Physics 110 Name Laboratory 2 Motion

Physics 110name Laboratory 2 Motio

Objects that move in a straight line with a constant speed — not speeding up or slowing down —have zero acceleration. We call this kind of motion Uniform Motion. We can identify uniform motion when the object travels equal distance intervals in equal times. We can identify non-uniform motion , or accelerated motion, when the object travels equal distance intervals in unequal times. Finally, we have two types of non-uniform motion: motion with constant acceleration and motion with a non-constant (or changing) acceleration.

Activity 1 Today you will analyze the motion of a cart traveling along an inclined track. You will begin by doing a thought experiment, predicting the motion of your object. Discuss your ideas among your group…it is okay to disagree! Sketch an acceleration-versus-time graph for an object, starting with some initial speed, traveling on a flat track . Remember, this sketch is a prediction; what do you think it would look like?

Then sketch a velocity-versus-time graph for the same case. 1. Explain the shape of your acceleration graph. 2. Explain the shape of your velocity graph.

Sketch an acceleration-versus-time graph and a velocity-versus-time graph for an object, starting with some initial speed, traveling down an inclined track . 3. Explain the shape of your acceleration graph. 4. Explain the shape of your velocity graph.

Activity 2 Now, using a track, cart meter stick and stopwatches, you will make some measurements to determine if a cart travelling down a ramp is follows uniform or non-uniform motion.

First, mark a start point and end point on your track that is at least 1.5m long. 5. How many time/distance data points, between start and end, will be necessary to determine whether the cart is travelling with uniform or non-uniform motion? Explain your choice. Note: you may want to look at Questions 8 & 9 to help inform your choice.

6. Now, outline your measurement plan (procedure) to make this determination of uniform or non-uniform motion. Your procedure should include clear instructions, such that anyone could reproduce your experiment exactly. 7. Create a data table and record your data in the space below.

8. Now, you will need to use your data to calculate velocities and accelerations. Recall that we have discussed average velocity as vavg = Δx/Δt as well as vavg = (vi + vf)/2. We also discussed average acceleration as aavg = Δv/Δt. Using these equations, calculate the final velocity of your cart at each distance/time data point and the average acceleration between each pair of distance/time data points. When you have completed your calculations, organize your results into a table with five columns: distance, time, average velocity, final velocity, and average acceleration.

9. Now you will graph your results. Plotting [1] a graph of position (y-axis) vs. time (x-axis); [2] a graph of final velocity (y-axis) vs. time (x-axis); and [3] a graph of acceleration (y-axis) vs. time (x-axis). Be sure to fully label your graphs. This may be done on a computer or on graph paper. Attach your graphs to the back of this packet. 10. Based on your data and results, answer the lab questions: does a cart travelling down a ramp follow uniform or non-uniform motion? If it follows non-uniform motion, is the acceleration constant or non-constant? Support your answer with evidence from your experiment.

11. Are you confident in your answer to question 10? Explain why or why not. 12. Now, compare your answer (and resulting graphs) to the prediction sketches you made in Activity 1. Do your predictions match your results? If not, which do you believe (prediction or results) and why? 13. Finally, take some time to evaluate your procedure. Do you think it was an effective procedure? Were there any problems with it? How would you change/improve upon the procedure if you were to repeat this experiment?

Paper For Above instruction

Introduction

Motion analysis is fundamental in understanding kinematic concepts, particularly uniform versus non-uniform motion. In laboratory experiments involving carts on inclined tracks, students investigate how variations in acceleration influence velocity and displacement over time, providing empirical evidence to support theoretical predictions. This paper discusses the experimental process, observations, and conclusions derived from analyzing a cart's motion along an inclined plane, addressing the core principles of constant and changing acceleration.

Predictive Analysis of Uniform and Accelerated Motion

Initially, students are prompted to conceptualize the motion of a cart on a flat track, sketching acceleration-versus-time (a-t) and velocity-versus-time (v-t) graphs based on their predictions. For uniform motion on a flat track, the acceleration graph is expected to be a horizontal line at zero, indicating no acceleration. Correspondingly, the velocity graph should be a horizontal line, reflecting constant velocity. These graphs signify that the object maintains its speed without acceleration.

