Physics Chapter 6: Forces and Moments
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Questions and Answers

What defines collinear forces?

  • Forces that meet at one point
  • Forces whose lines of action lie on the same line (correct)
  • Forces that do not meet at one point
  • Forces acting on different planes

Which type of forces are described as non-coplanar concurrent forces?

  • Forces that meet at one point but do not lie on the same plane (correct)
  • Forces that do not meet but lie in the same plane
  • Forces that meet at multiple points
  • Forces that act on different lines

Which characteristic of a force indicates its intensity?

  • Point of application of the force
  • Direction of the force
  • Nature of the force
  • Magnitude of the force (correct)

What effect can a force have on a body at rest?

<p>It can set the body in motion (C)</p> Signup and view all the answers

Which of the following is a characteristic maintained while determining the effects of a force?

<p>Direction of the line of action (C)</p> Signup and view all the answers

If a body is already in motion, what can a force do to it?

<p>Accelerate or change its motion (B)</p> Signup and view all the answers

What is the formula for the moment of a force about point O?

<p>P × OC (B), AB × OC (C)</p> Signup and view all the answers

Which of these describes coplanar non-concurrent forces?

<p>Forces that do not meet at one point but lie in the same plane (A)</p> Signup and view all the answers

What are the units of moment when force is measured in Newtons and distance in meters?

<p>Newton-meter (B)</p> Signup and view all the answers

What effect does a force produce when it retards the motion of a body?

<p>Sets the body in a non-moving state (A)</p> Signup and view all the answers

Which type of moment is considered positive according to general conventions?

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

According to Varignon’s Principle, what is true about the algebraic sum of the moments?

<p>It equals the moment of the resultant force about the same point. (C)</p> Signup and view all the answers

What is the least pull required to turn a wheel over the corner of a block if the wheel has a diameter of 600 mm?

<p>2.5 kN (C)</p> Signup and view all the answers

If a force causes an anticlockwise moment, what is its conventionally assigned value?

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

Which scenario best illustrates the concept of a clockwise moment?

<p>A door swinging outward (D)</p> Signup and view all the answers

What does the area of triangle ABO represent in the context of moments?

<p>Half the moment of the force about point O (C)</p> Signup and view all the answers

What is the formula for calculating the moment of inertia of a force about a point?

<p>Force multiplied by the distance (A)</p> Signup and view all the answers

What are the units for moment of inertia if area is in mm² and length is in mm?

<p>mm⁴ (A)</p> Signup and view all the answers

For which type of section is the theorem of perpendicular axis applicable?

<p>I-section (B)</p> Signup and view all the answers

Which of the following dimensions defines the height and radius of a circular solid cone?

<p>40 mm height and 30 mm radius (C)</p> Signup and view all the answers

What is the second moment of force commonly called?

<p>Moment of inertia (B)</p> Signup and view all the answers

Which shape can have a hollow rectangular section's moment of inertia calculated?

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

What is the purpose of the theorem of parallel axes when calculating moment of inertia?

<p>To find the moment of inertia about any axis parallel to the centroidal axis (C)</p> Signup and view all the answers

What dimensions are given for the unequal angle section example?

<p>100 mm × 80 mm × 20 mm (D)</p> Signup and view all the answers

What is the maximum value of frictional force called when a body just begins to slide over another surface?

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

Which of the following statements about the coefficient of friction is true?

<p>It is the ratio of limiting friction to the normal reaction. (A)</p> Signup and view all the answers

What does the angle of friction relate to in terms of a body on an inclined plane?

<p>The angle at which the body begins to slide down. (A)</p> Signup and view all the answers

Which law of static friction states that the force of friction acts in the opposite direction of motion?

<p>First law of static friction (D)</p> Signup and view all the answers

How does the force of friction depend on the surfaces in contact?

<p>It is independent of the area of contact. (C)</p> Signup and view all the answers

What is the angle of repose?

<p>The steepest angle at which a body can rest without sliding. (C)</p> Signup and view all the answers

Which of the following describes dynamic friction?

<p>It opposes the motion of a body already in motion. (C)</p> Signup and view all the answers

What is defined as a couple in mechanics?

<p>Two equal and opposite parallel forces (C)</p> Signup and view all the answers

What does the arm of a couple refer to?

