Hooke’s Law

Hooke’s law is basically a rule that shows the relationship between the Force of a spring and the extension of a spring. All springs have a spring constant (measure in Newtons per Metre or N/M) which tells us how many Newtons (or how much force) is needed to extend that spring ( or whatever material it is) by 1 Metre. So a spring with a spring constant of 10N/M will extend by 1 metre for every 10 Newtons of force. Remember that the extension of a spring is not the total final length of the stretched spring, but how many cm/m it has stretched by.

This relationship is shown with a formula of F=kx where F = force applied (Newtons), K = Spring Constant (N/m), and x = the extension of the spring (m or cm normally)

F=kx

or rearrange to get

k=F/x           or           x=F/k

 

In an exam question if they ask you to calculate the spring constant of a spring, they will give you a scenario for example:

Spring y is measured to be 2cm. When 2N is added the final measured length is 10cm. What is the spring constant?

The extension is the final length minus the normal un-stretched length. So here x = 10 cm – 2 cm = 8cm = x.  Using k=F/x   k = 2N/8cm = 1/4 = 0.25N/cm (spring constant)

The bigger the spring constant (k), the stiffer the spring. This is because a bigger spring constant requires more Newtons/force to stretch the spring by the same amount (1 metre or centimetre).Therefore sometimes the spring constant can be referred to by the stiffness of the spring.

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Standard/Base Units and Conversions

For many subjects you should know base quantity (measurement types) and their base/international units (the base units the measurements are measured in internationally). These are shown below:

  • Length  – Metre (m)
  • Mass – Kilogram(Kg)
  • Time – Seconds (s)
  • Electric Current – Amperes/Amps (A)
  • Temperature – Kelvin (K)
  • Amount of substance – Moles (mol)

Make sure you learn these.

Prefixes:

For super large or super small numbers we also use prefixes. For example, one thousand grams is called a kilogram. The prefix here is kilo which is a multiplying factor of a thousand. A kilo is abbreviated to the letter k. For many courses you must learn the following prefixes off by heart. You should also know what each prefix abbreviation stands for. Below shows each prefix name – the abbreviation – and the multiplying factor.

  • Femto =  f  =  10^-15
  • Pico  =  p  = 10^-12
  • Nano =  n  =  10^-9
  • Micro = μ  =  10^-6
  • milli  =  m  =  10^-3
  • Kilo  =  k  = 10^3
  • Mega =  M  = 10^6
  • Giga  =  G  =  10^9
  • Tera  =  T  = 10^12

Notice that some of the abbreviations have Lower and some Upper case- Do not confuse the two.

An example of using these prefixes:

3.9nA = 3.9 nano Amps = 3.9 x 10^-9 Amps

 

prefix-table

Standard Forms

For many subjects you will need to convert measurements to other forms. One main form is standard form.

This is normally asked for you to do when a really large or really small number is too difficult to write out fully.

Converting to standard form:

The general form of standard form is A × 10 n . You must take the first few digits of the number and write it as a decimal of a number smaller than 10 but larger than 1. Then write a (x 10) number next to it and have the power of the 10 as many times as it needs to increase/decrease by digits.

Example : Write 26 000 000 in standard index form.

Solution:

26 000 000 = 2.6 × 10 000 000

This can be rewritten as:

2.6 × 10 × 10 × 10 × 10 × 10 × 10 × 10

= 2.6 × 10 7

Another example: 0.000547 in standard form

= 5.47 × 0.0001

= 5.47 × 10 -4

To convert a standard form number into its real/long number simply do the reverse

Adding/subtracting standard form numbers:

You must convert the number into the ordinary number, then do the calculations, then reconvert back into standard form. (Or if you really like standard form just make sure each number is to the same power of 10 then you do the maths!)

Example:

4.5 × 104 + 6.45 × 105

= 45,000 + 645,000

= 690,000

= 6.9 × 105

Multiplying/dividing standard form numbers:

Now you just do what you normally do with each of the numbers. You must remember the indices rules that:

  • To multiply powers you add, eg, 105 × 103 = 108
  • To divide powers you subtract, eg, 105 ÷ 103 = 102

 

E.g.:   Simplify (2 × 103) × (3 × 106)

Multiply 2 by 3 and add the powers of 10:

2 x 3 = 6

103 + 106 = 109

(2 × 103) × (3 × 106) = 6 × 109

 

 

Try this next one and write your answer in the comments:

Simplify (36 × 105) ÷ (6 × 103)