Engineering Mechanics: Rotation and Elasticity

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Questions and Answers

What is the purpose of balancing a rotating component?

To increase the speed of rotation

To enhance the aesthetic appearance of the component

To reduce friction between components

To align the center of gravity with the center of rotation (correct)

Which factor is integral in preventing excessive vibration in high-speed rotating components?

Temperature fluctuations

Material weight distribution (correct)

Rotational speed variance

Air resistance

According to Hooke's Law, what happens when stress is doubled within the elastic limit?

Strain remains constant

Strain increases proportionally (correct)

Material permanently deforms

Elastic limit is exceeded

What describes the relationship between stress and strain under elastic limits?

Strain is related to stress by a constant factor Signup and view all the answers

How can imbalance in a rotating component typically be corrected?

By adding or removing mass from the affected side Signup and view all the answers

What unit is stress measured in?

Newton per square meter Signup and view all the answers

Which of the following components is commonly balanced during manufacture?

Landing gear wheel assemblies Signup and view all the answers

What happens when the strain exceeds a material's elastic limit?

Material remains permanently deformed Signup and view all the answers

What type of stress results from forces that try to pull an object apart?

Tension Signup and view all the answers

What occurs when external forces push an object together?

Compression Signup and view all the answers

Which type of stress involves adjacent layers of material sliding over one another?

Shear stress Signup and view all the answers

How does the weight of an aircraft affect the runway?

It causes compressive stress. Signup and view all the answers

What happens to a rivet shank when compressive loads are applied during riveting?

It expands to fill the hole. Signup and view all the answers

What is the primary effect of shear stress on a body?

To slice the body apart Signup and view all the answers

Which forces are described as causing alternating stresses on an airplane wing during flight?

Both aerodynamic and gravitational forces Signup and view all the answers

What type of stress is caused by a twisting force applied to a fixed rod?

Torsional stress Signup and view all the answers

What is the primary characteristic of a force in physics?

It can change a body’s state of motion. Signup and view all the answers

Which of the following is true about vector quantities?

Vectors require both magnitude and direction. Signup and view all the answers

What is the process of adding vectors?

Attach one vector's head to the other's tail. Signup and view all the answers

Which statement best describes tension in the context of materials?

It is a force that attempts to stretch an object. Signup and view all the answers

What are the two main factors needed to fully define a vector quantity?

Magnitude and direction. Signup and view all the answers

Which of the following best describes the center of gravity of a mass?

It represents the average position of weight in a body. Signup and view all the answers

In the context of solids, which type of stress occurs when an object is pulled apart?

Tensional stress. Signup and view all the answers

What is buoyancy primarily a result of?

The pressure difference in a fluid. Signup and view all the answers

What does a hydrometer measure in a liquid?

The relative density or specific gravity of the liquid Signup and view all the answers

How does the density of the liquid affect the behavior of the float in a hydrometer?

Higher density liquids cause the float to ride higher Signup and view all the answers

If Body A has a specific gravity of 0.25, how submerged will it be in water?

1/4 submerged Signup and view all the answers

What principle states that changes in pressure in a confined liquid are transmitted equally throughout the fluid?

Pascal's Law Signup and view all the answers

What is the mechanical advantage (MA) if 1 psi is applied over 10 square inches?

10 Signup and view all the answers

If a body has a specific gravity greater than 2, what will happen when placed in water?

It will sink Signup and view all the answers

When using a hydraulic jack, what happens to the distance moved by the large piston compared to the small piston?

Moves half the distance of the small piston Signup and view all the answers

What does the differing area of a hydraulic system affect?

Both the force and speed of operation Signup and view all the answers

What is the primary factor that determines atmospheric pressure at a specific location?

Weight of the air column above the location Signup and view all the answers

How is Absolute Pressure calculated?

By adding atmospheric pressure to gauge pressure Signup and view all the answers

At a cruising altitude of 29,000 ft, if the outside pressure is 4.4 psi, what is the differential pressure if the cabin is maintained at 11 psi?

6.6 psi Signup and view all the answers

Which of the following characteristics is NOT true about solids?

Solids can change shape easily Signup and view all the answers

Which statement correctly describes the behavior of fluids exerting force on submerged objects?

