Chapter 7 #2

Question 1

Section 1: Basics of Deformation

Question 2

What is deformation?

Answer 2

Deformation is the change in shape of a solid body when forces are applied to it, which affects the spacing of its atoms.

Question 3

What is tensile deformation?

Answer 3

Tensile deformation occurs when forces applied along the axis of an object stretch it, making it longer.

Question 4

What is compressive deformation?

Answer 4

Compressive deformation occurs when forces applied along the axis of an object squash it, making it shorter.

Question 5

Define “extension” in the context of a spring.

Answer 5

Extension is the increase in length of a spring when a load is applied.

Question 6

What is the “load”?

Answer 6

The load is the weight or force attached to the spring that causes extension.

Question 7

What characterizes an elastic change?

Answer 7

In an elastic change, a body returns to its original shape and size once the applied load is removed.

Question 8

What characterizes a plastic change?

Answer 8

A plastic change is a permanent deformation where the body does not return to its original length after the load is removed.

Question 9

Section 2: Hooke’s Law and Spring Constants

Question 10

State Hooke’s Law.

Answer 10

Provided the limit of proportionality is not exceeded, the extension of a body is directly proportional to the applied load.

Question 11

What is the mathematical formula for Hooke’s Law?

Answer 11

F = kΔ L, where F is force, k is the spring constant, and Δ L is extension.

Question 12

Define the spring constant (k).

Answer 12

The spring constant is the force per unit extension (k = F/x).

Question 13

What is the unit of the spring constant?

Answer 13

Newton per metre (Nm⁻¹).

Question 14

Define the “limit of proportionality.”

Answer 14

It is the point on a graph after which Hooke’s law is no longer obeyed and extension is no longer proportional to the load.

Question 15

Define the “elastic limit.”

Answer 15

It is the point after which plastic deformation occurs and the material will no longer return to its original shape.

Question 16

Do the limit of proportionality and the elastic limit always occur at the same point?

Answer 16

No, they are two different points and do not necessarily overlap.

Question 17

Section 3: Spring Connections

Question 18

How is the total extension calculated for springs in series?

Answer 18

The total extension is the sum of individual extensions: Total ext. = x_1 + x_2 + x_3 + ….

Question 19

How is the total spring constant handled for springs in series?

Answer 19

It is dealt with like resistors in parallel: 1/k_total = 1/k_1 + 1/k_2 + 1/k_3 + ….

Question 20

How is the total extension calculated for springs in parallel?

Answer 20

Like resistors in parallel: 1/x_total = 1/x_1 + 1/x_2 + … (For N identical springs, extension is x/N).

Question 21

How is the total spring constant handled for springs in parallel?

Answer 21

It is dealt with like resistors in series: k_total = k_1 + k_2 + k_3 + ….

Question 22

Section 4: Strain Energy and Work Done

Question 23

What is strain energy (elastic potential energy)?

Answer 23

It is the energy stored in a body due to its change of shape.

Question 24

What are the two formulas for strain energy (W) for a spring obeying Hooke’s Law?

Answer 24

W = 1/2Fx and W = 1/2kx^2.

Question 25

How do you find strain energy from a load-extension graph?

Answer 25

It is represented by the area under the graph line.

Question 26

If the y-axis is extension and the x-axis is load, where is strain energy found?

Answer 26

It is the area to the left of the graph (between the line and the y-axis).

Question 27

Does elastic potential energy increase during compression?

Answer 27

Yes, it increases whether the object experiences extension or compression.

Question 28

What does the difference between the stretching and recoiling areas on a force-extension graph represent?

Answer 28

It represents the total energy dissipated as heat during the process.

Question 29

Section 5: Motion of a Mass on a Vertical Spring

Question 30

Describe the energy at the starting point (natural length) of a vertical spring.

Answer 30

Extension is 0 (EPE = 0), speed is 0 (KE = 0), and energy is entirely gravitational potential energy (GPE).

Question 31

What occurs at the equilibrium position when the mass is in motion?

Answer 31

The spring force equals the weight of the mass, but the mass overshoots this position because it still has kinetic energy.

Question 32

What is the first maximum extension (x) when a mass is released from a vertical spring's natural length?

Answer 32

The maximum extension is twice the equilibrium extension (x = 2x_e).

Question 33

What is the velocity of the mass at maximum extension?

Answer 33

The velocity is zero as it is at a point of instantaneous rest.

Question 34

Section 6: Stress, Strain, and Young Modulus

Question 35

Define tensile stress.

Answer 35

Tensile stress is the force applied per unit perpendicular cross-sectional area (σ = F/A).

Question 36

What is the unit for stress?

Answer 36

Newtons per metre squared (Nm⁻²) or Pascal (Pa).

Question 37

Define tensile strain.

Answer 37

Tensile strain is the extension per unit original length (ε = Δ L/L).

Question 38

What is the unit for strain?

Answer 38

Strain has no unit because it is a ratio of two lengths.

Question 39

Define the Young modulus (E).

Answer 39

The Young modulus is the ratio of stress to strain (E = stress/strain) provided the limit of proportionality is not exceeded.

Question 40

What is the unit for the Young modulus?

Answer 40

The same as stress: Nm⁻² or Pascal (Pa).

Question 41

Is the Young modulus dependent on the object's dimensions?

Answer 41

No, it is a characteristic property of the material itself; same material means same Young modulus.

Question 42

How does the Young modulus relate to stiffness?

Answer 42

It is proportional to the material's spring constant or stiffness.