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Mechanics and Materials

Mechanics and materials are closely connected. Mechanics studies the forces that produce motion, mechanical work, and concepts such as momentum and energy. A classical approach to mechanics includes Newton’s laws of forces interacting in bodies, which can be static or in motion.

The study of materials deals with the properties of solids, focusing on their mechanical properties and how these change depending on the forces interacting with them.

Mechanics

Mechanics is the area of physics that deals with the analysis of bodies, whether static or in motion. Mechanics can be divided into kinematics and dynamics. Kinematics studies the movements and displacement of the body, while dynamics focuses on the forces producing these movements.

Mechanics also studies the changes in the energy of a body in movement as well as the work produced by this object. A large portion of the classical study of dynamics is also dedicated to Newton’s Laws. Sometimes the combination of both is called ‘Newtonian Mechanics’.

Kinematics

The analysis of the changes in velocity, acceleration, or displacement of an object is an integral part of the area of kinematics. For this, objects can move in linear motion (linear kinematics) or circular motion (rotational kinematics). Examples of both can be found below:

Linear kinematicsImagine the movement of a ball over a straight rail or a car on a straight road. Velocity, displacement, or acceleration in these systems occur over just one axis and in only two directions, which simplifies analysis and calculations.

Rotational kinematics Think of the movement of a seat in a carousel or a satellite over the earth. These systems have more complex interactions between the positions and movements of their constituents. As an example, two objects rotating at the same speed around the same centre cover different distances by virtue of being at different distances from the centre. In linear systems, by comparison, two objects at the same speed cover the same distance, even if the directions and axis are not the same.

Mechanics and Materials. Rotational movement. StudySmarterFigure 1. In rotational movement, objects at different distances (displacement lengths) from the centre cover different distances on their rotational path even when travelling at the same speed and at the same interval Δt = t1-t0. Source: Manuel R. Camacho, StudySmarter.

Rotational kinematics also uses a different set of quantities and a different system of coordinates to make its work easier. While linear kinematics uses a classical 3D cartesian system, rotational kinematics normally uses a cylindrical system or even a spherical one.

Mechanics and Materials. Coordinate systems. Linear and rotational movement. StudySmarterFigure 2. Coordinate systems: linear kinematics is easy to represent using a) the cartesian system. Rotational movement is easier to represent using b) cylindrical or c) spherical coordinate systems. Source: Manuel R. Camacho, StudySmarter.

Dynamics

For dynamics, the displacement or velocity of a body is not important, but rather how it reacts to changes and why. Newton’s laws of motion are foundational for dynamics. We will introduce them very briefly below.

Newton’s first law

An object remains in its same state of motion unless it is disturbed by a force.

Newton’s second law

The rate of change in the momentum (per time) of an object is equal to the force acting on the object.

Newton’s third law

When two bodies exert forces over each other, the forces are equal in magnitude but have the opposite direction.

The combination of concepts of dynamics and Newton’s laws of forces interacting in bodies allows us to understand systems where multiple forces act on a body or where two bodies interact with each other.

Momentum, work, and energy

These three concepts are integral to the study of dynamics.

Momentum

Momentum is the product of the mass of an object and its velocity. When an object accelerates or decelerates, its momentum changes. Momentum is important in the analysis of some interactions where objects exchange energy by impacting each other, as the conservation of momentum applies. One example is an inelastic collision.

In an inelastic collision, the overall momentum of the objects before and after the collisions must be the same.

Energy

This is another important concept in mechanics. Objects can have kinetic and potential energy. In most systems, the rule of energy conservation applies, meaning that the total energy of a system is the same before and after something happened within it.

Work

This is the displacement produced by a force. Any work produced is directly linked to the forces moving the object.

Vectors and scalars

Vectors and scalars are two mathematical concepts widely used in mechanics. They allow us to express quantities that only have a magnitude as ‘scalars’, while quantities that have both a magnitude and a direction are known as ‘vectors’.

Vectors are particularly useful in dynamics, as they make it possible for a system of forces interacting with a body to be represented more easily. The representation uses a line along the path the force is being applied and an arrow to indicate its direction. A classic example of vectors and forces is the case of a body moving up a slope.

A car is being pulled up a slope by a security car. The steepness of the slope is 30 degrees. The force of gravity (red arrow) pulls the car down along the vertical direction.

