Deforming Physics! Trivia Quiz

Answer: Strain

The full equation is; 'strain = extension / original length'. By deriving units it is found that strain doesn't actually have a unit. By dimensional analysis, extension is measured in metres and length is also measured in the SI unit, metres. This is saying it is (m / m = m^1 x m^-1 = m^0 = 1). Though, sometimes for clarification, strain is sometimes given a percentage value.
So, you can gather from the equation that strain is the quantification of how a force has extended (or compressed) the length of an object.

Answer: Hooke

Hooke's law states that the magnitude of the extension increases proportionally to an increase in the load. This law can be notated in equation form as; 'F = kx', where 'F' stands for force (load), 'x' for extension and 'k' is a constant value.
If this formula is changed so that the subject is k, you will end up with the following; 'k = F / x'. This is known as the spring constant, or, sometimes the spring's stiffness.
Just as an editorial note, the letters used in equations are generally interchangeable and, in this instance, (x) for extension can be substituted with an (e) to represent the same thing.

Answer: Straight

The two key words in this question are 'proportional' and 'initially'. Proportionality will, in this example, mean that as the force applied increases, the extension of the object will also increase in line with the increase of force. Therefore, this will be represented on a graph as a straight line. (This is with a graph of equal increments of course)!
The second keyword is 'initially', this is due to the fact that every material has a certain limit, after which, this proportionality is discontinued. The line on the graph will then begin to curve.

Answer: Rubber

Rubber is just one of many polymeric substances that doesn't follow the same trend proposed by Hooke. The reason for this is that rubber does not have an elastic limit, it remains elastic until it reaches breaking point.
Glass is a material that follows Hooke's law until breaking point. This means that it doesn't have an elastic limit, it just changes from proportionality to breakage. Copper however, follows the traditional trend of most metals and springs in that it has both an elastic limit and a breaking point. The elastic limit is the point at which Hooke's law is no longer followed. When this point is passed, the material in question will not return to its original shape and size when the force applied to the object is removed.
Just as a quick note, the limit of proportionality and the elastic limit are often used interchangeably because the values for each phenomenon are very similar.

Answer: Stress

Stress is one of two factors which contribute to ascertaining the stiffness of an object of a given material. If a force (load) is applied to an object, the material will be put under stress. The stress can be calculated once a divisor is found. This divisor comes in the form of the cross-sectional area of the object. 'Stress = load / cross-sectional area', is quite long to write out in full, so, when a physicist or architect is attempting to work out stress it is shortened to,'stress = force / area'.

Answer: Sigma

The lower case of the Greek letter sigma is used to denote stress. Other scientific and mathematical uses of this lower case sigma include the denotation of electrical conductivity, nuclear cross-section and standard deviation.

Answer: Young's Modulus

The Young's modulus of an object, named after British scientist Thomas Young, is the stress of an object divided by the strain of the same object. 'Young's modulus = stress / strain'. The general rule is that the greater the Young's modulus the stiffer the material or object.

When put in to practice, this means that the material with the greater Young's modulus will be stiffer and therefore, will stretch less when a given force is applied.

Answer: Pascal (Pa)

The pascal is used to denote both stress and pressure as well as being the unit for Young's modulus. The unit is named after the French physicist and mathematician Blaise Pascal who is recognised for his contributions to the quantification of air pressure and the barometer.

Interestingly, he also had an interest in philosophy and was responsible for devising what is now known as Pascal's wager. This wager or gambit is the theory on the possibilities of belief in God. He states that it is best to believe in God, as, the consequences of not believing in His existence when He does indeed exist is far worse than believing in a figment of societal imagination.

Answer: False

This is all dependent on the modulus proposed by Young. The Young's modulus of steel is roughly 200 GPa (gigapascals) whilst the modulus of copper is generally less at roughly 110 GPa. These are approximations, however, many experiments have results that nucleate around these figures.

Therefore, as the Young's modulus quantifies the stiffness of a material, it is possible to find out which of the two metals stretches the furthest. As stiffness is the ability to resist stretching when a force is applied, it has been ascertained that the higher the Young's modulus, the stiffer the material.

This will conclude, ergo, that as steel has the higher modulus, it is going to be stiffer and will therefore stretch less than copper for a given force.

Answer: Giga

By the rules of indices, the result of the equation would be 10^6 x 10^3 = 10^9. Any unit, in this case arbitrary, that is multiplied by ten raised to the power nine uses the prefix giga. Others include; kilo = 10^3, tera = 10^12, peta = 10^15. From the very large we can go quite the opposite to the microscopic level and smaller. A good example is nano which is 10^-9.
This is relevant to the deformation of solids as this sort of conversion is necessary to change, for example, pascals to gigapascals to megapascals to even nanopascals!

I hope you have enjoyed this quiz and I hope you didn't have to "strain" too much in order to get the answers! Yes I am sighing at how terrible that was as well! Thanks for playing.