The force is perpendicular to the surface of the object Signup and view all the answers

What are the two main classifications of fluids?

Liquids and gases Signup and view all the answers

What can be said about the forces that keep atoms or molecules together in a solid?

They are strong and rigid Signup and view all the answers

Which characteristic is typically associated with metals as solids?

They are usually hard and strong Signup and view all the answers

What property distinguishes vector quantities from scalar quantities?

Vector quantities have both magnitude and direction. Signup and view all the answers

Which action best describes what happens to a body when a net force is applied to it?

It may accelerate, decelerate, start, or stop depending on the force. Signup and view all the answers

What is the primary purpose of scale drawings in physics regarding vectors?

To visually illustrate the magnitude and direction of vectors. Signup and view all the answers

When dealing with tension in materials, what is the fundamental nature of this type of stress?

It involves pulling forces attempting to elongate the material. Signup and view all the answers

What occurs when vectors are added using the head-to-tail method?

The resultant vector is drawn from the tail of the first vector to the head of the last vector. Signup and view all the answers

What happens to the resultant force acting on an object that is in a state of equilibrium?

It is zero. Signup and view all the answers

Which of the following accurately defines the relationship between load moment and effort moment in a lever?

Both moments must be equal for the system to be balanced. Signup and view all the answers

In vector resolution, how are the components of a tension force determined?

By using trigonometric ratios. Signup and view all the answers

When a car is pushed by equal forces from both ends and does not move, what statement describes this scenario?

The resultant force on the car is zero, indicating static equilibrium. Signup and view all the answers

What is the mechanical advantage (MA) of using levers as simple machines?

It allows for lifting heavier loads with less effort. Signup and view all the answers

What defines the mechanical advantage (MA) of a first-class lever?

The ratio of the effort applied to the load supported Signup and view all the answers

Which of the following best illustrates a first-class lever in action?

Raising a lid with a crowbar Signup and view all the answers

If a load of 200 kg is lifted with an effort of 20 kg, what is the mechanical advantage (MA) of this lever?

5 Signup and view all the answers

In a first-class lever, if the fulcrum is moved closer to the load, what happens to the mechanical advantage?

It increases Signup and view all the answers

At what point is the term 'leverage' most appropriately applied in the context of a first-class lever?

When raising a lid short distances with hand travel Signup and view all the answers

Which of the following best describes the relationship between the lengths of the load arm and the effort arm in a first-class lever?

The length of the effort arm will determine the MA Signup and view all the answers

What effect does using a longer effort arm in a first-class lever have on the effort required to lift a load?

It decreases the required effort Signup and view all the answers

In a mechanical advantage calculation, if the lifting arm is 8 times the length of the load arm, what is the mechanical advantage?

8 Signup and view all the answers

If an effort of 15 N is used to lift a load of 60 N, what is the mechanical advantage of this lever setup?

3 Signup and view all the answers

When operating a first-class lever, what is the relationship between the distances moved by the effort and the load?

The distance moved by the load is always shorter Signup and view all the answers

Study Notes

Rotating Components

An unbalanced rotating component will cause vibration.
To rectify this, the center of gravity (CG) must be shifted to coincide with the center of rotation.
Mass balancing can be achieved by adding or removing small masses of material to the heavy or light side.
Landing gear wheel assemblies, helicopter rotors, compressors, turbines, fans, and rotors in generators, magnetos, and gyroscopes are balanced during manufacture.
Unbalanced parts can cause significant vibration, even at high speeds.

Stress, Strain, and Elasticity

Stress is the external force acting on an object per unit cross-sectional area (Stress = Force / Area).
Strain is a measure of the deformation of a material due to stress (Strain = (Extension / Original size) x 100%).
Elasticity refers to a material's ability to return to its original length after stress is removed, as long as the strain is below the elastic limit.
Hooke's law states that strain is directly proportional to stress within the elastic limit.

Types of Stress

Tension stress occurs when forces tend to pull an object apart, like ropes and cables.
Compression stress occurs when forces push an object together, like the weight of an aircraft on the runway.
Shear stress occurs when external forces distort an object so that adjacent layers of material slide over each other. Shear stress tries to slice a body apart.