Mechanics and Materials. Forces. Vectors. StudySmarter Figure 3. Forces acting on a car being pulled up a slope. Source: Manuel R. Camacho, StudySmarter.

The gravitational force (red arrow) can be split up into two components (yellow arrows), one operating in the perpendicular direction to the slope and the other operating along the slope.

The force causes a response from the slope equal in magnitude but opposite in direction (pink arrow). The sum of these forces is zero, leaving as the resulting force pulling the car down the slope. The security car produces a force (blue arrow), pulling the car up the hill.

If the service car’s force is greater than the horizontal component of the gravity , the car moves upwards. If is smaller than , the car rolls down the hill.

The system of forces can be seen in the equations below:

If , the car gets pulled up the slope. If , the car rolls down the slope.

Materials

The study of materials and their mechanical properties is an important aspect of physics. The properties of a material can tell us how much force an object can withstand and how it will react to the forces acting on it. In mechanics, objects are non-deformable. However, in reality, the forces acting on a body deform and affect it.

Bulk properties are characteristics of any material that are the result of the atoms of that material working together as a ‘bulk’. Properties such as elasticity, density, hardness, and conductivity are all bulk properties.

Bulk properties

These arise as part of the internal mechanisms of the atoms that compose an object. Consider elasticity: the reasons why materials are elastic differ. Elasticity in metals is produced by the change in the atomic structure of the material, while in polymers, it is a product of the stretching of the chains that compose the material.

Let’s briefly look at some bulk properties.

Elasticity is defined as the ability of a material to resist deformation after a force is applied to it. The material, in this case, can come back to its original shape or be deformed. Please note that the elasticity of a material has a limit. Any elastic material will deform irreversibly after a certain amount of force is applied.

Hardness is defined as the resistance of a material to being locally deformed, usually demonstrated by making an indentation with a pointy object. An interesting relationship is that sometimes the hardness of a material is inverse to its elasticity. Very often, hard materials are not elastic, and elastic materials are not hard.

Conductivity is defined as the ease with which a material conducts electrical charges. The conductivity is related to the atomic structure of the material.

Young’s modulus

Within the subject of bulk properties, Young’s modulus is an important characteristic that tells us how easily a material will deform under forces that produce compression or tension.

The formula to calculate the modulus is:

Here, σ is the axial stress or the force per unit of length measured in Pascals, while ε is the proportional deformation equal to the length after the force is applied, divided by the original length of the object.

Mechanics and Materials (Physics) - Key takeaways

  • Mechanics is the branch of physics that studies the forces acting on an object and its movements.
  • Mechanics can be divided into dynamics and kinematics. Dynamics studies the displacement, trajectory, velocity, and acceleration of an object. Kinematics studies the forces producing the movement and how the object reacts to them.
  • Newton’s laws describe how a body reacts to forces altering its state of movement.
  • Materials, specifically their properties and responses to forces, are also a subject of study in physics. Important physical properties include elasticity, hardness, conductivity, and density.
  • An important characteristic of a material is its Young’s modulus. This tells us the rate of deformation on a body produced by a force.

Frequently Asked Questions about Mechanics and Materials

There is no one measure to know which material is the most elastic. There is, however, an interesting fact that will contradict your notion of elasticity, which is that steel is more elastic than rubber.


Elasticity is the property of a material to resist deformation and return to its original shape. Steel can resist higher forces without deforming irreversibly than rubber or plastics. The most elastic material, in this case, is the stiffest one. (Although it can still deform a little under very large forces.)

They are those properties of any material that are affected by forces that stretch or compress it, or try to break, cut, or deform it. These mechanical properties arise from the bulk properties of a material, which are themselves the results of the interactions between the material’s constituent atoms.

Dynamics is focused on the study of the forces that affect a body and how it reacts to them. Kinematics, on the other hand, studies the trajectory, velocity, and acceleration of a body without taking into account the forces acting on it.

Rotational kinematics is the study of the movement of an object in a circular motion. The study does not take into account the forces exerted on the body.

Final Mechanics and Materials Quiz

Question

What are materials?

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Materials are the substances that an object consists of.

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Why does water flow so easily?

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The weakness of the water molecules gives water its ability to flow.

