Scientific Investigation
Definition: A scientific investigation is a careful and organised way that scientists use to explore something they are curious about in the world around them. It helps them understand how things work and develop new ideas or theories.
Approach: This process includes collecting information, looking closely at that information, and making sense of it in a way that follows clear steps. Scientists do this to make sure their findings are correct and reliable.
Recording results: After doing an investigation, scientists write down their results in a neat and logical way. This helps them see if any patterns or trends appear so they can explain what happened and why.
Process in a Scientific Investigation
Observation: Everything starts with observing something interesting in nature or in a situation. This makes scientists ask questions like “Why did that happen?” or “What causes this effect?”
Problem Statement: The observation is turned into a clear and testable question that the experiment will try to answer, such as “Does the length of a pendulum affect its swing time?”
Hypothesis: This is an educated guess about what might happen during the experiment. It must be something you can test, like “If I increase the length of a pendulum, then the time it takes to swing will also increase.”
Variables:
- Manipulated Variable: This is the thing you change on purpose in the experiment. For example, changing the weight or length of something.
- Responding Variable: This is what you measure or observe to see the effect of your change.
- Fixed Variable: These are things that stay the same throughout the experiment so that only one thing is being tested at a time.
Experimental Design: You plan and set up the experiment carefully, choosing the right tools and materials, and writing down every step to follow.
Data Collection: During the experiment, you record your results in a table or chart so you can keep track of what happened.
Data Analysis: You study the results using math and graphs to see what they tell you. This helps you understand the connection between the variables.
Conclusion: You decide whether your hypothesis was correct or not by explaining what your data showed.
Report: You write a full report from beginning to end, explaining what you did, what you found out, and what it means.
Graphing
Purpose: Graphs are important tools used in science to make information easier to understand. When we collect data in experiments, we often have lots of numbers in a table. But just looking at numbers can be confusing. A graph changes these numbers into a picture that helps us see patterns or trends more clearly. It shows us how things are connected—like how one thing changes when we change something else. This is really helpful for figuring out how the world works.
Data Plotting: Before you can draw a graph, you need to organize your information. The first step is to put your results into a data table, where one column has the values you changed (like time or weight), and another column has the values you measured (like temperature or length). After this, you can draw a graph by putting these numbers into a visual format. This makes it easier to understand how the two sets of data are related. For example, it might help you see if one value always goes up when the other does.
Axes Convention: When making a graph, it’s important to follow the right rules for the axes.
- The independent variable (this is what you control or change during an experiment) is always placed on the x-axis(the horizontal line at the bottom).
- The dependent variable (this is what you measure to see how it was affected) is always placed on the y-axis (the vertical line that goes up the side).
- For example, if you are doing an experiment to see how adding different weights affects the length of a spring, the weight is what you are changing, so it goes on the x-axis. The length of the spring is what you are measuring, so it goes on the y-axis.
Types of Graphs
Straight Line Through Origin:
- This graph starts at the zero point and goes up in a straight line.
- It shows that both variables increase together in the same way. If you double the value on the x-axis, the y-axis value also doubles.
- This kind of pattern is called a directly proportional relationship, and it is written as y ∝ x.
Straight Line With Y-Intercept:
- This is a straight line graph that does not start at zero. It starts higher up on the y-axis.
- It shows that there’s a steady, regular increase, but something was already there at the beginning before the changes started.
- The rule for this graph is y = mx + c, where m is the gradient (steepness) and c is the y-intercept (starting value).
Curve with Positive Gradient:
- This graph goes up, but in a curved line, not a straight one.
- It shows that as the x-values increase, the y-values also increase, but not always at the same speed.
- This is called a non-linear increase, which means the rate of change keeps growing.
Curve with Negative Gradient:
- This graph curves downward, showing a decrease.
- It means that when one value gets larger, the other one gets smaller.
- Like the positive curve, it’s non-linear, but instead of going up, it goes down.
Inverse Curve:
- This graph shows an inverse relationship.
- This means as one value goes up, the other one goes down.
- The rule for this is y = k/x, where k is a number that stays the same (a constant).
Graph Analysis
Gradient (m):
- The gradient of a line tells us how steep it is.
- It also tells us how fast the value on the y-axis changes for every change in the x-axis.
- To calculate it, we use this formula: gradient = change in y ÷ change in x. This is like finding out how much something has increased or decreased over a certain distance.
