LAB 11 - Work-Kinetic Energy Theorem
Tony Wu, Isaiah Hernandez
October 5, 2016
Experimental Procedure:
Data and Calculations:
The work done is also the integral of the force graph over a distance. The work done in our test run was 1.558 N*m.
Conclusions: The work done on the cart by the spring is equal to its change in kinetic energy. The change in the kinetic energy of an object is equal to the net work done on the object. This fact is referred to as the Work-Energy Principle and is often a very useful tool in mechanics problem solving. We were able to examine the relationship between Force, Work and Kinetic Energy as well as gain a better understanding of springs, Hooke's Law and the Elastic Potential Energy equation.
Lab Goal: To measure the work done when a spring is stretched a measured distance.
Theory/Introduction: In this lab we explore both Hooke's Law ( F = k * x) and the elastic potential energy equation ( EPE = 1/2 * k * x^2 ). Hooke's Law states that the force required to stretch a spring is directly proportional to its displacement. K is the spring constant for a given spring. The value of k varies from spring to spring. The elastic potential energy equation states that potential energy of a stretched spring is proportional to the 1/2 * displacement squared. The Elastic Potential energy formula is used for the problems where displacement, elasticity or elastic force are mentioned. It is expressed in Joules.
Apparatus: Track with force probe and motion sensor. The spring is attached to a vertical rod. The cart has a plate attached to it to ensure that the motion detector is able to read the movement of the cart through the whole test run.
Theory/Introduction: In this lab we explore both Hooke's Law ( F = k * x) and the elastic potential energy equation ( EPE = 1/2 * k * x^2 ). Hooke's Law states that the force required to stretch a spring is directly proportional to its displacement. K is the spring constant for a given spring. The value of k varies from spring to spring. The elastic potential energy equation states that potential energy of a stretched spring is proportional to the 1/2 * displacement squared. The Elastic Potential energy formula is used for the problems where displacement, elasticity or elastic force are mentioned. It is expressed in Joules.
Apparatus: Track with force probe and motion sensor. The spring is attached to a vertical rod. The cart has a plate attached to it to ensure that the motion detector is able to read the movement of the cart through the whole test run.
Experimental Procedure:
We set up the track, cart, spring, and force sensor. We zeroed the force probe with a force of 4.9 N applied. By pulling the cart back a distance x, we determined the value of the spring constant k using Hooke's Law. In order to determine the k value, we had to plot Position (m) vs. Force (N) graph and take the slope of the graph. This gives us the k value because Hooke's Law is a linear line fit.
Y = m * x
F = k * x
m = k
The value of k for our spring was 8.417 N/m. The mass of our cart was 0.752 kg. We created a new Calculated Column in Logger Pro in order to calculate the kinetic energy of the cart at any point. Be sure to zero the motion detector and the force probe.
Y = m * x
F = k * x
m = k
The value of k for our spring was 8.417 N/m. The mass of our cart was 0.752 kg. We created a new Calculated Column in Logger Pro in order to calculate the kinetic energy of the cart at any point. Be sure to zero the motion detector and the force probe.
We stretched the cart and spring and began graphing in Logger Pro. Our graphs had Position (m) vs. Force (N) and Position (m) vs. Kinetic Energy (J). These graphs allow us to calculate the work done by the spring and the kinetic energy of the cart at any given position. The work done by the spring is simply the area under the curve of the Position vs. Force graph.
Data and Calculations:
The work done is also the integral of the force graph over a distance. The work done in our test run was 1.558 N*m.
Position (m) vs. Force (N) and Position (m) vs. Kinetic Energy (J)
Conclusions: The work done on the cart by the spring is equal to its change in kinetic energy. The change in the kinetic energy of an object is equal to the net work done on the object. This fact is referred to as the Work-Energy Principle and is often a very useful tool in mechanics problem solving. We were able to examine the relationship between Force, Work and Kinetic Energy as well as gain a better understanding of springs, Hooke's Law and the Elastic Potential Energy equation.
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