Velocity and Acceleration Lab results.pdf
- 1. Introduction: Overview ● In our Lab 1 experiment, we focused on studying the fundamental concepts of velocity and acceleration using a fan cart setup. our experiment consisted of three different cases: Uniform Velocity (Case I), Uniform Acceleration-1 (Case II), and Uniform Acceleration-2 (Case III). ● In Case I, the fan was deactivated, and the cart received an initial push. The motion sensor tracked position and velocity, demonstrating uniform velocity and establishing a linear relationship between position, velocity, and time. Case II involved positioning the cart, activating the motion sensor, turning on the fan, and releasing the cart—representing motion under uniform acceleration due to gravity. The collected data allowed for the analysis of acceleration and displacement. In Case III, the fan was initially turned off, and the cart received a quick push in the opposite direction before the fan was turned on, introducing a scenario of uniform acceleration.
- 2. Introduction: Equations ● Equation 1: x(t) = x0 + v0 t + .5a*t2 ● Equation 2: v(t) = v0 + a*t Key: - Equation 1 or x(t) is position in relation to time. - Equation 2 or v(t) is velocity in relation to time. - x0 is the initial position of the object (in meters). - t is the selected point in time (in seconds). - a is the acceleration of the object (in meters per second squared or meters per second per second). - v0 is the initial acceleration of the object (in meters per second).
- 3. Lab Description: Apparatus ● Our experiment consisted of a flat table in which we had a base track. ● To perform the experiment, we had a battery powered car that ran on the track and was moved by a large fan attached to itself that moved the car in different directions, opposite to which direction the fan was pointing. There were also different speeds on the fan for different velocities the car could travel. ● In order to measure the data, there was a sensor on one side of the track that sent out sonic waves and measured the waves that bounced off our fan-car. The disparity in waves sent out and when they were received over a period of time gave us accurate data to graph velocity over time. ● We ran the program Pasco Capstone, which took all the data collected from the sensor and graphed it for us.
- 4. Lab Description: Diagram ● The Gray figure is the table. ● The Yellow shape is the ramp. ● The Red cube is the sensor. ● The Aquamarine cylinder is the car’s body. ● The Green oval is the car’s fan. Diagram 1
- 5. Lab Description: Procedures ● Carrying out the experiment we had a fan cart placed at one end of the ramp and when ready we would turn on the motion sensor on our computer using pasco capstone. The pasco capstone software was very ideal for recording the motion of the fan cart. Once we turn on the motion sensor another experimenter pushes the fan so that it moves across the ramp. ● We made 2-3 recordings for the each case and then we made crucial comparisons of data. The different cases of the experiment produced different shaped graphs like when we switched on the fan it changed the results we obtained from pasco capstone.
- 6. Data: Case I, Uniform Velocity Figure 1.a Figure 1.b
- 7. Data: Case II, Uniform Acceleration-1 Figure 2.a Figure 2.b
- 8. Data: Case III, Uniform Acceleration-2 Figure 3.a Figure 3.b
- 9. Analysis: Case I Through a thorough look at Figure 1.a, it is obvious that there is a linear relationship between position and time. Shown more effectively in Figure 1.b through use of the line tool, there is a more effective comparison, highlighting both the strait, proportional, relationship, as well as, even giving an estimated velocity in the form of the equivalent of the variable m (.823 meters per second). If that were to plug into either Equation 1 or 2, m would represent v0 , as there is no acceleration in Case I, due to acceleration preventing an object from having uniform velocity. The constant increase in distance over time supports that the velocity is positive. Finally, there is some room for error in the equation provided by PASCO Capstone, but the value is so small, it’s insignificant in how the graph and data turned out.
- 10. Analysis: Case II and III Similar to the data analysis of Case I, the analysis of Case II and III all comes down to the data graphed by the program PASCO Capstone. Both Figure 2a and Figure 3a demonstrate an obvious curve which is highlighted more in Figures 2b and 3b respectively. Considering that in Case I, a linear relationship implies a uniform velocity and a lack of acceleration, the curves on both these graphs show the effect of acceleration on movement. Further, both of these Figures line up perfectly with parabolas that were assigned to them, supporting that the acceleration was, in fact, uniform. There were no significant outliers from when the object started moving to when it stopped. Additionally, taking the values for the variable A in Figure 2b and 3b, and coinciding it with acceleration in Equation 1, we can conclude that the acceleration for Case II and III were .338 meters per second per second and -.598 meters per second per second respectively. The way Figure 2a slopes up supports the positive acceleration, and the way Figure 3a opens downward supports the negative acceleration. Once again, there is some room for error in the equation provided by PASCO Capstone, but the value is so small, it’s insignificant in how the graph and data turned out.
- 11. Discussions The experiment was simple to carry out and it didn't use to many apparatus and it helped to record motion of small car using motion sensor. It puts a lot if understanding in what we learned in class relating to motion and kinematics. It was difficult to balance the ramp so that the fan cart is not slanted and moves in straight motion and we did have to familiarize ourselves with apparatus especially the software. The sources of error may have come from the unevenness of the ramp it would have affected the movement of the fan cart across the track and possibly make it move faster or slower. Overall the graphs were evidently differentiable from one another which helps support our case for the velocity and acceleration of the cart. For case 3 the graph displayed parabola to show uniform acceleration and case 1 was a straight line which showed the uniform velocity of the fan cart.
- 12. Conclusion Case I demonstrated that without a significant constant force acting on an object to alter its movement (the fan), the velocity applied to it will stay relatively constant. That’s shown well in Figure 1a, with the relationship between time and distance being linear. Cases II and III demonstrated the effect of constant acceleration on an object of no initial velocity and some initial velocity. Case II in particular had the fan providing constant acceleration which allowed it’s graphed distance and time in Figures 2a and 2b show not a linear relationship, but one resembling near half of a parabola. Case III was the most unique of the cases. It took the same idea of acceleration from Case II, but added an initial velocity that was, in turn, counteracted by the acceleration. The cart was pushed with the fan pointed in a way it acts as a counter force to the push, and in Figures 3a and 3b, you can see the slope or velocity of the line decrease as the acceleration works on it until the distance reaches a maximum and the cart makes its way back to where it started, accelerating all the way.