SI units

What does the SI unit refer to?

SI (Le système international d'unités) is founded upon seven fundamental or base units, including mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol). and luminous intensity (cd).

The base units each have a unique definition agreed at world conventions.

a. i. Explain what is meant by a base unit. 

    ii Give four examples of base units. 

b. State what is meant by a derived unit.

a. i. A base unit is one of a set of fundamental units in a system of measurement

    ii. mass (kg), length (m), time (s), current (A)

b. Derived units consist of some combination of the base units. The base units may be multiplied together or divided by one another, but never added or subtracted. For instance, the unit of frequency that is hertz (Hz) will have derived unit of `s^(-1)` or the moment of a force is measured in newton metre (`N.m`) or `kg.m^2.s^(-2)`.

Express the unit of following physical quantities in terms of SI base units:

i work done,

ii the moment of a force.

i.  Work done is defined as the product of force and displacement. We know that The base unit of force is Newton, which can be expressed as: `kg.m.s^(-2)` and the base unit of displacement is meters, which is denoted as `m`. Hence, the base unit of work done is `(kg.m.s^(-2)).m=kg.m^2.s^(-2)`.

ii. The moment of a force (torque) is defined as the product of the force and the distance from the pivot point, i.e., `"moment of force" = "force" xx frac{"perpendicular distance"}{"lever arm"}`. Same as work done, the base unit of the moment of a force is `kg.m^2.s^(-2)`

The volume V of liquid that flows through a pipe in time t is given by the equation 

`V/t = (piPr^4)/(8Cl)`

where:

P is the pressure difference between the ends of the pipe of radius r and length l. The constant C depends on the frictional effects of the liquid.

Determine the base units of C.

Rearrange the given equation to solve for C:

`C = (piPr^4t)/(8Vl)` (1)

The base units of variables in formula

Volume (V) has units of `m^3` (cubic meters) 

Time (t) has units of `s` (seconds)

Pressure (P) has units of `kg.m^(-1).s^-2` (Pascals) 

Radius (r) has units of `m` (meters) 

Length (l) has units of `m` (meters) 

Substitute everything into equation (1), we will have

`C = (pi.kg.m^(-1).s^(-2).m^4.s)/(8.m^3.m)`

Simplify everything to determine the base unit of C:

`C = kg.m^(-1).s^(-1)`

i. Define pressure
ii. Show that the SI base units of pressure are `kg.m^(-1).s^(-2)`

i. Pressure is defined as force per unit area

ii. The SI unit of pressure is Pascal (Pa), which is defined as `1 "Pascal" = 1 Nm^(-2)`

we have the formula of pressure is `P=F/A`

The SI unit of force is Newton (N), which is defined as `1N=1kg.m.s^(-2)`

The SI unit of area is square meters (`m^2`)

Thus, the combination of everything, the pressure is expressed as 

`P=F/A=N/(m^2)=(kg.m.s^(-2))/m^2=kg.m^(-1).s^(-2)`

Gas flows through the narrow end (nozzle) of a pipe. Under certain conditions, the mass m of gas that flows through the nozzle in a short time t is given by

`m/t = kC sqrt(rhoP)`

where 

`k` is a constant with no units, 

`C` is a quantity that depends on the nozzle size, 

`rho` is the density of the gas arriving at the nozzle, 

`P` is the pressure of the gas arriving at the nozzle.

Determine the base units of C.

We have: `m/t = kC sqrt(rhoP)`

Rearrange this equation based on C:

`C= m/(kt sqrt(rhoP))`

The units of these variables in this equation

`m` represents mass, which has units of `kg`.

`t` represents time, which has units of `s` (seconds)
represents density, which has units of `kg.m^(-3)`. 

`P` represents pressure, which has units of `Pa` (Pascal) or `N.m^(-2)`. 

`k` is a constant with no units.

Thus,

`C=(kg)/("(dimensionless)".s.sqrt(kg.m^(-3).kg.m^(-1).s^(-2))`

Simplify everything to identify the base units of C

`C=1/(m^(-2))`

Therefore, the base units of C is `m^2`.

What is the symbol for the SI base unit of temperature?

A. C

B. K

C. `"^o`C

D. `"^o`K

The answer is B. The K doesn’t have degrees

Which list shows increasing lengths from beginning to end?

A. 1 cm - 1 nm - 1 mm - 1 `mu`m

B. 1 `mu`m - 1 mm - 1 nm - 1 cm

C. 1 nm - 1 `mu`m - 1 mm - 1 cm

D. 1 mm - 1 cm - 1 `mu`m - 1 nm

The answer is C.

Each quantity has just one unit and this unit can have multiples and sub-multiples to cater for larger or smaller values. The unit is given a prefix to denote the multiple or sub-multiple.

Which of the following is an SI base unit?

A. ampere 

B. coulomb

C. newton

D. joule

The answer is A.

It is noticed that SI is founded upon seven fundamental or base units.

Which of the following is not a SI base quantity?

A. current 

B. energy 

C. mass 

D. temperature

The answer is B.

It is noticed that SI is founded upon seven fundamental or base units including mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol). and luminous intensity (cd). Thus, energy doesn’t belong to 7 base units.