Tension and Compression in Aircraft

An aircraft wing and helicopter rotor blades experience alternating compression and tensile stresses due to aerodynamic and gravitational forces.
The top and bottom surfaces of the wing must be strong enough to withstand fatigue from these alternating stresses.

Torsional Stress

Torsional stress or torque causes shear stress.
A twisting force applied to a fixed rod will cause sections of material to slide over each other.

Forces, Moments, and Couples

A force is defined as that which can produce a change in a body’s state of motion.
Forces can start, stop, accelerate, or decelerate a mass.
Forces can do work if energy is available.

Vectors

A vector quantity describes magnitude (size) and direction.
Most quantities are scalars, defined only by size, such as temperature, length, and time.

Buoyancy

Hydrometers measure the relative density or specific gravity (SG) of liquids using Archimedes' principle.
The density of the liquid determines how high or low the float rides in the liquid.
A calibrated scale gives a direct reading of the liquid’s SG.

Pascal's Law

When pressure is applied to a confined liquid, the pressure changes are transmitted undiminished to all parts of the fluid and its container.
Pascal’s Law can be used to provide mechanical advantage, as in a hydraulic jack.

Differential Area

Pressure can exert different forces depending on the direction of travel due to differing areas available.
This affects the speed of the operation.

Atmospheric Pressure

Atmospheric pressure at a location depends on the weight of the column of air above that location.

Absolute Pressure vs. Gauge Pressure

Gauge pressure reads pressure above or below atmospheric pressure.
Absolute pressure includes gauge pressure and atmospheric pressure.

Differential Pressure

Modern aircraft maintain a cabin altitude equivalent to 8000' or 11 psi for passenger comfort.
At cruising altitude of 29,000 feet, outside pressure is 4.4 psi.
This creates a differential pressure of 6.6 psi on the aircraft structure, a significant component of the total stress.

Solids

Solids have a definite shape and definite volume, independent of their container.
The forces (bonds) that keep the atoms or molecules together in a solid are strong.
Solids do not require outside support to maintain their shape.

Fluids

Liquids and gases are both classified as fluids.
The force exerted by a fluid on a submerged object is perpendicular to the surface of the object.

Forces

Forces are the result of an interaction that can change an object's state of motion.
Objects can be started, stopped, accelerated, or decelerated by applying forces.
Energy is required for forces to do work.

Vectors

Forces are vector quantities.
Vectors need both magnitude and direction to be defined completely.
Scalar quantities, such as temperature, length, and time, are defined by size only.
Vectors are conveniently represented using scale drawings.

Vector Addition

Vectors can be added by moving one vector's tail to the other vector's head while maintaining their direction and magnitude.
The resultant vector forms a triangle with the other two vectors where its head connects to the free head of the added vector.

Resolution of a Vector

Vectors can be resolved into components using standard trigonometric ratios.
A 60N tension force in a chain can be resolved into horizontal and vertical components.

Resultant Force & Equilibrium

When forces act on a body in different directions, the resultant force can be calculated by resolving the forces.
An object is considered to be in equilibrium when the resultant forces acting on it are zero, and it does not change its state of motion or rest.
A car pushed by two equal and opposite forces remains stationary due to the resultant force being zero.

Moments

A moment is the force multiplied by the distance from the fulcrum, also known as the arm.
A system is balanced when the load moment and the effort moment are equal.
A smaller effort force can move through a larger arc, resulting in a heavier load moving a shorter distance.

Levers

Levers are simple machines that utilize mechanical advantage.
Levers are used to work with a load, utilizing an effort and pivoting around a fulcrum.
A lever has a positive mechanical advantage when the load moved exceeds the effort used.
Levers are categorized into three classes: first-class, second-class, and third-class.

First Class Lever

A crowbar is an example of a first-class lever.
The fulcrum is located between the load and the effort.
The load is usually greater than the effort in a first-class lever.
The mechanical advantage of a first-class lever depends on the distance moved by the effort compared to the load.