Y-Intercept (c):
- The y-intercept is where the line crosses the y-axis (the vertical line).
- It tells you the starting point or original value of the thing you are measuring, before the x-variable starts changing.
- For example, it might show the starting height of a ball before it’s dropped.
Relationship Detection:
- When you look at a graph, you can figure out what kind of relationship exists between the two variables.
- If the graph is a straight line, the variables are likely directly proportional.
- If the graph is curved, it means the connection between the variables is more complicated or changes over time.
Example:
- A displacement vs. time graph tells you how far something has moved over a period of time.
- The gradient of this kind of graph tells you the object’s velocity, which is the speed in a certain direction.
Analysing Graphs
Gradient:
- Helps us understand how quickly something changes in response to another thing.
- For example, if you draw a graph of force vs. extension for a spring, the gradient tells you the spring constant.
- This spring constant tells you how hard it is to stretch the spring—a higher gradient means a stiffer spring.
Y-Intercept:
- This value tells you what the measurement was at the very beginning, before any changes were made.
- In a distance vs. time graph, the y-intercept might tell you how far an object already was from the start point before the experiment began.
Area Under Graph:
- Sometimes, the area under a graph line or curve gives us another important measurement.
- For example, in a force vs. distance graph, the area under the line shows the work done—this means how much energy was used to move something over a certain distance.
Interpreting Graphs
Purpose:
- Interpreting a graph means taking time to study the graph carefully and understand what it shows.
- It helps you figure out how two things are related and lets you find useful numbers like the gradient or a constant.
Example:
- In a force vs. extension graph, if the line is straight, it means the spring is obeying Hooke’s Law.
- You can then calculate the spring constant by finding the gradient of the line.
- The spring constant tells you how much force is needed to stretch the spring by one unit (like one meter or one centimeter).
Determining Area Under a Graph
Physical Meaning: The shaded part under a graph line or curve often represents a real quantity that we can measure in science, especially in physics. For example, in a force vs. distance graph, the area under the curve shows the amount of work done. This is because work is calculated by multiplying force by the distance the force is applied. So, the shape under the graph is more than just a drawing—it tells us something meaningful, like how much energy is used, how far something travels, or how much effort is involved in doing work.
Units: To figure out what the area under the graph means, we look at the labels on the x-axis and y-axis. The units for the area are found by multiplying the unit on the horizontal axis (x-axis) by the unit on the vertical axis (y-axis). For example, if the x-axis shows distance in meters (m) and the y-axis shows force in newtons (N), the area gives you energy or work, which has units of joules (J). That’s because 1 newton × 1 meter = 1 joule.
Simple Shapes: If the shaded part under the graph is a simple shape, like a rectangle or triangle, we can use basic math formulas to find the area. These shapes are easy to calculate. For example:
- Rectangle: Area = length × width (just multiply the two sides)
- Triangle: Area = ½ × base × height (multiply the base by the height and divide by 2) These formulas help us turn graph shapes into useful numbers.
Complex Shapes: Sometimes, the area under the graph forms a shape that isn’t simple. In these cases, we divide the area into smaller, easier parts, like triangles, rectangles, or trapezoids. Then we find the area of each small shape and add them together. This is called approximation, and it helps us estimate total values when the graph has curves or uneven lines.
Using Interpolation
Definition: Interpolation is a way to estimate a value that is between two known points on a graph. It is useful when we have data but want to know what happens in between the measured points. It’s like filling in the blanks.
Application: For example, if you know that a spring stretches 2 cm when a 2 N force is applied, and 4 cm when a 4 N force is applied, then you can estimate the spring will stretch about 3 cm when the force is 3 N. You find this value by drawing a line between the two points and choosing the value in the middle. This is helpful when you can’t measure every single point.
Using Extrapolation
Definition: Extrapolation means making a guess about what might happen outside the range of data you already have. You extend the graph’s line beyond your measured points and use it to estimate what could happen next.
Caution: While extrapolation can be useful, it is also risky. The further away you go from your real data, the more likely it is that your prediction might be wrong. This is because the pattern might change beyond the range you measured. So always be careful when using this method.
Conducting Experiments
Purpose: Experiments help us test our scientific ideas, called hypotheses. When we do an experiment, we are trying to see if our guess about how things work is true. Experiments also help us learn more about how different things are connected, and they give us real data to use.