<p>The perpendicular distance between the lines of action of the two forces (A)</p> Signup and view all the answers

Which law of friction states that the limiting friction has a constant ratio to the normal reaction?

<p>Second law of static friction (B)</p> Signup and view all the answers

What is the moment of a couple calculated from?

<p>The product of one force and the arm of the couple (C)</p> Signup and view all the answers

Which of the following best describes a clockwise couple?

<p>It rotates the body in a clockwise direction (D)</p> Signup and view all the answers

Which characteristic is TRUE for a couple?

<p>The algebraic sum of the forces is zero (A)</p> Signup and view all the answers

How can multiple co-planar couples be summarized?

<p>They can be adjusted to a single couple based on their moments (B)</p> Signup and view all the answers

In the context of a couple, what does the term 'negative couple' refer to?

<p>An anticlockwise couple (D)</p> Signup and view all the answers

What happens when a couple is applied to a body?

<p>It causes rotation without translational motion (C)</p> Signup and view all the answers

What is the definitive characteristic of a center of gravity (C.G.)?

<p>It acts through the whole weight of the body. (A)</p> Signup and view all the answers

Where is the center of gravity located for a uniform rod?

<p>At the midpoint of the rod. (A)</p> Signup and view all the answers

For a rectangle, where is the center of gravity found?

<p>At the intersection of its diagonals. (A)</p> Signup and view all the answers

What is the center of gravity for a triangle determined by?

<p>The intersection of its medians. (A)</p> Signup and view all the answers

How far is the center of gravity from the base of a semicircle?

<p>$ rac{4r}{3 imes ext{π}}$ (B)</p> Signup and view all the answers

Where is the center of gravity for a hemisphere measured from its base?

<p>$ rac{3r}{8}$ (C)</p> Signup and view all the answers

For a right circular solid cone, where is the center of gravity located relative to its base?

<p>$ rac{h}{4}$ (C)</p> Signup and view all the answers

What can be inferred about the center of gravity of a cube?

<p>It's at a distance of $ rac{l}{2}$ from every face. (A)</p> Signup and view all the answers

Flashcards

Moment of a Force

The turning effect of a force about a point, calculated by multiplying the force by the perpendicular distance from the point to the line of action of the force.

Clockwise Moment

A moment that tends to rotate a body in the same direction as the hands of a clock.

Anticlockwise Moment

A moment that tends to rotate a body in the opposite direction to the hands of a clock.

Varignon's Principle

The sum of the moments of individual forces acting on a point is equal to the moment of their resultant force about the same point.

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What units are used for moment?

Moment is expressed in units of force multiplied by distance, such as Newton-meters (N-m), kilonewton-meters (kN-m), or Newton-millimeters (N-mm).

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How to calculate the moment of a force?

The moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation to the line of action of the force.

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What is a clockwise moment?

A clockwise moment is a moment that tends to cause a rotation in the same direction as the hands of a clock.

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Rolling Friction

The friction experienced when a body rolls over another body.

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What is an anticlockwise moment?

An anticlockwise moment is a moment that tends to cause a rotation in the opposite direction to the hands of a clock.

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Limiting Friction

The maximum force of friction that can be exerted before an object starts sliding.

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Static Friction

The friction experienced when the object is at rest, opposing any force trying to move it.

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Coefficient of Friction (μ)

The ratio between limiting friction and the normal reaction between two surfaces.

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Angle of Friction

The angle at which a body on an inclined plane just starts to slide.

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Angle of Repose

The angle of an inclined plane where a body placed on it just begins to slide.

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Force of Friction - Direction

The force of friction always acts opposite to the direction the object tends to move.

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Force of Friction - Magnitude

The force of friction equals the force trying to move the object, but only up to the limiting friction.

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Collinear Forces

Forces whose lines of action lie on the same line.

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Concurrent Forces

Forces that meet at a single point. They may or may not be collinear.

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Coplanar Concurrent Forces

Forces that meet at a point and their lines of action lie on the same plane.

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Coplanar Non-Concurrent Forces

Forces that do not meet at a point, but their lines of action are on the same plane.

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Non-Coplanar Concurrent Forces

Forces that meet at a point, but their lines of action are not on the same plane.

