Materials 3.4

Question 1

Tensile forces

Answer 1

Forces that produces extension and act away from the centre of the spring in both directions

Question 2

Compressive forces

Answer 2

Forces that shorten/compressed an object and act towards the centre of the spring in both directions.

Question 3

Hooke’s Law

Answer 3

Hooke’s Law states for a material within its elastic limit, the force applied is directly proportional to the extension of the material.

Question 4

The gradient of a force-extension graph is…

Answer 4

the force constant k, representing the stiffness of a spring.

Question 5

the area under a straight line force-extension graph represents…

Answer 5

the total work done on the spring by a force (ΔF) over a displacement (Δx), which is transferred into elastic potential energy within the spring. This energy is fully recovarable because of the elastic behaviour of the spring.

Question 6

Derive the elastic potential energy formula

Answer 6

Area of graph = 1⁄2 Fx
F=kx
E = 1⁄2Fx
E=1⁄2kx²

Question 7

For a metal wire, a force-extension loading graph will be…

Answer 7

parallel for forces greater than the elastic limit with its unloading counterpart, but identical up until for forces less than the elastic limit. And the area between the 2 lines is the work done in permanenlty deform the wire.

Question 8

For a rubber band, the force-extension graph does not obey…

Answer 8

Hooke’s Law, as the loading and unloading graph are both curved and different. The loop formed by the curves is called hysteresis loop

Question 9

What does the hysteresis loop for a rubber band suggest that happens in regards of work done/energy transferred

Answer 9

More work is done when stretching the rubber band (loading) than is done when extension decreases. Thus, the resulting energy lost is dissipated in the form of thermal energy. The area in the hysteresis loop represents this energy lost/difference

Question 10

For a polyethene, a force-extension graph will be..

Answer 10

made up of a loading curved graph and a straight line graph, showing plastic deformation has occured. Again, like withnrubber bands, more work is done when stretching polyethene than when extension decreases, and thus, the resulting energy is disspated in the form of thermal energy or used to permanetly changed the position of the polyethene’s particles.

Question 11

Under tensile forces, materials will have 2 of the following behaviours…

Answer 11

Tensile strain
Tensile stress

Question 12

Define tensile stress

Answer 12

The force applied per unit cross-sectional area of the wire, measured in Pa.
σ = F/A

Question 13

Define tensile strain

Answer 13

The fractional change in the original length of the wire

ɛ = X/L

Question 14

Define the breaking strenght of a material

Answer 14

The stres value at the point of fracture of a material

Question 15

Define the ultimate tensile strenght (UTS)

Answer 15

The maximum stress a material can withsatnd when it is being stretched before it breaks.

Question 16

Within the limit of proportionality, stress is directly proportional to…

Answer 16

strain. Hence, the ratio between stress and strain for a particular material is constant and known as the young modulus E, measured in Pa.
young modulus E = tensile stress/ tensile strain

E = σ/ℇ

Question 17

The gradient of the stress-strain graph represents…

Answer 17

the young modulus E of a material

σ = Eℇ === y = mx+c

Question 18

You can compare the stiffness of a material by using its…

Answer 18

young modulus in respect to others’

Question 19

What do you need to shape a spring or wire?

Answer 19

To shape a spring or wire, a pair of equal and opposite forces are required

Question 20

What is k, from the relationship F ∝ x?

Answer 20

K is the force constant of the material and a measure of stiffness.

The force constant is measured in Nm-1, and can only be used within the elastic limit of the material.