NG 1 - What is the relationship between position and time for a cart rolling down a ramp?
The time stays the same but the position increases because the cart is accelerating since there is no friction.
What is the relationship between velocity and time for a cart rolling down a ramp?
The time stays the same but the velocity increases proportionally. time stays the same?? what does that mean?
NG 2 - Investigating
First we set up the ramp at an angle by propping it up with 2 boxes. Next we set up a 60 Hz ticker timer using carbon paper. We taped the end of the carbon paper to the cart and placed it at the top of the ramp. We then let the cart go after turing on the ticker timer. The ticker timer made a motion map and I used that to calculate the time and position. Every six dots, which was 0.1 seconds, I calculated the position using a meter stick.
variable names?
0s - 0cm
0.1s - 1.5cm
0.2s - 5cm
0.3s - 10.4cm
0.4s - 17.5cm
0.5s - 26.4cm
0.6s - 37cm
0.7s - 49.4cm
0.8s - 63.2cm
0.9s -79.4 cm
I cut my ticker tape every 6 dots because that counted as 0.1s then pasted it on the graph to show how the velocity changed every 0.1s
NG 3
Position Graph I can't see this??
Verbal Model: As the time increases, the position increases increasingly
Math Model: x = (88.485 cm/s^2) t^2
Velocity Graph
VM: As the time increases the velocity increases proportionally.
MM: y = mx +b
Vf =at + Vi
^
slope = (cm/s)/s = cm/s^2 what does the slope mean?
y-intercept?
DeltaX = 1/2 at^2
NG 4
The displacement is the area under the velocity graph. When plugging the slope of X and V into a chart we found that X is equal to 1/2 V so we replaced it with the variable a because it is the acceleration and t always stays the same. Therefore to find the change in position you use DeltaX=1/2at^2 equation.
The second equation is saying that the final velocity is equal to the initial velocity plus the acceleration. We know that a is equal to the slope of V and the units are equal to the change in y over the change in x. That simplifies to (cm/s)/s= cm/s^2. Every second of time (s
NG 5
Each experiment didn't have the same numbers for the constant slopes because it all depended on the angle of the ramp. Some were higher and others were lower. One error could have been the measurements of the position on the ticker tape. Since I used a meter stick it is hard to make it exact. Something else I would like to test is my acceleration when I am running. It would be cool to race other people and see who had a greater acceleration and try to prove it. good ideas!