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How can the forces that bind atoms together modify an object’s properties?

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Large forces keep the atoms together, thus producing solids, while small forces or a lack of forces allow liquids to flow.

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Do the atoms or molecules of liquids and gases possess a clear structure?

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No, they do not possess a clear structure.



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What is hardness?

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The ability of a material to resist penetration.

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Name the hardest known material.

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Diamonds.

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Are pencil leads and diamonds made of the same element?

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Yes, they are.

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How do diamonds obtain their hardness?

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From the high pressure and heat to which they were exposed while forming.

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Name some extensive properties.

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Mass, volume, length.

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Name some intensive properties.

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Density, temperature, conductivity, malleability.

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What is a bulk property?

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A property that describes how atoms work together in bulk.

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What is density, and what is its unit?.

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Density is the property that defines the amount of mass per unit of volume. Its unit is kg/m^3.

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What is conductivity, and what is its unit?

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Conductivity defines how easily a material conducts electricity. It is measured in Siemens over cubic metres or S/m^3.

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What is elasticity, and what is its unit?

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Elasticity defines how easily a material deforms. It is measured in Pascals.

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How do we measure a material’s properties?

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By conducting mechanical tests to determine each property.

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Which two topics are studied by mechanics?

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Dynamics and kinematics.

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The study of kinematics focuses on the analysis of the displacement, velocity, trajectory, and acceleration of objects in movement. True or false?

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True.

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Dynamics studies the movement and displacement of objects, not considering the forces that act upon them.

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False.

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Rotational dynamics uses cylindrical and spherical systems as coordinate systems. True or false?

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True.

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Which of the following laws help the study of mechanics?

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Newton’s laws.

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Newton’s Laws comprise three laws. True or false?

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True.

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Newton’s third law states that when two objects interact with each other, they exert equal forces with contrary directions. True or false?

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True.

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Vectors have …

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Direction and magnitude.

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What is a scalar quantity?

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Quantities that have magnitude.

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Vectors are particularly useful in mechanics. True or false?

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True.

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What is a bulk property?

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A property that is the result of the atoms composing the material as ‘bulk’.

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Two objects orbiting at the same speed but at different distances around a centre of rotation, cover …

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Different distances during the same time interval.

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Which unit does Young’s modulus use?

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Pascals.

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What is a vector?

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A quantity that has magnitude and direction.

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A vector v is given. The horizontal component of v is vx, while the vertical component of v is vy. The vector v has an inclination angle of a. Which equation helps us determine vx?

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vx = v * cos (a).

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A vector v is given. The horizontal component of v is vx, while the vertical component of v is vy. The vector v has an inclination angle of a. Which equation helps us find vy?

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vy = v * sin (a).

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When determining the resultant vectors by using scale diagrams, how should we connect the vectors?

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Tip-to-tail.

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What is adding two vectors together called?

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Finding their resultant.

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What are the two ways we can add two vectors together?

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Using scale diagrams or trigonometry.

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Which of the following quantities is not a vector?

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Energy.

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When do we need to resolve vectors into components?

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In complex vector problems.

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Into which two components can we resolve a vector?

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Into a vertical and a horizontal component.

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Speed is a vector quantity. True or false?

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False.

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In which conditions can we use the Pythagorean Theorem to find the resultant of two vectors?

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When they are perpendicular to each other.

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Velocity is a vector quantity. True or false?

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True.

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Is force regarded as a vector quantity?

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Yes, it is.

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Under what condition is energy conserved?

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Energy is conserved in a given condition that the system is closed.

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What is Kinetic Energy?

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Kinetic Energy is defined as the Energy possessed by a body by virtue of its state of motion.

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What is Potential Energy?


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Potential Energy is defined as Energy possessed by a body of a definite mass by virtue of its position in the presence of a gravitational field.

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What is Energy Dissipation?


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The loss of energy while energy transfers is known as Energy Dissipation.

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What is Elastic Energy?


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The Energy possessed by a body to retain its original configuration.

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What is Chemical Energy?


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The Energy possessed by a chemical substance.

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What is nuclear energy?


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Energy possessed by the nucleus of an atom.

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What is Tidal Energy?


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Energy possessed by the flowing water.

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Question

Give an example of mechanical energy converted to electrical energy.


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Power generator.

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