CAPM Practicum Challenge

a. First, we drew a visual representation of the ramp. The materials we used are two wooden blocks, motion detector, ramp, ruler, cart, chalk, metronome, and the table. We used the block to prop up the table and create a ramp that is on an angle. 

b.  Then our group took a series of trials and marked the location of the back of the cart (so that the data was consistent) every second on the table with chalk. The metronome counted the seconds and indicated when we should mark. We did five trials and then entered the data into excel to make a graph. In column A, we entered the increments of time and in column B we entered the distance per second that the cart traveled.

c. In order to make the data linear, we square the B column. This also helped us find the equation of the line and to calculate our slope. The equation of the line is y=mx+b, so we plugged in the variables from our graph. Based on our graph, the equation of the line is
y=5.6958x+14.564.

Above is the table before we graphed our data. 

d. Lastly, we calculated the acceleration by using the formula slope=1/2a. In order to calculate this, we changed the units to meters. 

Our predicted acceleration is
.113916m/s^2. The prediction appears high because we calculated it in centimeters as opposed to meters.

To solve for t=4:

y=5.6958(4)+14.564

=.1056968 m/s^2 after 4 seconds

Conclusion:

I learned that by squaring the data you can make the line of the graph appear linear. You also can plug in an x,y coordinate pair to solve for b in the equation of the line. (y+mx+b)

The actual acceleration was .197m/s^2. Our group was not within 10%.

BFPM Practicum Model

BFPM Practicum Model:

a.First, we drew a picture of the suspended weight as a visual aid.

b. Then we drew a free body diagram with components. There are two tensions going up at an angle to represent the cables, and a gravity vector going down. Our group then added the angle measurements and calculated the newtons for each force. Underneath the FBD's are the horizontal and vertical equations of the FBD.

c. Then our group used sin to calculate the predicted weight.

sin (35) x .8N = 0.45

+

sin (70) x 2.2N = 2.067

= 2.5N

Our predicted weight is 2.5N.

 

Conclusion: Our prediction was within the 10% discrepancy. 

CAPM Unit SUmmary

CAPM Unit Summary:

•       In CAPM model, we learned that the curved lines on the graph indicates acceleration. We also learned that the positive direction indicates an object is moving forward and a negative direction indicates an object in moving backwards.

Displacement:

The displacement is the distance the object traveled from it’s starting point. The formula used to calculate the displacement is x final - x initial.  

Velocity

The velocity of an object is the change in position over the change in time.  

To calculate the velocity, use the formula: (change in position over change in time)

V= DeltaX

      Delta T 

The instantaneous velocity can be found at any point by finding the average velocity. The average velocity will be the same as the instantaneous velocity at the mid time. If the graph has a constant velocity and starting position you can predict the velocity at any point. 

Reading a V vs T Graph:
 

In a velocity vs time graph anything above the X axis is the positive direction. If the line is going in the upwards direction, away from the X axis, it is increasing. If the line is above the X axis it also means it is going forward. Anything below the X axis is going backwards in the negative direction. The closer the line is to the X axis, the slower it is moving. The steeper the slope is, the faster the object is going.

Interpreting Velocity vs Time and Acceleration vs Time:

The acceleration versus time graph's directly relates to the velocity versus time graph. If you are given one of these graphs, you can look and identify to make the coinciding graph.

All of the velocity versus time graphs on the left have a positive slope, so therefore that acceleration versus time graphs have positive acceleration. On the right, all of the velocity versus time graph's have a negative slope, so they also will have a negative acceleration on the coinciding A vs T graphs. On the far right the velocity is constant but the slope is zero, therefore it has an acceleration of zero.

Velocity vs Time Graphs:

·      To show a constant velocity, a straight horizontal line will be drawn.

·      If the graph has a positive slope, then the velocity is increasing. If the graph has a negative slope, then the velocity is decreasing.

·      In V vs T graphs, the X axis is referred to as the origin. The farther away from the X axis, the faster the object is moving. The closer the object is to the X axis, the slower it is moving.

·      The area above the origin represents the positive side of the graph, which indicates an object is moving forward. The area under the X axis (negative side) indicates that the object is moving backward.

