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 (m 2 ), centimetres squared (cm 2 ) or kilometres squared (km 2 ). Finding the area of a shape Square: Rectangle: Triangle: Circle: Area = length X length Area = length X width Area = ½ Base X perpendicular height. Area = Pi X Radius X Radius = Π X r 2
Finding area of irregular shaped object 1. Draw the outline of the object on graph paper. 2. Count the number of 1cm 2 squares that are half-way or more inside the boundary. 3. This number is equal to the area of the shape in cm 2.
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 m 3 Another unit often used to measure volume is the Litre (l) 1litre = 1000 millilitres or 1000 cm 3 1millilitre = 1cm 3 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 radius 2 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 cm 3 of water is 1g but the mass of 1 cm 3 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 cm 3 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/cm 3 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/s 2 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