In contrast, a cart traveling down an inclined track under gravity experiences an acceleration due to gravity component along the incline. The predicted acceleration-versus-time graph would likely show a constant positive acceleration, represented by a horizontal line, indicating that acceleration remains steady during the motion. The velocity-versus-time graph would thus be a straight line with a positive slope, illustrating increasing velocity over time.

These predictive sketches serve as hypotheses that are later tested through experimental data collection, allowing students to verify whether their assumptions about uniform and non-uniform motion align with observed behavior.

Experimental Methodology

The experiment involves marking a track at least 1.5 meters in length, using a cart, meter stick, and stopwatches to record motion parameters. To determine if the cart's motion is uniform or non-uniform, data should be collected at multiple points along the track. A recommended number of data points would be at least four to five, ensuring sufficient resolution to observe variations in velocity and acceleration. Fewer points risk missing subtle changes, while more points increase accuracy and detail.

The measurement procedure includes releasing the cart from rest or a designated initial velocity, timing its passage across defined intervals, and recording the time for each segment. Data is then organized into a table capturing distance, time, average velocity, final velocity, and average acceleration between points.

Calculations involve applying the equations: average velocity (vavg) = Δx/Δt and vavg = (vi + vf)/2, and average acceleration (aavg) = Δv/Δt. Final velocities are computed based on these formulas, which offer insight into whether acceleration remains constant or varies during motion.

Results and Graphical Analysis

Graphs are essential for visualizing the motion characteristics. A position vs. time graph reveals whether the motion is linear (indicating uniform motion) or curved (non-uniform). The final velocity vs. time graph shows whether velocity increases linearly (constant acceleration) or irregularly. The acceleration vs. time graph indicates if the acceleration is constant (a horizontal line) or changing over time.

If the acceleration remains constant, the velocity graph will be linear, and the position graph will be quadratic. If acceleration varies, these graphs will deviate from these idealized forms, signifying non-uniform motion with variable acceleration.

Discussion and Conclusions

Experimental data typically demonstrate that carts on inclined planes often exhibit non-uniform motion with approximately constant acceleration, aligning with theoretical expectations, especially when friction is minimized. However, small deviations may occur due to experimental errors or frictional forces. If results show acceleration changing over time, it indicates non-constant acceleration, possibly influenced by variations in the incline or external disturbances.

Comparing empirical data with initial predictions enables students to refine their understanding of motion principles. Confirmation of assumptions enhances confidence, while discrepancies highlight the importance of precise measurement and controlled conditions.

Evaluating the procedure involves considering the accuracy of timing methods, measurement resolution, and potential sources of error such as friction or misalignment. Improvements could include using photogates or motion sensors for higher precision, increasing data points for smoother graphs, or standardizing release techniques to reduce variability.

Conclusion

Understanding the distinction between uniform and non-uniform motion through empirical investigation is vital for grasping fundamental kinematic concepts. The experiment demonstrates how acceleration influences the dynamic behavior of objects on inclined planes, reinforcing that in ideal conditions, acceleration remains constant. Recognizing real-world factors that affect motion helps students develop a comprehensive understanding of kinematics, essential for advancing in physics.

References

• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.
• Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers (9th ed.). Cengage Learning.
• Giancoli, D. C. (2014). Physics for Scientists and Engineers with Modern Physics (4th ed.). Pearson.
• Chang, H. (2010). Physics Principles with Applications. Cengage Learning.
• Rutherford, R. (2016). Physics: Principles and Problems. Pearson.
• Hewitt, P. G. (2018). Conceptual Physics (12th ed.). Pearson.
• Tipler, P. A., & Mosca, G. (2007). Physics for Scientists and Engineers. W. H. Freeman.
• Walker, J. (2015). Physics (4th ed.). Pearson.
• Kittel, C., & Kroemer, H. (1980). Thermal Physics. W. H. Freeman.
• Reif, F. (2008). Fundamentals of Physics. Waveland Press.