Unit 1 Summary Blog Post

Fundamental Lab Skills 

In this unit, we started off covering the fundamentals and subjects relating to Scientific Methods and the Constant Velocity Particle Model. We kicked off the year with a Mass and Pullback Lab which not only gradually introduced us to important course material, but it also gave us the chance to refresh our skills and techniques on how to perform a thorough experiment. We went over the importance of keeping up with our data from experiments in a scientific notebook

in order to keep the same data throughout the whole experiment and not have to recollect data, which is a hassle.We also reviewed how you should collect at least 5-8 data points to make a line to ensure the consistency and credibility of your data. Other fundamental lab skills we learned was about how to record data in an organized and understandable way by making a chart with variables thoroughly labeled, and then how to use that data to make a graph in excel with a trendline that we would then use to make predictions. We learned that the independent variable is always plotted on the x axis, and it is the variable which is needed to change the dependent variable, which is plotted on the y axis.

Making a Graph on Excel

One of our goal's was to make an X Y Scatter plot, and to do so, we entered the x values, or independent variables vertically in the first column, and the y values, or dependent variables in the second column next to it. Next you highlight both columns, look under Insert, Chart, then XY Scatter, which should plot the points as were listed, but a trendline, which is the line that runs through the middle of all the points and serves as an “average” between them all, could not exist because the points were not linear. We learned the different methods of linearizing a graph, and the examples are pictured below:

Methods of Linearizing a Graph

It is necessary to have a linear graph because if not, we don't know that the values are increasing at a constant rate, so therefore, we will be unable to make accurate predictions using the equation derived from the line after the graph is linearized. The methods of linearizing graphs can be seen in the model above. In the first example, the straight line is already linear so nothing has to be done and the equation is just y=b because y stays constant as x increases. In the second example, nothing has to be done to linearize the data either, the equation is simply y=mx+b. In the third example, the hyperbolic parabola, 1 must be divided by all x values to linearize the data, and below that one, the top opening parabola requires you to square the x value to linearize the data. In the final example, the side opening parabola requires you to square y to make it linear. We were able to use at least one of these methods when linearizing our graphs for the Mass/Pullback Lab.

Mass/Pullback Lab Overview

 In this lab, we performed two separate experiments, one testing pullback distances up to 25 cm in order to predict how far we think it will travel pulled back at 50 cm. We performed several trials in order to have consistent and reliable data, averaged the values together to plot on the x axis, with time on the y, then we made the XY Scatter plot in excel.   

Above is a sample graph from the Mass/Pullback Lab. The graph on top represents the non linearized graph, and the graph below is the same graph but linearized.  The dotted blue line is the trendline, and the y=5086.5x-1.1447 is the equation used to make the prediction. In order to linearize it we have to use the formula :1/x since it was a hyperbolic parabola. We learned how to substitute the variables on the X and Y axes into the equation for a more clear representation, and an example of that based off the equation would be: distance=5086.5(mass) -1.1447. To actually use the equation to make predictions, you would just substitute the value you're trying to test into the equation, but it’s not as simple as just plugging in the number, but you have to plug in the number in the same form you used to linearize the graph, so as previously stated, the graph required us to divide 1/x, so we had to plug 1/500 into the equation to make the prediction. 5086.5(1/500)-1.1447= 9.02, which is our predicted distance of travel.

Percent Error

To test and see if our predictions were accurate or not, we were able to calculate the percent error after collecting our final results, with the optimum range being under 10%, but for other experiments we have been given up to 20% depending on how exact we should have been able to collect data. To find percent error you would use the predicted value- actual value divided by the actual value times 100. After the percent error was calculated, we learned the importance of analyzing our results and drawing conclusions by writing our fist lab report. We had to reflect on how close our predicted value was to the actual, and explain why if we were off. We had to evaluate the meaning of the slope, whether it was positive or negative and what that means for the line, as well as the significance of the y intercept. 

 Constant Velocity Particle Method: Position Time Graphs

We finished off the unit studying the Constant Velocity Particle Method. One of our main focuses was on position vs. time graphs and velocity vs. time graphs. A position vs. time graph marks the location of an object at any given point in time, so the x axis is time, and the y axis is distance. I like to look at a position vs. time graph as being the basic form of the location of an object, for example, if you're wondering where the skater is at 3 seconds, you would just find the x,y coordinate on the graph and that would be his location. Sometimes the object turns around and goes in the opposite direction, and that is represented by turning the line down to form a negative slope. The velocity of the object at any given time can be determined using a position vs time graph’s change in y over the change in x, or change in position over change in time. The average velocity of the object over the entire period of time would be found using the displacement, which is final position-initial position (x final-x initial), over total time. 

This is an example of a position time graph which shows that the object is going 10m/s.

Motion Maps

Before getting into the velocity vs. time graph, our overview of motion maps will be described because they are closely correlated with position time graphs. Mrs. Lawrence has told us that a motion map is practically the y axis of a position time graph on its side. The motion map, as described by our Constant Velocity Particle Model Reasoning: Motion Maps handout says, “a motion map represents the position, velocity, and acceleration of an object at equally spaced times.” Each mark on the motion map represents a position, and the dots and arrows represent where the object is in the given amount of seconds, so for example, if the object was at 2 meters at 0 seconds, the first arrow will start at 2 meters, and based on the velocity, whether the object is going 1m/s or 2m/s, determines how long the arrow is and where it stops for the next one to start. A motion map can describe the location of one or two objects, and in the case of two objects, the lengths and location of the arrows in relation to each other represent their different velocities and locations. An example of a 2 object motion map is below:

Velocity Time Graph

A velocity vs. time graph represents how fast an object is going for certain periods of time, so rather than showing location, it is showing velocity. For example, the velocity time graph would represent a situation like the following: if an object starts off going 2m/s for 3 seconds, stops for 1 seconds, then resumes going 1m/s for 2 seconds. Because I don’t have a picture representing that particular example, I will attempt to describe it in words. Time is on the x axis  in increments of 1 seconds, and velocity is on the y in increments of 1 meter. The line would start off coming from the 2 on the y axis, and continue to the right for 3 seconds, at the 3 second mark, the line would drop done to be even with the x axis for 1 second which represent that the object had stopped. Finally, the line would increase up to the 1 meter line on the y axis and continue horizontally for 2 seconds. When what is traveling turns around and goes back in the opposite direction, you would draw the velocity line below the x axis in the same fashion. You can calculate displacement on a velocity time graph by using the area of the location in which you're calculating, so the height on the y axis and the length on the x axis will give you the displacement, and you can divide the number of boxes and displacement to give you the distance that each box represents.

This is a velocity vs time graph which shows a wide variance in velocities as well as a change in direction. 

The motion of the object can be described by merely interpreting the velocity time or position time graphs, the only difference is for one of them you’ll be saying that an object is going a certain speed, while in the other the object is in a location or at a certain distance. 

Basic facts/ equations we learned:

x=vt+xo, which means, position=(velocity)(time) + starting position

STEEP SLOPE= faster velocity

LESS STEEP SLOPE= slower velocity 

velocity= distance/time, and the equation can be manipulated to find any of the values 

speed= distance/time

Application

I was mainly able to relate our study on velocity time graphs, position time graphs, velocity, and displacement with life because everyday we travel in a car, going at an average velocity or a certain speed. We travel using path lengths, and displacement, and we often times use intersection points when it comes to location whether we're on foot or in a car.