Material, Hooks Law and Youngs Modulus

Question 1

What is density? What is its equation?

Answer 1

Density is mass per unit volume of an object. Measured in kgm-3 or gcm-3

p = m/v

Density = mass/volume

Question 2

A slab has a mass of 73 kg and dimensions 40 mm × 500 mm × 850 mm(millimetre).
Calculate the density, in kg m^-3 of the material from which the flooring slab is made.

Answer 2

4300kgm-3

Question 3

What is the relationship between density in gas, liquid and solid states?

Answer 3

Solid has the highest desity with gas being the lowest. Liquids fall in the middle.

Question 4

What is the difference between dense material and less dense materials

Answer 4

Dense materials cannot be easily compressed while less dense material such as cotton can.

Question 5

What is the SI unit of Density?

Answer 5

Kgm-3

Question 6

You’re preparing to travel to Mars. You’ve been given a 1.34-meter-long cubical box to pack. Your box’s final density must be no more than 5 kg/m^3 due to fuel and space constraints. What is the maximum weight you can carry?

Answer 6

12kg

Question 7

What is deformation? What causes it?

Answer 7

The changing of a shape of an object. Whenever force is applied to an object, the object is deformed.

Question 8

What are elastic deformations?

Answer 8

Once the altering force is removed from the deformed object, the object will spring back to its original form. Most deformations are elastic.

Question 9

What is plastic deformation?

Answer 9

Once the altering force of an object is removed from the deformed object, the object remains permanently deformed.

Question 10

What are tension forces?

Answer 10

Equal and opposite forces which cause extension in an object.

Question 11

What are compressive forces?

Answer 11

Equal and oppsite forces which cause compression of an object.

Question 12

What is hooke’s law?

Answer 12

Hooke’s Law is a principle in physics which states that the force F needed to extend or compress a spring by some distance x is proportional to that distance. Mathematically this is shown as F directly proportional to x or

F=kx

Where k is force contact measured in Nm-1
f is force producing extension
x is extension

Question 13

What does Hooke’s law explain?

Answer 13

The relationship between force and extension. The stiffness of a spring, wires under tension or compression, atom behaviour in solids

Question 14

What type of deformations does hooke’s law apply to?

Answer 14

Only elastic deformations

Question 15

What is stress?

Answer 15

Stress refers to a body’s resistance to deformation. It is the restoring force per unit area of a body. Force applied per unit area.

=F/A

measured in Nm-2
Unit is Pascal
Scalar quantity

Question 16

What is a restoring force?

Answer 16

A force that acts to bring a body to its equilibrium position. It is equal and opposite to the deforming force applied on the body.

Question 17

What is the gradient of a force-extension graph?

Answer 17

Force constant k, which can be used to describe the stiffness of a spring

Question 18

What is strain?

Answer 18

The proportion of change in the configuration (shape, length or volume) to the original configuration of the body.

Strain is defined as the amount of deformation experienced by the body in the direction of force applied divided by original dimensions of the body.

Has no unit as the unit cancels out but is quotes in percent

=dx/x

Extension per unit length of a solid object.

Question 19

Does stress cause strain?

Answer 19

How much strain is caused depends on the stiffness of the object.
* With a stiff material like iron a large stress will only produce a small strain.
* But with a soft material like rubber a small stress is enough to produce a large strain

Question 20

What is the mathematical relationship between stess and strain?

Answer 20

Stress = Constant x strain

Stess is directly proportional to strain

Question 21

When does Hooke’s Law fail?

Answer 21

It fails to describe the behaviour of materials beyond the elastic limit

• It assumes materials will return to their original shape and size once external force is removed

-When a material undergoes plastic deformation by being subject to high force or extreme condition it does not follow Hookes law

-When a material experiences permanent deformation or brakes the relationship between stress and strain is no longer linear and cannot be accurately described by hookes law.

Question 22

What is simple harmonic motion?

Answer 22

A special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It is the oscillatory swing motion of objects commonly found in springs.

Question 23

What is the equation for spring force?

Answer 23

Spring Force = -(Spring Constant) x (Displacement from equilibrium)

F=-kx

The negative sign shows the reaction force is acting in the opposite direction.

