KCL Section 2: Force-extension graphs (Materials)

Question 1

State three SI base quantities

Answer 1

meters second kilograms

Question 2

State 2 SI derived units

Answer 2

kgms^-2

kgms^-1

Question 3

Define ‘drag force’

Answer 3

Drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid.

Question 4

________ deformation: the material will return to its original shape when the deforming force is removed
________ deformation: the material will remain deformed when the deforming force is removed

Answer 4

Elastic deformation: the material will return to its original shape when the deforming force is removed
Plastic deformation: the material will remain deformed when the deforming force is removed

Question 5

Can a single material often show both types of deformation, depending on the size of the force applied?

Answer 5

Yes

Question 6

—–FLASHCARD NOT READY YET——-

A=
B=
C=

Answer 6

A: the limit of proportionality
O-A: Hooke’s Law applies
B: the elastic limit
C: the yield point

Question 7

What are the y- and x-axes labelled on a force-extension graph?

Answer 7

y = N
x = m

Question 8

What does an upwards slope represent?

Answer 8

elastic region

Question 9

What does a downwards slope represent?

Answer 9

plastic region

Question 10

What does a linear section of a graph show?

Answer 10

F is proportional to the change in x

Question 11

What does a curved section of a graph show?

Answer 11

F is not proportional to the change in x

Question 12

What’s happening inside the material?

In the elastic region
Beyond the elastic limit (in the plastic region)
Beyond the yield point (still in the plastic region)

Answer 12

What’s happening inside the material?

IN THE ELASTIC REGION: the bonds between atoms increase in length, due to the forces on the material, but revert to their usual length when the force is removed and the atoms return to their equilibrium positions.
BEYOND THE ELASTIC REGION: the arrangement of atoms has changed and the material has undergone permanent (plastic) deformation. It may contract when the force is removed, but not to its original shape.
BEYOND THE YIELD POINT: the atoms move as layers, which slide over each other with no restorative forces. The material will not contract when the force is removed.

Question 13

.

Answer 13

.

Question 14

Explain the meaning of the following terms relating to a copper wire that has been loaded to breaking point:

a) limit of proportionality
b) elastic limit
c) yield point
d) plastic flow.

Answer 14

a) Limit of proportionality is the point where Hooke’s law ceases to be obeyed.
b) elastic limit is the point beyond which the wire will not regain its original shape when the deforming force is removed.
c) Yield point is at the onset of plastic flow.
d) Plastic flow is the region where [be wire deforms plastically. Layers of atoms slide over each other and when the load is removed there will be no change in the length of the wire.

Question 15

What is elastic strain energy and how is it calculated?

Answer 15

Elastic strain energy represents the ability of a material to do work as it returns to its original dimensions.
It is calculated as work done = average force x distance moved
W = FavΔx
For an object obeying Hooke’s Law, this becomes: Eel = ½F∆x
For an object not obeying Hooke’s Law throughout, the area underneath a graph should be calculated.

Question 16

A spring is 0.38 m long. When it is pulled by a force of 2.0 N, it stretches to 0.42 m. What is the spring constant? Assume that the spring behaves elastically.

Answer 16

50Nm^-1

Question 17

A spring is 0.38 m long. When it is pulled by a force of 2.0 N, it stretches to 0.42 m. What is the spring constant? Assume that the spring behaves elastically.

Answer 17

50Nm^-1

Question 18

A spring is 32 cm long. It is stretched by a force of 6.0 N until it is 54 cm long. How much energy is stored in the stretched spring?
Hint: make sure the distance measurements are always In metres!

Answer 18

0.66J

Question 19

Force-extension graphs are drawn for two different wires. How would you determine

i) which wire was stiffer?
ii) which was tougher?

Answer 19

i) Stiffer material will have a steeper gradient.

ii) Tougher material has a greater area under the curve.

Question 20

If the wires were loaded until they snapped, how would you know if either wire was brittle?

Answer 20

The brittle line will show little or no plastic deformation when it breaks.

Question 21

A load of 12 kg causes a wire to extend by 2.5mm. If the wire obeys Hooke’s law

a) calculate the stiffness of the wire
b) calculate the elastic potential energy transferred to the wire.

Answer 21

4. 7 x 10^4 Nm^-1

0. 15J

Question 22

Explain the statement, ‘natural rubber Is a polymer’.

Answer 22

A polymer Is made up of molecules consisting of many atoms (mainly carbon and hydrogen) in long chains.

Question 23

How would you estimate the value of the work done stretching a rubber band from the resulting force-extension graph for the band?

Answer 23

Work done = area under the graph.
This can be estimated by calculating the energy represented by each square and counting the squares, or by drawing angles, rectangles or trapeziums that give an approximate fit of the curve and finding their areas,

Question 24

What is tension?

Answer 24

Tension is a force acting within a material in a direction that would extend the material.

Question 25

What is extension?

Answer 25

Extension is an increase in size of a material sample caused by tension force.

Question 26

What is compression?

Answer 26

Compression is a force acting within a menial in a dire.. that would squash the material. A.. the decrease in aire °fa material sample under a compressive force.

Question 27

What is the limit of proportionality?

Answer 27

The limit of proportionality is the maximum extension (or strain) that an object (or sample) can exhibit which is still proportional to the load (or stress/applied

Question 28

What is a material’s elastic limit?

Answer 28

A material’s elastic limit is the maximum extension or compression that material can undergo and still return to it original dimensions when the force is removed.

Question 29

What is the spring constant?

Answer 29

The spring constant is the Hooke’s law constant of proportionality, k is for a spring under tension.

Question 30

What is hysteresis

Answer 30

For the extension of a material sample, hysteresis is where extension under a certain load will be different depending on it’s history of past loads and extensions.