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Non-Coplanar Non-Concurrent Forces

Forces that do not meet at a point and their lines of action are not on the same plane.

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What is the Magnitude of a Force?

The strength or intensity of the force, often expressed in units like Newtons (N) or Kilonewtons (kN).

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What is the Line of Action of a Force?

The imaginary line along which the force acts. Indicates direction.

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What is a couple?

A couple is formed by two equal and opposite forces acting parallel to each other. It cannot cause linear motion but creates rotational motion.

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What is the arm of a couple?

The perpendicular distance between the lines of action of the two forces in a couple is called the arm.

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Moment of a couple

It's calculated by multiplying the magnitude of one of the forces by the arm of the couple. It represents the rotational effect of the couple.

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Clockwise couple

A couple that tends to rotate the body in a clockwise direction.

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Anticlockwise couple

A couple that tends to rotate the body in an anticlockwise direction.

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Characteristics of a couple (1)

The algebraic sum of the forces in a couple is always zero.

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Characteristics of a couple (2)

The moment of the couple about any point is the same and equal to the moment of the couple itself.

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Characteristics of a couple (3)

A couple cannot be balanced by a single force. It can only be balanced by another couple of opposite sense.

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Centre of Gravity (C.G.)

The point where the entire weight of an object acts, regardless of its position.

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Centroid

The centre of area for plane figures like triangles or circles.

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C.G. of a uniform rod

The centre of gravity lies at the middle point of the rod.

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C.G. of Rectangle/Parallelogram

The point where the diagonals intersect. Also, the middle point of length and breadth.

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C.G. of a Triangle

The point where the three medians (lines connecting a vertex to the midpoint of the opposite side) meet.

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C.G. of a Trapezium

Located at a distance of (a + 2b)h / (3(a + b)) from the side b (where a and b are the parallel sides, h is the height)

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C.G. of a Semicircle

Located 4r/3 π from the base, measured along the vertical radius.

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C.G. of a Circular Sector

Located at a distance of (2r sin(α) / 3α) from the center (where r is the radius, α is the semi-vertical angle).

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Moment of Inertia

The second moment of a force about a point, calculated as the product of the force and the square of the perpendicular distance from the point to the line of action of the force.

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Units of Moment of Inertia

Moment of inertia's units are determined by the units of area and length. For example, if area is in meters squared (m²) and length in meters (m), then moment of inertia is expressed in meters to the fourth power (m⁴).

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Moment of Inertia of a Rectangular Section

The moment of inertia of a rectangular section about its centroidal axis is calculated by dividing the product of its width (b) and the cube of its height (h) by 12.

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Moment of Inertia of a Hollow Rectangular Section

The moment of inertia of a hollow rectangular section about its centroidal axis is calculated by subtracting the moment of inertia of the inner rectangle from the moment of inertia of the outer rectangle.

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Theorem of Perpendicular Axes

The moment of inertia of a plane area about an axis perpendicular to its plane is equal to the sum of moments of inertia about two perpendicular axes lying in the plane of the area and intersecting at the point where the perpendicular axis meets the plane.

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Moment of Inertia of a Circular Section

The moment of inertia of a circular section about an axis passing through its centroid and perpendicular to its plane is calculated by multiplying pi (π) by the fourth power of the radius (r) and dividing by 4.

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Moment of Inertia of a Hollow Circular Section

The moment of inertia of a hollow circular section is calculated by subtracting the moment of inertia of the inner circle from the moment of inertia of the outer circle.

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Theorem of Parallel Axes

The moment of inertia of a body about any axis is equal to the moment of inertia about a parallel axis passing through its centre of gravity plus the product of the mass of the body and the square of the distance between the two axes.