Mechanical Advantage

In a first-class lever, if the lifting arm is seven times longer than the load arm, the load can be lifted with seven times less effort.
The distance moved by the load and the distance moved by the effort are proportional and equal to the mechanical advantage.
The mechanical advantage can be utilized to reduce the effort required to move a load.

Stress

Stress is categorized into tension, compression, shear, and torsion.
When a material resists applied force, it exerts an internal force to counteract the applied force.
Stress is measured in Pascals (Pa) or N/m2

Shear Stress

Shear stress is caused by forces applied in opposite directions but across the same plane.
Shear stress can be seen in rivets and bolts.

Torsion

Torsion is a twisting force that causes shear stress in a cylindrical object.
The stress resulting from torsion is distributed across the object's cross-section; the maximum stress occurs at the outer edges.
The stress is proportional to the applied force and the distance from the axis of rotation.

Tension

Tension stress is caused by a pulling force and results in stretching.
When a rope supports a weight, the rope experiences tension stress.
Tension is important in determining the strength of chains and cables.

Compression

When an object is squeezed, it experiences compressive stress.
The stress is proportional to the applied force and the cross-sectional area of the object.
Compression stress is observed in columns and beams.

Strain

Strain is measured in a unitless ratio of the change in length or shape to the original length or shape.
Strain can be measured as tensile strain, compressive strain, shear strain, or volume strain.
Strain is used to determine the elongation or deformation of materials.

Hooke's Law

Hooke's Law describes the relationship between stress and strain for elastic materials.
The relationship is linear, meaning that the stress is directly proportional to the strain.
However, this relationship only holds true within a material's elastic limit.

Elasticity

Elasticity is a material property that describes how much it can deform under stress and then return to its original shape when the stress is removed.
Materials have both elastic and plastic properties.
Each material has an elastic limit, which determines the largest stress it can sustain before permanent deformation.

Plasticity

Plasticity refers to a material's ability to permanently deform under stress.
Once a material exceeds its elastic limit, it enters the plastic region and will not return to its original shape when the stress is removed.
Bending or shaping metal is an example of plasticity.

Poisson’s Ratio

Poisson's ratio describes the ratio of lateral strain to axial strain applied to an object.
It is a positive value for most materials.
When a material is stretched in one direction, it shrinks in the other direction.

Yield Strength

The yield strength is the point where a material exhibits permanent deformation under a specific stress.
It is determined in a tensile test, where a sample is stretched until it changes shape permanently.
The yield strength is an important parameter in determining the maximum stress that a material can safely withstand.

Ultimate Tensile Strength

The ultimate tensile strength represents the maximum stress a material can withstand before breaking or fracturing.
It is also determined in a tensile test.
The ultimate tensile strength is a crucial parameter for ensuring that a material is suitable for a particular application.

Residual Stress

Residual stress is the stress left in a material after it has been processed or heat treated.
Temperature changes can cause residual stress.
Residual stress can be both beneficial and detrimental to a material's strength and performance.

Fatigue

Fatigue is a type of failure that occurs due to repeated stress cycles.
Fatigue failure is characterized by the initiation and growth of cracks in a material.
It is a major concern in applications where materials are subjected to repetitive loading or vibrations.

Velocity Ratio

Velocity ratio is the ratio of two speeds within a system.
For example, in a pulley system with an MA of 4, the operator would pull the rope four times faster than the load is raised.
Velocity ratio is related to the mechanical advantage and distance ratio.

Couples

A couple is a moment generated by two parallel forces of equal magnitude acting in opposite directions.
Couples cause a twisting force or torque.
The torque produced by a couple is calculated by multiplying the force by the distance between the two forces.

Centre of Gravity

The centre of gravity (CG) is the point where the weight of an object appears to act, regardless of its orientation.
The CG of uniformly distributed objects is located at its geometric centre.
The CG of irregularly shaped objects can be found by hanging the object from two points and finding the intersection of the vertical lines passing through the suspension points.
The entire weight of an object is considered to act through its CG.

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Description

This quiz focuses on key concepts of rotating components and the principles of stress, strain, and elasticity in materials. It covers the importance of mass balancing in rotating systems and the definitions and calculations related to stress and strain. Test your understanding of these fundamental mechanical engineering topics.

