_Acceleration and Circular Motion (Lab Report 2)
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Acceleration and Circular Motion Lab
Sophia Tran
October 25rd, 2023
Physics 1301W, Professor: Dr. Dan Cronin-Henessey, TA: Evan Skinner
Abstract
In this experiment, the purpose was to relate the acceleration and circular
motion of a mass to a spring constant. This showed scientists that if they spun
the mass attached to the spring in a circular motion causing circular
acceleration the mass would cause the spring to stretch. In this experiment,
the magnitude of the hanging mass vs. the stretched length was 6.53N/m with
an uncertainty of ± 0.035m. The calculated spring constant (k) was
0.0245N/m with an uncertainty of 0.049m, this value was taken from the
angular velocity^2 graph. After analyzing the data they concluded the
relationships were linear.
Introduction
Hypothetically, scientists used a spring catapult that uses circular
motions to a launch ball. What is the relation between the ball’s mass and the
spring constant from the catapult? Scientists put the mass of the ball in a tube
on a rotating platform that is hooked onto the spring from the catapult to
calculate the relationship. They did that by measuring the mass and
measuring the stretched length of the spring.
Procedure
The setup of this lab was a tube zip-tied to a rotating platform, within
that tube there was a spring attached to a stationary object, and the other side
of the spring was hooked onto a mass. This way as the platform rotates the
mass slides away from the spring causing the spring to stretch. They then
took videos of the platform rotating for multiple time intervals with four
different masses. Then used Vernier Video Analysis to further analyze and
measure data points. Using the software's data, they made the weight vs.
spring stretch length graph. The slope from said graph would be the predicted
spring constant (k). With the predicted k they were able to get the X/R ratio
by dividing k by the radius squared of the circular motion. Afterward, find ω²
using (2p
𝜋
/Δt)². Using those values to make a graph showing the
relationship between the X/R ratio and the ω². The slope of that graph will be
the calculated spring constant (k). The position uncertainty is the length of
the spring when it is unstretched. To determine X/R uncertainty, find the
maximum of the following equation: (Spring length
土
position
uncertainty)/(radius
土
position uncertainty). A possible error could be skewed
data plots on Vernier Video Analysis, causing inaccurate data for graphs
resulting in uncertainties in the calculated spring constant (k). Another
possible cause of error could be the lack of calculation for friction.
Analysis
(Figure 1)
Vernier data plot at weight vs. Distance stretched, the slope of the
line of best fit was y=6.53x+0.0897, meaning the predicted spring constant
was 6.53 N/m with an uncertainty of
土
0.035m.
(Figure 2)
Vernier data plot at X/R ratio vs Angular Velocity Squared,
the slope of the line of best fit was y=0.0245*x+0.489, meaning that the m/k
was 0.0245 with an uncertainty of
土
0.489
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