Cart on a Ramp Lab
9/14/2018
Partners: Dylan Torrey, Charles Stewart
Question: How is the position of a car affected by time as it rolls down an incline?
9/14/2018
Partners: Dylan Torrey, Charles Stewart
Question: How is the position of a car affected by time as it rolls down an incline?
The dependent variable in this lab was the position of a cart on a ramp with the dependent variable being the time elapsed since the cart was let go at the top of the ramp. Variables kept constant include the cart's initial position on the ramp, the incline of the ramp, and the type of cart used, meaning its mass and rolling resistance remained constant.
We decided to use a motion sensor for this experiment because it collects a large number of data points in quick succession, which was essential as the cart rolled down the entire ramp in only a matter of seconds. Because the motion sensor is not dependent on reaction time, only one trial was necessary, streamlining the data collection process. The cart rolled across a specially designed piece of extruded aluminum track, under one end of which was placed an adjustable jack. Because we wanted the incline of the ramp to remain constant, we made sure not to adjust the jack. The motion sensor was placed at the very top of the ramp with the initial position of the buggy in front of it. We were to place the buggy at least 10 cm in front of the motion sensor, as this is the device's minimum range. We activated the motion sensor just as we let the cart begin to roll down the ramp, which recorded the data of the cart's position over the next five seconds directly into Logger Pro.
We decided to use a motion sensor for this experiment because it collects a large number of data points in quick succession, which was essential as the cart rolled down the entire ramp in only a matter of seconds. Because the motion sensor is not dependent on reaction time, only one trial was necessary, streamlining the data collection process. The cart rolled across a specially designed piece of extruded aluminum track, under one end of which was placed an adjustable jack. Because we wanted the incline of the ramp to remain constant, we made sure not to adjust the jack. The motion sensor was placed at the very top of the ramp with the initial position of the buggy in front of it. We were to place the buggy at least 10 cm in front of the motion sensor, as this is the device's minimum range. We activated the motion sensor just as we let the cart begin to roll down the ramp, which recorded the data of the cart's position over the next five seconds directly into Logger Pro.
Time (s) | Position (m) | Velocity (m/s) |
---|---|---|
0.050 | 0.174 | 0.013 |
0.100 | 0.175 | 0.015 |
0.150 | 0.174 | 0.042 |
0.200 | 0.177 | 0.100 |
0.250 | 0.185 | 0.148 |
0.300 | 0.193 | 0.177 |
0.350 | 0.203 | 0.195 |
0.400 | 0.212 | 0.210 |
0.450 | 0.223 | 0.227 |
0.500 | 0.235 | 0.244 |
0.550 | 0.248 | 0.263 |
0.600 | 0.261 | 0.284 |
0.650 | 0.276 | 0.302 |
0.700 | 0.292 | 0.316 |
0.750 | 0.308 | 0.332 |
0.800 | 0.325 | 0.349 |
0.850 | 0.343 | 0.368 |
0.900 | 0.362 | 0.386 |
0.950 | 0.381 | 0.400 |
1.000 | 0.402 | 0.416 |
1.050 | 0.423 | 0.434 |
1.100 | 0.445 | 0.452 |
1.150 | 0.468 | 0.471 |
1.200 | 0.492 | 0.488 |
1.250 | 0.517 | 0.504 |
1.300 | 0.542 | 0.521 |
1.350 | 0.569 | 0.540 |
1.400 | 0.596 | 0.562 |
1.450 | 0.625 | 0.592 |
1.500 | 0.656 | 0.612 |
1.550 | 0.687 | 0.617 |
1.600 | 0.717 | 0.631 |
1.650 | 0.749 | 0.650 |
1.700 | 0.782 | 0.675 |
1.750 | 0.818 | 0.689 |
1.800 | 0.852 | 0.683 |
1.850 | 0.884 | 0.700 |
1.900 | 0.922 | 0.716 |
1.950 | 0.956 | 0.729 |
2.000 | 0.994 | 0.759 |
2.050 | 1.032 | 0.789 |
2.100 | 1.074 | 0.796 |
2.150 | 1.111 | 0.813 |
2.200 | 1.155 | 0.839 |
2.250 | 1.197 | 0.836 |
2.300 | 1.239 | 0.830 |
2.350 | 1.282 | 0.780 |
2.400 | 1.313 | 0.796 |
2.450 | 1.358 | 0.890 |
2.500 | 1.406 | 0.928 |
2.550 | 1.453 | 0.942 |
The motion sensor had an error about 2.5 seconds into recording the data. The recorded position of the cart remained the same even though the cart continued to roll down the ramp. It is most likely that the cart rolled beyond the maximum range of the sensor which would appear to be about 1.5 meters according to the data.
The equation for the position of the cart vs. time is:
The equation for the velocity of the cart vs. time is:
The position of the cart follows a constant acceleration model, represented by a quadratic function. The relationship of the velocity and time, however, lis linear, as the velocity changes at a constant rate. This change is the acceleration of the cart, which is represented by the slope of the velocity-time graph. The A term of the position-time equation represents the acceleration of the cart, as its unit is m/s/s. This is because the term represents meters, so after being multiplied by time squared, the term must be divided by time squared, giving meters/time squared, or m/s/s. While this term is in units of acceleration, the actual acceleration of the cart is twice the A term, as this is the slope of the velocity-time graph.
The B term in the quadratic model represents the initial velocity of the cart. It is nearly zero because the cart starts down the hill from rest. The C term or Y-intercept represents the the initial position of the cart, which is also nearly zero for the same reason. The fact that both of these terms are positive points to the fact that the cart started to roll just before the motion sensor started recording. When the sensor started, the cart would have already moved slightly away from it and gained some speed, accounting for both positive values.
This error is the result of the one element of the experiment that relies on reaction time and the biggest source of uncertainty in the experiment: releasing the cart and starting the motion sensor at the same time. Even if one person drops the cart and starts the data collection, there is a small delay from when the 'collect data' button is clicked to the time the motion sensor starts recording. We had to start the experiment multiple times in order to get used to compensating for the delay. Another source of uncertainty in the experiment was the accuracy of the motion sensor's readings. While we no other data to compare with the motion sensor, it clearly proved itself unreliable for distances over about 1.5 meters as evidenced by the raw data. However, the delay of activating the motion sensor created the most uncertainty. However, this discrepancy could be mitigated by electronically tying the release of the cart to the activation of the motion sensor, possibly with an electric release mechanism.
The B term in the quadratic model represents the initial velocity of the cart. It is nearly zero because the cart starts down the hill from rest. The C term or Y-intercept represents the the initial position of the cart, which is also nearly zero for the same reason. The fact that both of these terms are positive points to the fact that the cart started to roll just before the motion sensor started recording. When the sensor started, the cart would have already moved slightly away from it and gained some speed, accounting for both positive values.
This error is the result of the one element of the experiment that relies on reaction time and the biggest source of uncertainty in the experiment: releasing the cart and starting the motion sensor at the same time. Even if one person drops the cart and starts the data collection, there is a small delay from when the 'collect data' button is clicked to the time the motion sensor starts recording. We had to start the experiment multiple times in order to get used to compensating for the delay. Another source of uncertainty in the experiment was the accuracy of the motion sensor's readings. While we no other data to compare with the motion sensor, it clearly proved itself unreliable for distances over about 1.5 meters as evidenced by the raw data. However, the delay of activating the motion sensor created the most uncertainty. However, this discrepancy could be mitigated by electronically tying the release of the cart to the activation of the motion sensor, possibly with an electric release mechanism.