Engineering Mechanics: Rotation and Elasticity

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Questions and Answers

What is the purpose of balancing a rotating component?

Which factor is integral in preventing excessive vibration in high-speed rotating components?

According to Hooke's Law, what happens when stress is doubled within the elastic limit?

What describes the relationship between stress and strain under elastic limits?

How can imbalance in a rotating component typically be corrected?

What unit is stress measured in?

Which of the following components is commonly balanced during manufacture?

What happens when the strain exceeds a material's elastic limit?

What type of stress results from forces that try to pull an object apart?

What occurs when external forces push an object together?

Which type of stress involves adjacent layers of material sliding over one another?

How does the weight of an aircraft affect the runway?

What happens to a rivet shank when compressive loads are applied during riveting?

What is the primary effect of shear stress on a body?

Which forces are described as causing alternating stresses on an airplane wing during flight?

What type of stress is caused by a twisting force applied to a fixed rod?

What is the primary characteristic of a force in physics?

Which of the following is true about vector quantities?

What is the process of adding vectors?

Which statement best describes tension in the context of materials?

What are the two main factors needed to fully define a vector quantity?

Which of the following best describes the center of gravity of a mass?

In the context of solids, which type of stress occurs when an object is pulled apart?

What is buoyancy primarily a result of?

What does a hydrometer measure in a liquid?

How does the density of the liquid affect the behavior of the float in a hydrometer?

If Body A has a specific gravity of 0.25, how submerged will it be in water?

What principle states that changes in pressure in a confined liquid are transmitted equally throughout the fluid?

What is the mechanical advantage (MA) if 1 psi is applied over 10 square inches?

If a body has a specific gravity greater than 2, what will happen when placed in water?

When using a hydraulic jack, what happens to the distance moved by the large piston compared to the small piston?

What does the differing area of a hydraulic system affect?

What is the primary factor that determines atmospheric pressure at a specific location?

How is Absolute Pressure calculated?

At a cruising altitude of 29,000 ft, if the outside pressure is 4.4 psi, what is the differential pressure if the cabin is maintained at 11 psi?

Which of the following characteristics is NOT true about solids?

Which statement correctly describes the behavior of fluids exerting force on submerged objects?

What are the two main classifications of fluids?

What can be said about the forces that keep atoms or molecules together in a solid?

Which characteristic is typically associated with metals as solids?

What property distinguishes vector quantities from scalar quantities?

Which action best describes what happens to a body when a net force is applied to it?

What is the primary purpose of scale drawings in physics regarding vectors?

When dealing with tension in materials, what is the fundamental nature of this type of stress?

What occurs when vectors are added using the head-to-tail method?

What happens to the resultant force acting on an object that is in a state of equilibrium?

Which of the following accurately defines the relationship between load moment and effort moment in a lever?

In vector resolution, how are the components of a tension force determined?

When a car is pushed by equal forces from both ends and does not move, what statement describes this scenario?

What is the mechanical advantage (MA) of using levers as simple machines?

What defines the mechanical advantage (MA) of a first-class lever?

Which of the following best illustrates a first-class lever in action?

If a load of 200 kg is lifted with an effort of 20 kg, what is the mechanical advantage (MA) of this lever?

In a first-class lever, if the fulcrum is moved closer to the load, what happens to the mechanical advantage?

At what point is the term 'leverage' most appropriately applied in the context of a first-class lever?

Which of the following best describes the relationship between the lengths of the load arm and the effort arm in a first-class lever?

What effect does using a longer effort arm in a first-class lever have on the effort required to lift a load?

In a mechanical advantage calculation, if the lifting arm is 8 times the length of the load arm, what is the mechanical advantage?

If an effort of 15 N is used to lift a load of 60 N, what is the mechanical advantage of this lever setup?

When operating a first-class lever, what is the relationship between the distances moved by the effort and the load?

Study Notes

Rotating Components

Stress, Strain, and Elasticity

Types of Stress

Tension and Compression in Aircraft

Torsional Stress

Forces, Moments, and Couples

Vectors

Buoyancy

Pascal's Law

Differential Area

Atmospheric Pressure

Absolute Pressure vs. Gauge Pressure

Differential Pressure

Solids

Fluids