Ramp on Cart Lab

Grace Chung September 23, 2021

Partners: Ryan Rong, Jongwoo Park, James O'Neill (rip king) Written: September 30, 2021

Question:

How will putting a cart on a ramp affect the position as time passes? How can you see this graphically through a position time graph and a velocity time graph? Is this graph positive or negative and linear, quadratic, or cubic?

Variables:

The independent variable, or the variable that is actively changed by us (also the x coordinates of the graph), is time measured in seconds (s). The dependent variable, the variable that is dependent on the independent variable (the y coordinates of the graph), is the position of the cart, from the initial position zero measured in meters (m). There are several control variables or variables that must stay consistent in order for the experiment to be successful. These variables include the use of the same cart, which will control speed, mass, and air resistance. In addition, the direction of the cart, the track of where the cart goes, the height and angle of the ramp and the starting point of the car must all be the same in order to ensure an accurate experiment.

Developed Method:

Because the speed increases so rapidly and the ramp is only about a meter long, we decided our best approach for this lab would be to record a video of the cart going down the ramp, and use LoggerPro technology in order to ensure accurate and precise results. Within the filming of our video, we had to arrange a tripod for our phones, as our hands would be too shaky, affecting the pixels and accuracy of the graph. We also included within the video a whole meter stick, so the amount of pixels to a meter stick could be quantified. The view was interested into Logger Pro, and after setting an origin we were able to graph the points directly on the video, which showed up on the position time graph. After making a position time graph, we also inserted a velocity time graph to see how much acceleration the graph had.

Procedure:

1. We set up a tripod and the ramp at an angle.

2.We then lined up the cart straight do it wouldn't fall off the ramp mid-video.

3. We recorded the video of the cart falling down the ramp.

4. We loaded this video into Logger Pro, using the technology to create both a position time graph and a velocity time graph.

5. We compared these results with other members of the class, seeing if our data was accurate.

In this diagram, we have the meter stick in shot, with the ramp propped up with books, creating a slant. The cart sits at the top of the ramp, waiting to fall as soon as we let go of it.

Unprocessed Data:

I had about 100 raw data points, ensuring maximum accuracy with this lab. For every/every other video frame I would plot a data point. There are no calculations to make with this data, besides converting into into a velocity time graph which Logger Pro does for you.

The equation of this line is X = -0.2019t^2-0.1411t-0.0002758. This is a decreasing quadratic function. In reality, the speed is actually increasing, but because of the orientation of the video, it is decreasing. If we were to flip it over the x-axis, we would see that the increasing position function. This one outlier on the graph is caused by a simple misclick, which doesn't affect the overall formula, because it is one dot out of one hundred.

For this velocity-time graph, it is linear with the equation Vx= -0.09784t-0.3857. Again the position is negative and decreasing because of the orientation of the graph. As velocity is the derivative of position, it makes sense that the velocity graph is linear and the position graph is quadratic.

Evidence to Purpose of Lab:

From this evidence, we can infer that as time increases, a cart going down a ramp will increase the velocity as time passes, making this a quadratic. So we can generalize it for all objects going downhill that their speed will gradually increase as time increases. As a whole, as time passes on a downhill ramp, the acceleration will have an upward slope, causing the velocity to rapidly increase quadratically.

Conclusion:

Overall, this lab taught us a lot about downhill motion and velocity. As time passes on a downhill ramp, the position exponentially increases, causing the velocity line to be quadratic, making the acceleration line to be linerly in the positive direction. With our data, it heads in the negative direction because the orientation of the video is fro right to left rather than left to right. With this negative position, it causes the velocity to be negative, causing the acceleration to be negative. With this unprocessed raw data, we were able to make a velocity time graph, showing us more about the acceleration of the graph. Compared to the Buggy Lab, in which the results of the position time graph were linear, these results are quadratic because we changed one key variable: the incline of the track. Compared to other groups, they also had a negative velocity and acceleration, after facing the same problem as our group. One group had a similar slope to ours, around -0.4, and the two other groups both had slopes close to -1. This is because we both had our ramps set at similar inclines, while the other groups had a bigger incline of their ramps, making the speed bigger.

Evaluating Procedures:

For this lab, we definitely should've switched the orientation of the video before putting it into Logger Pro. For me personally, I could've used fewer data points, as 100 is perhaps too many. I also should've been more careful when plotting the points, as I had several outliers and could've been more precise when placing the other ones.

Improvement:

If I were to repeat this lab, I would use only around 40-50 data points, as well as change the orientation of the video as well as changing the origin point within LoggerPro to make the graph increasing rather than decreasing. I would also take more time to collect the data points, in order to get them as accurate as possible. My graph was not as accurate as others in my group, so I definitely needed to take more time plotting the points.