-force members, small member weight, and pin joints) made for easier truss analysis.

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Truss Analysis

The process of determining the forces in the members of a truss

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Study Notes

Example Problem 1

  • A rigid structural member is subjected to a couple of two 100-N forces.
  • The couple is replaced by an equivalent couple with two forces, P and -P, each with a magnitude of 400 N.
  • The angle θ needs to be determined.

Example Problem 2

  • Replace an 80-lb horizontal force acting on a lever with an equivalent system of force and couple at point O.
  • The lever's dimensions are provided as 9 inches and 60 degrees.

Example Problem 3

  • Determine the moment associated with a couple applied to a rectangular plate.
  • Forces are applied perpendicular to the plate.
  • The plate's dimensions are height (h) and width (b).
  • Angle θ represents the force's direction.

Example Problem 4

  • Calculate the tension (T) in a cable supporting a 1000-lb load with a pulley arrangement.
  • Each pulley is free to rotate.
  • Weights of pulley components are negligible.
  • Find the total force on bearing C.
  • Angle θ is 30 degrees.

Example Problem 5

  • A uniform 100-kg I-beam is initially supported by rollers at A and B.
  • Cable at C is used to elevate end B 3 meters above end A.
  • Calculate the required tension (P) in the cable.
  • Find the reaction at point A.
  • Determine the angle θ of the beam in the elevated position relative to the horizontal.
  • Dimensions: 6 meters and 2 meters are given.

Example Problem 6

  • Determine the tension (T) in the supporting cable and the force on pin A for a jib crane.
  • Beam AB is a 0.5-meter I-beam with a mass of 95 kg per meter of length.
  • Dimensions: 0.25 m, 0.5m, 0.12 m, 1.5m, and 5m are provided.
  • Weight: 10 kN,
  • Angle: 25 degrees

Example Problem 7

  • Find the tilt angle (θ) of a smooth cylinder resting on two inclined surfaces.
  • The contact force at B should be half of that at A.
  • Angles are 45 degrees each.

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Problem Set 2 PDF
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