Question 24

What is the dimensional formula for spring constant?

Answer 24

K = -F/X
F = MLT^-2
X= L

Therefore K = -F/X = MT^-2

Question 25

What is potential energy?

Answer 25

Potential energy is the energy an object has by feature of its position above the surface of the earth. It is the stored energy of position possessed by an object.

Question 26

What is spring potential energy?

Answer 26

The energy stored in a compressible or stretchable object is referred to as spring potential energy. It is also called Elastic potential energy.

It is equal to the force multiplied by distance travelled.

Question 27

What is the equation to calculate Elastic Potential Energy?

Answer 27

Elastic Potential Energy = 0.5 x spring constant x extension^2

Ee = 1/2ke^2

elastic potential energy (Ee) is measured in joules (J)
spring constant (k) is measured in newtons per metre (N/m)
extension (e), referring to the increase in length, is measured in metres (m)

Question 28

A spring has a spring constant, (k), of 3 N/m. It is stretched until it is extended by 50 cm. Calculate the elastic potential energy stored by the spring, assuming it is not stretched beyond the limit of proportionality.
First convert centimetres to metres:
50 cm = 50 ÷ 100 = 0.5 m
Then calculate using the values in the question:

Answer 28

Ee = 0.375

Question 29

What are the limitations of Hooke’s Law?

Answer 29

• It is only applicable under the elastic limit of any material, which means that material must be perfectly elastic in order to obey Hooke’s Law

-Hooke’s Law does not apply beyond the elastic limit

Question 30

What are the applications of Hooke’s Law?

Answer 30

• most commonly applied in springs due to elasticity
• engineering and medical science
• lungs, the spring beds, jumping boards and automobile suspension systems
• Fundamental principle underlying the manometer (measure pressure) and spring scale.
  -Basis of seismology (earthquakes) and molecular mechanics

Question 31

What are the disadvantages of Hooke’s Law?

Answer 31

Hooke’s Law is only applicable in the elastic region after that it fails

Hooke’s law produces accurate results only for solid bodies with small force and deformations

Hooke’s Law is not a general rule

Question 32

What is Young’s Modulus?

Answer 32

The property of the material which allows it to resist the change in its length according to stress applied to it. It is also called modulus of elasticity. it is a mathematical constant which defines the elastic characteristics of a solid that is subjected to tension or compression in only one direction.

It is a measure of a materials capacity to tolerate changes in length when subject to longitudinal tension or compression.

It is the measure of the deformation in the length of the solid such as rods or wires when the stress is applied along the x-axis

The ability for an object to resist deformation

Represented using the letters E or Y.

Question 33

What does Young’s Modulus explain?

Answer 33

It provides a relationship between stress and strain in any object

When a certain load is added to a rigid material, it deforms.

When the weight is withdrawn from an elastic material, the body returns to its original form, this property is called elasticity.

Elastic bodies have steady linear Young’s modulus.

Young’s modulus of steel is 2x10^11 Nm^-2

Question 34

Briefly describe stress and strain.

Answer 34

Stress is the force applied per unit length of the object

Strain is the change in shape or length of the object with respect to its original length

Question 35

What is the elastic property of an object?

Answer 35

When the force is applied to an object it changes its shape and as soon as the force is removed from the object it regains its original position

Question 36

What is the relationship between stiffness and Young’s Modulus?

Answer 36

•A solid with a low Young’s Modulus value is Elastic.
•A solid with a high Young’s Modulus value is Inelastic or stiff.

Question 37

How can Young’s modulus be calculated?

Answer 37

Mathematically Young’s modulus is the ratio of stress applied to the material and the strain corresponding to the applied stress in the material.

Young’s Modulus = Stress/ Strain

Measured in Pascal or Nm-2

Y = σ / ϵ where
•Y is Young’s Modulus of the material
•σ is the stress applied to the material
•ϵ is the strain corresponding to the applied stress

Question 38

What is the dimensional Formula for Young’s Modulus?

