01 Kinematics - Lab 1 PDF

Preview

Summary

Lab 1...

Description

09/08/2020 PHY 133 Thomas Hemmick Kinematics

Introduction: Kinematics is a topic in classical mechanics that focuses on the motion of points, bodies or systems and the forces around them that causes movement. This lab focuses on the displacement, velocity and acceleration of an object moving on a one-dimensional plane. equations ax= dv  x [accel. = slope of v vs. t] dt 1 v - v0 = ∫ a xdt [Δ velocity = area under a vs. t] 0 vx = dx   [velocity = slope of x vs. t] dt 1 x - x0 = ∫ v xdt [Δ position = area under v vs. t] 0 If these equations are correct, then using the data gathered from the experiments they should be proven correct every time. Procedure: Part 1: 1. Plug the iOLab device into the computer and orientate it so that the wheels are facing downwards towards the surface it's on. The sensor should appear when it is connected. 2. Slide the device back and forth so that it is only moving along the y axis. It should quickly be changing directions while constantly on the move. 3. Highlight the motion of two hits, find the slope of displacement and the average velocity during the same interval. 4. Find the area under one interval of velocity. 5. Find the starting and end points of one interval 6. Find the area under one of the acceleration spikes, and then find the average velocity both before and after. Then calculate the difference between them. 7. Compare the slope of the displacement curve, the change in position to the area under the velocity curve for the same time interval, and the change in velocity to the area under the acceleration curve. Part 2: 1. Make sure the iOLab is connected on the right of the screen and have the z  facing upwards on the table 2. Record ten seconds of the iOLab motionless on the table.

3. Then with the z s till facing upwards, raise it up and drop it onto a soft surface. Results:

Figure 1 Slope of displacement graph.

Figure 2 Area under acceleration spike.

Figure 3 Part 2: graph of dropped iOLab. Calculations: 1. Slope of displacement= 0.50 m/s; average velocity= 0.44 m/s 2. Area under one section of the velocity= -0.22 3. Starting and end point of same interval; 0.441 to -0.602 4. Area of acceleration spike= -1.001; average velocity= -0.602-0.441=-1.043 5. Compare the slope of the displacement curve to the value of the average velocity Δ displacement vs. average velocity: -0.180 vs. -0.122 6. Compare the change in position to the average velocity curve change in position vs. area under curve: 0.083-0.111=-0.028 vs. -0.022 7. Compare change in velocity to area under acceleration change in velocity vs. area of acceleration: -0.602-0.441=-1.043 vs -1.001 Discussion: To calculate the percent error the equation (change in velocity)-(area under acceleration)/(change in velocity)*100. When plugging in the results of the experience ((-1.043)-(-1.001))/(-1.043)*100 you get an error of about 4.03%. The reason for this error to exist in the first place is purely due to an accuracy when calculating measurements of the graph. The results of this experiment pertains close to the originally stated hypothesis. When comparing the values of certain data, there is little percent error which is only due to human error and not a fault in the rules of kinematics. Any further explanations will refer to the equations in the intro. The slope of the displacement is equal to the average velocity, and as seen by the comparison -.180 vs. -.122 is fairly close with a larger percent error of 32.22%. Following that is the proof that the change in position is equal to the average velocity, and when using the comparison of -0.028 vs. -0.022 there is only a percent error of 21.43%. The final piece of data

and closest to proving the initially stated hypothesis is the change in velocity=area under acceleration, which as demonstrated with how to find the percent error is 4.03. When the iOLab device was still for the first ten seconds, the value of the acceleration was zero simply because it wasn't moving. There was no increase in the displacement, velocity or acceleration. When the iOLab device was dropped gravity took over which has a standard rate of acceleration being -9.81 m/s^2....