Validity: For an experiment to give correct results, it must be done properly. This means the plan should be clear and the steps should be followed carefully. If you don’t plan well or if you make mistakes, the results won’t be trustworthy. A good experiment also keeps everything fair and controlled.
Steps: A well-planned experiment includes the following:
- Write the aim or purpose of the experiment clearly.
- Make a hypothesis: a smart guess about what you think will happen.
- Identify the manipulated variable (what you change), the responding variable (what you measure), and fixed variables (what stays the same).
- Create a step-by-step plan for how to do the experiment.
- Collect and record the data during the experiment.
Identifying Variables
Types:
- Manipulated Variable: This is the factor that you purposely change to see what effect it has.
- Responding Variable: This is what you measure to see how it changes as a result of what you changed.
- Fixed Variables: These are the parts of the experiment you keep the same throughout the test so it stays fair.
Example: Let’s say you are doing an experiment with a swinging pendulum:
- The manipulated variable could be the length of the string.
- The responding variable would be how long it takes to swing back and forth once.
- The fixed variables could include the mass of the object on the string and the angle from which it is released.
Experiment Example: Spring Extension
Aim: To investigate how the extension of a spring is affected when different amounts of force are applied to it. In other words, we want to find out how much the spring stretches when we pull on it with different weights.
Hypothesis: If we increase the force (add more weight), then the spring will stretch more. The stretch (called extension) will increase in a straight-line pattern, showing a directly proportional relationship.
Variables:
- Manipulated Variable: The force applied to the spring (measured in newtons).
- Responding Variable: The extension of the spring (how much it stretches, measured in centimeters or meters).
- Fixed Variable: The same spring must be used each time, and the way we measure must stay the same.
Procedure:
- First, measure the spring’s original length before any weights are added.
- Hang a known weight on the spring and measure how long the spring becomes.
- Subtract the original length from the new length to find the extension.
- Repeat this by adding different weights and measuring the new extensions each time.
- Record all your results in a table to keep them organized.
- Draw a graph of force (x-axis) against extension (y-axis) to see the relationship.
Analysis: When you look at the graph, the slope (also called the gradient) tells you how stiff the spring is. This value is called the spring constant. A steeper line means a stiffer spring.
Experiment Example: Simple Pendulum
Aim: To investigate how the length of a pendulum affects the time it takes to swing back and forth (this time is called the period).
Hypothesis: If the length of the string is longer, then the pendulum will take more time to swing one full cycle (forward and back). This means the period will increase as the length increases.
Variables:
- Manipulated Variable: The length of the pendulum string (measured in meters or centimeters).
- Responding Variable: The period of the pendulum (time for one complete swing, measured in seconds).
- Fixed Variable: The mass of the pendulum bob and the angle it is released from must stay the same.
Procedure:
- Set up the pendulum and measure the length of the string carefully.
- Pull the pendulum to one side and release it. Use a stopwatch to time how long it takes to complete 20 full swings.
- Divide the total time by 20 to find the period (time for one swing).
- Repeat the experiment using strings of different lengths.
- Record the time for each length in a table.
- Draw two graphs: one with period (T) vs. length (l), and another with period squared (T²) vs. length.
Analysis: If the graph of T² vs. l is a straight line, it shows that T² is directly proportional to l. This proves that longer pendulums take more time to complete one swing.
Experimental Procedures
Accuracy: It’s important to follow the steps exactly the same way every time you repeat the experiment. This makes your results more accurate and reliable. Don’t rush—take your time to measure and record correctly.
Measurement: Always use the right tools, like a ruler, measuring tape, or stopwatch. Make sure to read the tools at eye level to avoid mistakes, and always start from zero.
Experimental Design and Precautions
Variable Identification: Before starting the experiment, be sure you understand which variable you’re changing, which one you’re measuring, and which ones you need to keep the same. This will make your experiment fair.
Planning: Write out your experiment steps clearly. Think ahead about the materials you need and the possible challenges you might face.
Error Minimisation: Try to reduce mistakes by taking multiple readings and using good quality tools. Then take the average of your readings to get more accurate results.
Safety and Setup: Set up your experiment in a clean, safe place. Make sure all equipment is used correctly and safely to avoid any injuries or accidents.
Instrument Use: Choose the right measuring instrument for the job. Before you start measuring, make sure it is set to zero. When you read a scale, look straight at it to avoid parallax error, which happens when you look from an angle and get a wrong reading.