LECTURE 2: SCIENTIFIC UNIT AND MEASUREMENT
BIOPHYSICS MLB 108
ISAAC KWESI ACQUAH (MPHIL)
ACCRA TECHNICAL UNIVERSITY
DEPARTMENT OF MEDICAL LABORATORY
TECHNOLOGY
SCIENTIFIC UNIT AND MEASUREMENT
If you want to know biophysics, then you need to know
that many words in everyday speech come from physics.
In physics though, these words have specific meanings
that are blurred in everyday speech. For example, people
have a tendency to interchange the words mass and
weight to mean the same thing, but they’re very different
things in physics.
This lecture provides an overview to the language of
biophysics, including how your everyday words fit in the
language.
This lecture also explains the shorthand notation
(mathematics) of biophysics, dealing specifically with the
physics concepts that apply to all areas of biophysics.
SCIENTIFIC UNIT AND MEASUREMENT
Physics is an experimental science and experiments
require measurement of physical quantities.
Measuring a physical quantity involves comparing the
quantity with a reference standard called the unit of the
quantity.
The Système International (SI) unit is a unit of
measurement that is understood and accepted by people
all over the world.
There are two types of units.
Base unit
Derived unit
SCIENTIFIC UNIT AND MEASUREMENT
BASE: these are the fundamental units from which all
derived unit can be obtained. There are basically seven
basic units.
OUANTITY
SI UNIT
SYMBOL
Length
Meter
m
Mass
Kilogram
kg
Time
Second
s
Electric current
Ampere
A
Temperature
Kelvin
K
Luminous intensity
Candela
cd
Amount of substance
mole
mol
SCIENTIFIC UNIT AND MEASUREMENT
DERIVED UNIT: these are unit that are formed by the
combination of two or more base unit.
QUANTITY
SI UNIT
SYMBOL
DERIVED UNIT
Force
Newton
N
kgm𝑠 −2
Work and energy
Joule
J
kg𝑚2 𝑠 −2
Power
Watt
W
kg𝑚2 𝑠 −3
Quantity of electricity Coulomb
C
As
Electric potential
Volt
V
kg𝑚2 𝑠 −3 𝐴−1
Electric resistance
Ohm
Ω
kg𝑚2 𝑠 −3 𝐴−2
SCIENTIFIC UNIT AND MEASUREMENT
DIMENSION
Dimensional equation is an equation which expresses a
physical quantity in terms of its dimension.
In mechanics, virtually all quantities can be expressed in
terms of mass, length and time.
The dimension of a quantity is an algebraic symbol
assigned to the individual quantity.
QUANTITY
DIMENSION
Mass(kg)
M
Length(m)
L
Time (s)
T
SCIENTIFIC UNIT AND MEASUREMENT
SCIENTIFIC UNIT AND MEASUREMENT
USES OF DIMENSIONS
Find the unit of quantities.
Derive an equation between quantities
Check the validity of equation
Conversion from one system of unit to another.
SCIENTIFIC UNIT AND MEASUREMENT
PREFIX IN MEASUREMENT
SCIENTIFIC UNIT AND MEASUREMENT
PREFIX IN MEASUREMENT
Examples: convert all in meters (m)
𝑺𝒐𝒍𝒖𝒕𝒊𝒐𝒏
1. 5km
1. 5km = 5 × 103 𝑚
2. 7mm
2. 7𝑚𝑚 = 7 × 10−3 𝑚
3. 20pm
3. 20𝑝𝑚 = 20 × 10−12 𝑚
4. 16nm
4. 16𝑛𝑚 = 16 × 10−9 𝑚
5. 12hm
5. 12ℎ𝑚 = 12 × 102 𝑚
6. 49am
6. 49𝑝𝑚 = 49 × 10−18 𝑚
SCIENTIFIC UNIT AND MEASUREMENT
SCALARS, VECTORS, AND THEIR PROPERTIES
Scalars and vectors are very important in biophysics
because most physical quantity in biophysics is either a
scalar or a vector.
Scalar: A scalar is a quantity with only magnitude, but has
no direction.
An example is the temperature in a room. The temperature
has a value of 68 degrees Fahrenheit (20 degrees Celsius),
which is the magnitude. No matter whether you’re facing
north or south or standing or lying down, the temperature is
the same value.
Examples of scalar quantities are mass, length, time,
temperature, volume density
SCIENTIFIC UNIT AND MEASUREMENT
Vector: A vector is a quantity with both magnitude and
direction.
For vectors, the direction is as important as the
magnitude, even though some books give the impression
that the direction isn’t as important.
Examples of vector quantities are displacement, velocity,
acceleration, momentum, force etc.
SCIENTIFIC UNIT AND MEASUREMENT
REPRESENTATION OF A VECTOR
Symbolically it is represented as AB
SCIENTIFIC UNIT AND MEASUREMENT
VECTOR APPLICATION
ADDITION: When two (2) vectors point in the SAME
direction, simply add them together.
When vectors are added together they should be drawn
head to tail to determine the resultant or sum vector.
The resultant goes from tail of A to head of B.
 Example: A man walks 46.5 m east, then another 20 m
east, Calculate his displacement relative to where he
started.
+
46.5 m, E
66.5 m, E
20 m, E
SCIENTIFIC UNIT AND MEASUREMENT
SUBTRACTION: When two (2) vectors point in the opposite
direction, simply subtract them.
Example: A man walks 46.5 m east, then another 20 m
west. Calculate his displacement relative to where he
started.
46.5 m, E
-
20 m, W
26.5 m, E
SCIENTIFIC UNIT AND MEASUREMENT
when two (2) vectors are perpendicular to each other, you
must use the Pythagorean theorem.
A man travels 120 km east then 160 km north.
Calculate his resultant displacement.
FINISH
c a b
2
2
2
 c a b
c  resultant 
2
2
the hypotenuse is
called the RESULTANT
120  160 
2
160 km, N
2
VERTICAL
COMPONENT
c  200km
120 km, E
S T A R T
HORIZONTAL COMPONENT
SCIENTIFIC UNIT AND MEASUREMENT
A boat moves with a velocity of 15 m/s, N in a river which
flows with a velocity of 8.0 m/s, west. Calculate the boat's
resultant velocity with respect to due north.
8.0 m/s, W
15 m/s, N
Rv

Rv  8  15  17 m / s
2
2
8
Tan 
 0.5333
15
1

  Tan (0.5333)  28.1
SCIENTIFIC UNIT AND MEASUREMENT
ASSIGNMENT 1
1. If a cyclist is traveling along a road due east at 12km/h
and wind is blowing from south-west at 5km/h. find the
velocity of the wind relative to the cyclist.
2. A river is 120m wide and the water flows at 2.5km/h. a
ferryman who can scull in still water at 3km/h wishes to
cross the river in a direction at right angle to its bank.
Find either by accurate scale drawing or by calculation
a. the direction in which he must steer the boat.
b. the time it takes him to cross.
SCIENTIFIC UNIT AND MEASUREMENT
3. A man rows a boat in still water at 6.0km/h, he wishes to
row due north across a river 3.0km wide which is flowing
due east at 2.0km/h. calculate
a. The direction in which he must head the boat
b. The time taken to reach the other bank
4. A swimmer whose velocity in still water is 4km/h sets out
at right angles to the bank of a river which is flowing at
3km/h. draw a sketch of his path through water. Calculate
his actual velocity through the water.