Acceleration:

The rate of change in the velocity of a given object. The slope of a graph shows the acceleration. Acceleration can be calculated by:

1.     Finding the slope on a velocity vs time graph.

2.     2. Using the formula A=(1/2)bh +l x w

3.     Find the constant acceleration or instantaneous velocity by: V= at + V^0

4. a= Delta V

          Delta T (change in)

Acceleration vs Time Graphs:

·      These graphs tell us the acceleration of an object and if it is in the positive or negative direction, and tells us the slope that would be depicted on an V vs T graph.

·      If a line is straight, it shows a constant velocity.

·      The Y intercept in a A vs T graph tells us the starting position.

·      The area underneath the line tells us the change in velocity. By calculated the area underneath the line you can find the change in X, also known as Delta X.

·      In an A vs T graph, you cannot determine the objects position.

Position vs Time Graphs: 

How is the CAPM applicable to real life?Acceleration is commonly associated with speed, particularly when driving a car. In class, we often do problems that have to do with the acceleration it would take for a car to come to a complete stop for the amount of time it would take a driver to reach a certain speed. This unit has also taught us the scale of being able to predict any point on the graph that a line will intersect with if it has a constant velocity and starting point. Being able to make predictions and draw conclusions from graphs and other visual aids is a crucial skill that is a necessity in most business settings.

Constant Velocity PArticle Model

Nikki's Blog Post Unit 1

Unit One Summary:

Constant Velocity Particle Model

What did I learn from this unit?
This unit taught how to identify relationships on a graph, read a graph, and make predictions based on the data on a graph. I also learned how to identify relationships in an experiment, and be able to manipulate data using my independent variable and excel. I also learned how to create and read motion maps, create a graph with excel, position verses time graphs, and identify the factors in a graphs. These factors include velocity, time, position, distance verses displacement, and variables. In this blog, I will convey the skills we have learned and examples of how I used them.

Constant Velocity Particle Model Example Questions and Analysis:

If the curve is straight it indicates constant velocity and a linear relationship. In the picture to the left, I solved to find the velocity of the line by using the equation rise. 

                                   run

Then, to find the mathematical equation to describe the object's motion I used:
X= Vt + Xo

I plugged in the variables from the graph that I knew and solved for X. 

How to Make a Line with Excel:

1.     Enter data in columns.

2.     Highlight data

3.     (In insert menu) insert chart

4.     Choose XY on the marked scatter.

5.     Add trend line and equation on the graph.

Motion Map (Diagrammatic):

The motion map represents the velocity, position, and acceleration of an object at equally spaced times. The purpose of the motion map is to show you these factors at various time reading in a visual representation other than a graph.

Here is an example of a motion map. This map displays an object moving at a constant velocity. 

Velocity:

Velocity is the rate of change of an object.

V = slope     D= Velocity

T                  T

Position vs. Time Graphs:

The position verses time graph helps distinguish the displacement and total distance of an object. It also reveals key information about the velocity of the object. For example, a steep slope means a faster velocity. A straight (linear) slope means a constant velocity. A curved line means the velocity changes over time. Here is an example of a constant slope:

Equation of a graph:

X= Vt + X⁰

X⁰= position

V= velocity

T= time

The equation X= Vt + X⁰ describes the motion of an object.This equation can also be used to predict the position of an object at a certain point.

Path length:

The path length in the total distance something traveled.

Independent variable:
The variable over which the experimenter has complete control (x axis).

Dependent variable:
The variable that responds to change in the independent variable (y axis).

Displacement:

The movement of something from its original position; difference in position from origin and final point.

Speed:

Speed is how fast the object is going. A faster speed can be identified by a steeper slope on a graph.

Describe the Motion of the Object:

The motion of the graph can be read on a motion map, position verses time graph, or the constant velocity particle model. The image below shows an example of how all the same information can be displayed in the different models.

Shapes on a Graph: By being able to identify these shapes and trends on a graph it improved our ability to interpret graphical relationships and express it in written form. 

Connections:

This unit can be applicable in everyday life because it is important to understand graphs and charts. The ability to understand and make a graph is crucial in business. It is a required skill for making predictions and analyzing data. Also, these skills are applicable in our every day life. Everywhere we go, we are in a specific position. Although the starting point could be anywhere, it can still be displayed on a graph. We consider distance vs. time every day when calculating how long it will take to arrive at a specific point of location. People often try to predict these times themselves, but it could easily be predicted using the CVPM. For me personally, I could use the CVPM to measure how fast I run when exercising. I can use the CVPM to see if I am staying at a constant speed, of if my speed decreases sporadically.