Silas Clark
Moses Cooper
Robert Cornwell
Miriam Conde
General Physics with Calculus Lab 2 Report
Q1-Q4
Q5
Q6
Q7
The model a = g*sin⁡(θ) predicts a linear relationship between acceleration and the sine of the
incline angle. In the model, 9.8 would represent the variable m, sin(θ) would represent x, and b
would be 0. Our initial plot of a vs. θ was curved, indicating a nonlinear relationship. After
linearizing by plotting a vs θ, the data fit a straight line with a slope of 0.1245x, a y-intercept of
0.9334, and an R^2 value of 0.9729. This linear correlation supports the theoretical model,
establishing the connection that acceleration increases proportionally with sin(θ).
Q8
The experimental value g was found to be 7.3 m/s^2 by taking the arcsine of the slope 0.1245x
and using the point slope formula to calculate the slope. The experimental slope is close to what
we expected because in reality, as the slope approaches 0, acceleration also approaches 0, but our
trendline approaches 0.9334. The y intercept of the trendline does match what we would have
expected for the model because our gravity coefficient is less than what the real gravity
coefficient is.
Q9
Our group explored the relationship between acceleration and the angle of the incline. We
acquired data on acceleration for multiple incline angles, recorded our data in Excel, and then
analyzed the results using both graphical and mathematical methods. We first plotted
acceleration versus angle and observed a curved relationship, suggesting that the data were not
linearly related. Plotting acceleration against sin⁡(θ) produced a straight line with a slope close to
9.81 m/s^2, confirming that acceleration increases proportionally with the sine of the incline
angle.
Q10
Miriam: This lab helped me understand how linearization reveals physical relationships in
motion data that aren’t obvious from curved plots. Turning the position-time data into a straight
line made it much easier to confirm constant acceleration. I still wonder how much experimental
error or friction affects the linearity of that plot. I feel fairly confident using Excel for calculating
uncertainty and doing linear regressions now. Our group worked well by checking in with each
other and keeping communication open, which helped us work through tough spots in the lab.
Silas: This lab showed me how linearizing data that would usually appear as exponential makes
it easier to understand the data I’m looking at. I don’t fully understand what velocity uncertainty
means in the context of the data, and I am still confused why the LINEST() function didn’t work
like it showed in the lab instructions. Other than that, I am confident in my Excel skills. This
week, our group made sure to be much more proactive in our group chat, and we scheduled more
times to work together on call.
Moses: This week I learned how linearization can be used to analyze data and identify
relationships between variables. I don’t have any unanswered questions, though much of the
material is still new to me. I’m becoming more comfortable using Excel, but I’m still learning
how to use the LINEST() function effectively. Our group did a great job communicating our
availability and questions, which helped keep everyone involved and on track.
Robert: This week in lab 2 I learned how multiple data points can change your data and scatter
plots. I don't have any unanswered questions.I need to watch the excel help videos and get more
comfortable with putting data in for angular velocity and uncertainty. We all have busy schedules
so us being able to communicate well has helped a lot with group projects. Whenever ive had a
question about excel or what the lab is about I have gotten solid answers from my group..
Q11
In this experiment, we analyzed the relationship between acceleration and angle of
incline. Using position data collected from multiple detectors, we calculated the velocity and
acceleration of the cart and examined how the measured acceleration compared to theoretical
predictions. The main goal was to determine the experimental acceleration, its uncertainty, and to
evaluate whether the measured data supported the theoretical model. For this lab, we did not use
any physical materials, and we used Excel for our calculations. The slope of the linearized graph
was 0.1245x, and it was close to what we expected due to the variability of our tests. The
acceleration vs angle table best communicates our findings. When each group member’s
acceleration values were compiled, the combined acceleration vs. angle dataset revealed a clear
increasing trend, showing that acceleration rises as the incline angle increases. Our group’s data
was approximately linear, the trendline was close to the actual coefficient for gravity, it passed
near the origin, and overall supported the model.The data supported the expected model because
the slope was close to the expected slope.