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Study Notes

Engineering Mechanics Lecture Notes

  • Engineering Mechanics is the branch of applied science that deals with the laws and principles of mechanics, along with their applications to engineering problems.
  • The subject can be divided into two main groups: Statics and Dynamics.
  • Statics deals with forces and their effects on bodies at rest.
  • Dynamics deals with forces and their effects on bodies in motion, further sub-divided into Kinetics and Kinematics.
  • Kinetics analyses motion caused by forces.
  • Kinematics analyzes motion without considering the forces causing it.
  • A rigid body is a solid body in which deformation is negligible.
  • Force is an agent that tends to cause, destroy, or change motion.
  • Systems of Forces:
    • Coplanar forces: Forces whose lines of action lie in the same plane.
    • Collinear forces: Forces whose lines of action lie on the same line.
    • Concurrent forces: Forces which meet at a common point.
    • Coplanar concurrent forces: Coplanar forces that meet at a common point.
    • Coplanar non-concurrent forces: Coplanar forces that do not meet at a common point.
    • Non-coplanar concurrent forces: Forces that meet at a common point, but their lines of action do not lie in the same plane.
    • Non-coplanar non-concurrent forces: Forces that do not meet at a common point and their lines of action do not lie in the same plane.
    • Methods for finding the resultant force: Analytical methods (parallelogram law, method of resolution) and graphical methods.

Chapter Contents

  • Fundamentals of Engineering Mechanics: Covers basic concepts. (pages 1-11)
  • Equilibrium: Discusses forces in equilibrium. (pages 12-17)
  • Friction: Explains frictional forces. (pages 18-32)
  • Centroid & Moment of Inertia: Details centroids and moment of inertia. (pages 33-46)
  • Simple Machines: Covers various simple machines. (pages 47-64)
  • Dynamics: Details dynamics concepts. (pages 65-72)

Additional Topics

  • Characteristics of forces: Magnitude, direction, line of action, and the point of application.
  • Effects of forces: Change in motion, motion retardation, and internal stresses.
  • Principle of transmissibility: A force acting at a given point of a rigid body can be moved along its line of action.
  • Principle of superposition: The combined effect of a force system is the sum of the effects of individual forces.
  • Resolution of a force: Breaking down a force into components.

Equilibrium

  • Different concepts of equilibrium
  • Two force, Three force and Four Force Principles
  • Lami's Theorem

Friction

  • Introduction to friction
  • Static Friction
  • Dynamic Friction
  • Limiting Friction
  • Coefficient of Friction
  • Angle of Friction

Moment of a Force

  • Moment of a force is equal to the product of force and perpendicular distance from the axis.
  • Units are Newton-meter. (N-m.)
  • Types of Moments
    • Clockwise moments
    • Anticlockwise moments
  • Principle / Law of moments
  • Varignon's Principle

Moment of a Couple

  • A couple is a pair of equal and opposite parallel forces with different lines of action.
  • The moment of a couple is equal to the product of the force acting in the couple and the perpendicular distance between the lines of action of the two forces.

Equilibrium of a Body on Inclined Planes

  • Forces on a rough inclined plane.
  • Conditions for Equilibrium.

Equilibrium of a Body on a Horizontal Plane (with Force Acting Horizontally)

Center of Gravity

  • Centroid of plane figures
  • Locating the center of mass by geometry.
  • Methods for Locating Centers of Gravity
    • Centre of Gravity of Simple Figures
    • Centre of Gravity by Geometry
  • Axis of Reference.
  • Locating the centre of gravity of unsymmetrical sections.
  • Symmetry rules in locating the center of gravity

Moment of Inertia

  • Moment of Inertia formula.
  • The moment of inertia of a plane area is a measure of a body's resistance to angular acceleration.
  • Moment of Inertia of a Rectangular Section formula
  • Moment of Inertia of a Hollow Rectangular Section formula
  • Theorem of Perpendicular Axis
  • Moment of Inertia of Circular Section formulae
  • Theorem of Parallel Axis

Simple Machines

  • Simple Machine definition
  • Compound Machine definition
  • Lifting Machine definition
  • Mechanical Advantage definition.
  • Input of a machine definition
  • Output of a machine Definition
  • Efficiency of a machine definition
  • Ideal Machine definition
  • Velocity Ratio definition
  • Simple Gear Train
  • Compound Gear Train

Simple Lifting Machines

  • Wheel and axle
  • Single Purchase Crab Winch

Screw Jack

  • Principle
  • Components
  • Equation of efficiency and mechanical advantage

Hoisting Machines

  • Derricks (types and uses)

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Test your knowledge on the concepts of collinear forces, moments, and their effects on bodies in motion or at rest. This quiz covers various aspects of force application, including characteristics, units, and principles like Varignon’s Principle. Perfect for students studying mechanics in physics.

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