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. 

Texting While Driving

Texting While Driving Corrections

Texting While Driving Data:

Prediction: We predict the car will travel 0.02815 in 2.38 seconds at a constant velocity of 45 m/h.

distance = 45 miles = 45 miles = x miles 
time           1 hour        60 min      1 min

60x = 45       x= .75 miles per 7 min
60      60

.75 miles =  75 miles
1 min             60 sec

After setting up a proportion and canceling the units until it was miles/ seconds, we cross multiplied the equation to find the variable x, which represents miles:

75 miles  =  x miles        x= 0.02875
60 sec          2.3 sec

Therefore, in 2.3 secounds the car would travel about .03 or .02875 seconds at a constant velocity of 45 m/h.

This motion map describes the cars motion because it shows that it is moving at a constant velocity. The velocity vs. time graph shows how the car moves at a constant velocity, from an origin of 45 m/h. The position vs. time graph shows how the cars position changes, but the distance per second is consistent throughout the movement of the car.

Balanced Force Particle Model

Balanced Force Particle Model Reading and Notes: Force and Force Diagrams
 Forces can be thought of as pushes and pulls. They are an interaction between two objects- you can touched without being touched. Here are some of the forces in these interactions and how we identify them.

Gravity: exerts a force on you (pull) which holds you to the surface of the earth and occurs when forces are extended through a force field

Friction: forces parallel to the surface (pull)
    -Weight affects the friction by determining how gravity on an object can move.
    - Velocity affects the surface type (coefficient).
    - friction is calculated by the formula: mk=coefficient

Normal Force: when two surfaces touch, the force perpendicular to the surfaces are called normal forces. It also keeps an object balanced and from going through the ground.

Tension: extended links or material such as string or chain exert tension forces on an object (push)

Push or Pull: When we touch something, a combination of friction and normal forces are present, put for simplicity we refer to them as push of pull forces. 

Non-contact forces:  When two objects interact, they exert forces through a force field. For example, there is a gravitational force on the earth and the moon, even though they do not touch. Aside from gravitational, electric and magnetic are also non-contact forces.

Direction of Forces:
Gravity always points down towards the earth. The normal force is perpendicular to the surface and the frictional force is parallel to the surface.  
 
 Rules of Labeling Forces: 
When you label forces, we want to include the type of interaction between the two objects, what object the force is acting on, and what object the force is by. You would use the notation of a large capital F followed by the kind. Here is an example of how the push force would be written.

Fpush

Normal force is always perpendicular to gravity and friction is always parallel to gravity. The force of weight or gravity is always going down. Tension is only drawn when on a rope, extended link, or chain. 

Axis:
The axes should be drawn titled when the object is on an angle. The forces would be the same, the lines would just be titled on a slant. If the axis is not tilted, you don't need to add components.



Rules for Action-Reaction Pairs:
Every action has an equal and opposite reactions.The identification of these pairs are two statements stating who is pushing on who and the direction. 

Understanding and Deconstructing the Force Diagram:

STEP ONE: Shrink the shape of the object down to a point. Place it at an intersection of a set of coordinate axes with the direction of the axes parallel to the direction of motion.

STEP TWO: Indicate all points at which there is contact between the object and its surroundings. Construct qualitative vectors (vector: a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another) to represent these forces. 

STEP THREE: Indicate which forces are equal in magnitude to other forces. Keep in mind the forces left must equal the forces right and the forces down must equal the forces up. Uses hashes to indicate which forces are equal and congruent to one another.

STEP FOUR: Represent all relevant forces with a labeled vector. Remember the rules of labeling forces.
 
Newton's Law of Physics; How is this applicable to our unit?

Newton's First Law: An object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[
Newton's Third Law:  When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.


Activity: Bowling Ball Motion and Hovercrafts

What did we learn?
In result of Newton's first law, if the hovercraft or bowling ball was moving at constant velocity, no forces are acting upon it. The object in motion will stay in motion until an external force acts upon it. Once the person pushed the hovercraft and lost contact with it, no force was acting upon the hovercraft. The hovercraft kept moving until the person on the other side of the gym stopped it (external force).

Understanding Weight:
In order to find the weight of an object, you will use the formula:
W=mg
The M represents the mass (kg) and the G represents the gravitational constant (9.8m), which we round to 10. When you solve for the weight, the units will be Newtons. The mass measures the amount of matter and weight is a measure of the pull of gravity.


Example Problems:
 1. Q:You are driving down the road and you have a cup of coffee without a lid. You come to a stop and your coffee spills all over you. Using an FBD, explain why the coffee went all over you. 
     A: Newton's first law acts in this situation. It states that an object in motion stays in motion. When the car stops, the coffee was still moving forward, therefore when the car brakes, the cup comes to a stop which causes the liquid to spill. Without the lid, there is no force to push against the coffee to keep it from spilling. 

2) Draw a free body diagram for a ball that has been thrown upward and is moving at a constant velocity. 3) Draw and label an FBD for a ball that has been thrown at another person. 

No force keeps the ball moving. The only force acting upon the ball is gravity. I learned in the hovercraft experiment, that once an object is moving there is no force keeping it in motion. This also is true because of Newton's first law: an object in motion stays in motion. (The diagram on the right is 2.) and diagram on the left is 3.).

 

4.) Use FBD's to show how a team can win a tug of war. Explain your reasoning.

 

 

The diagram below represents Marcy (in black), who is losing the tug of war competition. The determining factor in her loss is friction. Newton's third law is applied here because each side is pulling and receives an equal and opposite force. Therefore the pull/tension is equal.

 

Debra (gray) is winning because she has greater friction. The more friction the team has, the less Marcy will be able to pull on her. (Note: the only force that is different is the friction, which is greater in the diagram below. The pull is equal) (Microsoft would not let me draw uneven arrows)

5.) How do seatbelts keep you safe? Use Newton's 1st law in your answer.

Seatbelts provide an unbalanced force in the vertical direction, which slows the car down when you keep moving forward. You keep moving forward because of Newton's 1st law (an object in motion stays in motion). The seat belt is the external force that stops the motion of your body. 

6.) Solve for the horizontal and vertical components of tension for the fishing line.

Decoding Triangles:

The component in the FBD are always the hypotenuse when trying to solve for the horizontal/ vertical components. The opposite it opposite the angle. The adjacent is next to the hypotenuse and the angle you are solving for. In order to solve, you will use SOH CAH TOA. Below is the equation determining whether you use Sin, Cosine, or Tangent.