Kinematics

1.) What is Kinematics?

The dictionary definition of kinematics: the branch of mechanics concerned with motion without reference to force or mass This means that kinematics is a branch of classical mechanics that helps study the motion of objects in different dimensions. In kinematics, an object is studied closely, then an equation is derived to help one understand the motion of that object.


2.)Experiments
Constant Speed Experiment
To get a hands-on understanding of the study of kinematics, we started with a constant-speed experimentWe put a car on a track and pushed it along at a constant speed where it did not slow down or speed up. We video-taped the caand uploaded it into Logger Pro to analyze it. Slope is the rate of change, and the rate that an object changes position in a period of time is velocity. Therefore we concluded that the slope of this graph was the velocity at which the object was moving.The graph was linear, so we were able to derive an equation using the linear equation, y=mx+b. Using the y and x values of our graph, we derived our new equation, s=vt+s0. We also calculated the uncertainty in our measurements by using the "error calculations" function. We used the "stat" function to find the exact velocity of our car.

Video of the car:


Loggerpro Graph:

constantspeed.JPG Acceleration Experiment

We took a video of a car rolling down a ramp and uploaded it onto Loggerpro. On Loggerpro, we created two graphs: position vs. time and velocity vs. time. Here are the graphs:

Position vs. Time:

acceleration.JPG

Velocity vs. Time:

acceleration2.JPG

The position vs. time graph we got was curved, meaning that the relationship between position and time with an accelerating object is quadratic. The velocity vs. time graph turned out kind of funky, but it was supposed to be linear. Since slope is the rate of change and acceleration is the rate that a velocity changes, we concluded that the slope of this graph was the acceleration. Using this information and the x and y values, we came up with a new equation: v=at+v0.

For a second equation, we used the the velocity vs. time graph as well. Since the graph was linear, you could say that it created the shape of half of a trangle. The area beneath this line is called the integral. The integral represents the distance the car traveled while we were collecting its data on loggerpro. To create a new equation, we used the formula for a trinagle (1/2bh) and the quanitities of the base and the height to come up with a new equation, v=at+v0.

3.) Resources (websites, videos, tutorials, etc.)

http://library.thinkquest.org/16600/intermediate/kinematics.shtml


This is a video of a popular web game, Line Rider. In the video, someone has made a really cool, roller-coaster like, line that a man travels on. It can help provide an example of Kinematics and the different types of slopes that we see in Logger Pro because you can watch the man accelerate depending on the way the line or slope is.

Example of acceleration graphs:

acceleration_graphs.gif


Click here for a helpful practice questions and explanations about motion graphs

Equations


s = vt + s0
v = at + v0
s = 1/2at^2
v^2 = 2as + v0 ^2
ΣF = ma



Variable symbols and their meaningsexternal image lft060108.jpg


s - Distance
v - Velocity
t - Time
s0 - Initial Position
a - Acceleration
v0 - Initial velocity
g - Acceleration due to gravity
F - Force
m - Mass
Σ - Sigma (meaning "the sum of")


Units m (meters/any form of distance measurement) - Distance s (seconds/any form of time measurement) - Time m/s ("meters"/"seconds") - Velocity m/s/s (meters / seconds / seconds, or velocity/ seconds) - Acceleration n (newtons)- Force

Tips & Important Points

Helpful Note: How to get s0: - Open up word, type "s", under the font key click the subscript button, and hit "o".

- If you want to put the s naught into Wikispaces, just copy and paste.

Important Vocabulary to Note:


scalar - a quantity that only has a magnitude (ex. distance, speed, time)
vector - a quantity that has magnitude and direction (ex. velocioty, displacement, acceleration)

distance - how far you travel
displacement - how far you are from your starting point

Example scenario for better understanding of distance and displacement:
You start from one side of the swimming pool and swim a total of 100 meters to the other side. You then swim back 100 meters to where you started to complete the lap. Your displacement is 0 meters because you're in the same spot that you started on; but your distance is 200 meters (100 meters swimming to the other side + 100 meters swimming back).