Area Volume Density
Speed Velocity Acceleration
Chapter 35
Science Matters
Area
Area of a shape is the amount of surface enclosed within its boundary
lines. Area is measured in metres squared (m2), centimetres squared
(cm2) or kilometres squared (km2).
Finding the area of a shape
Square:
Area = length X length
Rectangle:
Area = length X width
Triangle:
Area = ½ Base X perpendicular height.
Circle:
Area = Pi X Radius X Radius
= Π X r2
Finding area of irregular shaped object
1.
Draw the outline of the object on
graph paper.
2.
Count the number of 1cm2
squares that are half-way or more inside
the boundary.
3.
This number is equal to the area
of the shape in cm2.
Volume
The volume of an object is the amount of space it takes up
The SI unit of volume is the metre cubed or cubic metre m3
Another unit often used to measure volume is the Litre (l)
1litre = 1000 millilitres or 1000 cm3
1millilitre = 1cm3
Finding the volume of a liquid
1. Pour liquid into measuring cylinder.
2. Read the volume from the lowest part of the meniscus.
Finding Volume of regular shaped objects
Volume of a block:
Length X Width X Height.
Volume of a cylinder:
Pi X radius2 X height
Finding the volume of irregular objects
Volume of irregular shaped objects (e.g. a stone) found using
displacement. The Object is placed in water and it pushes its own volume
in water out of the way.
Finding volume of a small irregular object
1. A Known volume of water is placed into a measuring cylinder &
recorded (vol. 1).
2. Tie a string around the object and lower it into the cylinder.
3. Record new volume (Vol. 2)
4. Subtract vol 1 from vol 2 the answer is equal to the volume of the
object.
Finding volume of large irregular object
1. Fill a displacement can with water and let it stop dripping.
2. Place a measuring cylinder under the spout.
3. Put a string on the object to be measured and lower it gently into
the displacement can
4. Record volume of water that flows into the cylinder, this equals the
volume of the object
Density
Definition
The mass of an object is the quantity of matter in it
To compare the mass of substances fairly we must compare the mass of
the same volume of each substance.
The mass of 1 cm3 of water is 1g but the mass of 1 cm3 of lead is 11.2g
than so the mass of lead is 11.2 times heavier than the mass of the same
volume of water.
Lead packs a lot more matter into 1 cm3 than water does. This
measurement of mass per unit volume is called the density of a
substance.
No two substances have been found with exactly the same density. This
means density can be used to identify a substance
The density of a substance is its mass per unit volume.
The formula for finding density is:
Therefore:
And
We can use the Density Triangle to figure out any one of the three if the
other two are known
Cover the one you want to find and use the other two to find it
Units of Density
Density is mass divided by volume.
Unit of density is the unit of mass divided by the unit of volume.
The SI unit of Density is g/cm3
Finding Density
3 Steps
1. Find the Mass
2. Find the Volume
3. Divide Mass by Volume
Floatation
A substance will float on another substance that is more dense than
itself. Oil and wood float in water because they are less dense than water.
Lead and mercury sink in water because they are more dense. A ship
floats in water because its overall density (including the air inside it) is
less than water.
Speed
Speed is a measure of how quickly a body (object) can travel from one
point to another.
Speed of an object is the distance it travels per unit time.
Unit of speed is the unit of distance divided by the unit of time.
This is metres (distance) per second (time) or (m/s)
We also use kilometre per hour (Km/h)
Again we can use a D street triangle to figure out any one if the other
two are known.
Simply cover the one you want and use
the other two
Maths problems on Speed
An athlete runs 1500m in 4 minutes
Calculate the average speed in metres per sec
Answer:
Distance-Time Graphs
In science graphs are used to represent information so it can be used to
answer questions
Example of a distance time graph
Time is shown on the x axis and distance is shown on the y axis of the
graph
Velocity
The velocity of an object is its speed in a certain direction.
Example: a plane flying from Dublin to London, its speed might be
700km/h but its velocity would be 700km/h south-east.
Units of velocity are the same as speed but followed by a direction
Example: km/h south, or m/s (ms-1) west.
Acceleration
Acceleration is a measure of how quickly an object can change its speed
or velocity.
The unit of acceleration is the unit of speed divided by the unit of time.
metres per second per second or m/s/s or m/s2
Calculating Acceleration
A Cheetah accelerates from rest to a speed of 30m/s in 6 seconds. What
is its acceleration.
Answer:
Calculating Acceleration
Question
A bullet enters a tree trunk @ 300m/s, it comes to rest in the tree 0.2
seconds later. Find the acceleration of the bullet.
Because the bullet is slowing down we get a minus answer this is called
deceleration or negative acceleration.
Velocity-Time Graphs
These show how the velocity of an object varies with time.
Lots of information can be taken from the graph e.g. if the object is
accelerating or decelerating or if its accelerating steadily or unevenly