Answer 38

Units of Young’s Modulus
•SI unit for Young’s modulus is Pascal (Pa).
Pressure: Force/Area

•Dimensional formula for Young’s Modulus is [ML^-1T^-2].

•The values are most often expressed in terms of Megapascal (MPa), Newtons per square millimeter (N/mm2), Gigapascals (GPa), or kilonewtons per square millimeter (kN/mm2).

Question 39

What is used to explain the deformation in length of a material when force is applied?

Answer 39

Young’s Modulus

Question 40

If an object has a higher Young’s modulus what can we say?

Answer 40

We can say it is more elastic than the object compared with.

The lower value of Young’s Modulus in materials tells us that this material is not fit for dealing with large stress and applying large stress will change the shape of the object completely

Question 41

How can Young’s modulus be calculated on a stress to strain graph?

Answer 41

The figure discussed above it is the stress-strain curve and the initial slope of the first segment of the curve is Young’s modulus.

•If continuously increasing stress is applied to the material it reaches a point when its elasticity gets disappeared and any further stress can create a more significant strain. This point is called the elastic limit of the material.

•Further increasing the stress make the material such that it start to deform without even applying stress the point where this started to happen is called the plastic limit.

Question 42

What factors do the Young Modulus off a Material depend on?

Answer 42

•Larger the value of Young’s modulus of the material, the larger the value of the force required to change of length of the material.

•Young’s modulus of an object depends upon the nature of the material of the object.

•Young’s modulus of an object does not depend upon the dimensions (i.e., length, breadth, area, etc) of the object.

•Young’s modulus of a substance decreases with an increase in temperature.

•Young’s modulus of elasticity of a perfectly inflexible body is infinite

Question 43

Explain the mathematical interpretation of Young’s Modulus

Answer 43

Consider a wire of radius r and length L. Let a force F be applied on the wire along its length i.e., normal to the surface of the wire as shown in the figure. If △L is the change in length of the wire, then Tensile stress (σ = F/A), where A is the area of the cross-section of the wire and the Longitudinal strain (ϵ = △L/L).

Therefore, Young’s Modulus for this case is given by:
•Y = (F/A) / (△L/L)
• = (F × L) / (A × △L)
•If the extension is produced by the load of mass m, then Force, F is mg, where m is the mass and g is the gravitational acceleration.
•And the area of the cross-section of the wire, A is πr^2 where r is the radius of the wire.
•Therefore, the above expression can be written as:
•Y = (m × g × L) / (πr^2 × △L)

Question 44

Why can steel be said to be more elastic that a rubber band?

Answer 44

elasticity (Young’s Modulus) means how stiff a material is (i.e. how much it can resist plastic deformation). The more the value of young’s modulus, more force is required to deform it. Hence a material with higher young’s modulus is more elastic than a material with lower young’s modulus. (i.e steel is more elastic than rubber).

Question 45

What is the definition of the Spring Constant?

Answer 45

When a spring is stretched, the force exerted is proportional to the increase in length from the equilibrium length, according to Hooke’s Law. The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant. F denotes the force, and x denotes the change in spring length.

Question 46

How Does the Length Affect the Spring Constant?

Answer 46

Assume there is a 6 cm spring with a spring constant k. What happens if the spring is divided into two equal-sized pieces? One of these shorter springs will have a new spring constant of 2k. In general, assuming a specific material spring and thickness, the spring constant of a spring is inversely proportional to the length of the spring.

Question 47

What is Young’s modulus for a perfectly rigid body?

Answer 47

The Young’s modulus for a material is,

Y=(F/A) / (△L/L)

Here, △L = 0 for rigid body. Hence, Young’s Modulus is infinite.

Question 48

Young’s Modulus of steel is much more than that of rubber. If the longitudinal strain is the same which one will have greater tensile stress?

Answer 48

Since the Tensile stress of material is equal to the product of Young’s modulus (Y) and the longitudinal strain. As steel have larger Young’s modulus therefore have more tensile strain.

Question 49

What do you mean by Modulus of Rigidity?

Answer 49

Modulus of Rigidity is defined as the ratio of shearing stress (tangential stress) and shearing strain (tangential strain). It is denoted using the letter η.