100 POINTS!
This is a lab experiment:
This study investigates the equilibrium dynamics of a weight attached to a vertical spring and subsequently placed on a smooth incline. Initially, the weight of mass m is attached to a vertical spring with spring constant k, causing the spring to stretch by a distance x0. The system exhibits oscillatory motion with a period T. Afterwards, the weight, while attached to the spring, is transferred to a smooth incline inclined at an angle θ with respect to the horizontal plane. In conducting six tests, each employing a different angle θ, data on the stretch length L and the respective angle are recorded for each test in the investigation. The objective is to analyze the equilibrium behavior of the system in each configuration. This lab ultimately provides insights into the interaction between gravitational forces, spring forces, and the inclined surface.
x unstretched for the spring = 0.142 m
x stretched with mass m for the spring = 0.44 m
Do the following:
-Calculate the L values using the following angles (in degrees): 14, 16, 20, 30, 35, 40, 90
-Make a graph using your measurements, along with the best fit line (+ equation and R^2 value)
-Explain how you used the graph to figure out how L depends on theta.
-Find the %Error based on original L values (in meters): 0.226, 0.238, 0.245, 0.304, 0.324, 0.352, 0.44
A derivation of L and an illustration of the situation is posted below.
