14-Oct-2016: Work-Kinetic Energy Theorem Lab

Lab 11: Work-Kinetic Energy Theorem
Name: Andrew Martinez,
Lab Partner: Richard Mendoza, Lynel Ornedo, Mohammed Karim

Statement: In experiment 1 the object is to calculate work done by finding the area under the graph. In experiment 2 the objective is to find the spring constant.

Introduction: This lab is divided into two parts called EXPT 1: Work Done by a Non-constant Spring Force and EXPT 2: Kinetic Energy and the Work-Kinetic Energy Principle. The main objective of EXPT 1 is to find the work done by force by using the area and EXPT 2 is to find the spring constant by using graphs.

Apparatus

Cart attached to a spring and placed upon a long horizontal surface. A force probe is placed on the other end of the track to record the force over the distance traveled.

EXPT 1: Work Done by a Nonconstant Spring Force

Procedure
- Calibrate the force probe with a force of 4.9 applied
- Set up the apparatus
- Ensure that the motion detector is able to detect the cart.
-  Open up the file L11E2-2 and zero the force probe. Then begin graphing the force vs position graph as the cart is pushed forced to about .6 m
- Determine the spring constant and explain how
- Use integration routine in the software to find work done by the stretch of the spring.

Data recorded by the software as the cart is slowly pushed towards the force probe. The force probe should be set to reverse direction to plot in the positive x direction. We then use a linear fit to find the spring constant which should be our slope. Slope is 8.828 N/m which is the spring constant. We know that this is true because of hooke's law that states a spring force is equal to the spring constant times its position or F=k*x.

When then use the integration routine to find the work done by stretching the spring which is shown to be .3930 Nm W=F*d or work equals force times displacement but in this case we are using the area under the graph to find the work done by the spring. 

EXPT 2: Kinetic Energy and The Work-Kinetic Energy Principle

Procedure
- Measure the mass of the cart m=.6997 kg
- In new calculated column use a formula to find kinetic energy of the cart at any given point
- Repeat steps in previous experiment for setup
-  Find the change in kinetic energy after the cart is released from the initial to several different positions
- Find the work done by the spring up to those differing positions

Graph Analysis

As shown by the graphs we can find the work done at different positions as well as the kinetic energy

Conclusion: The work done on the cart by the spring shows how kinetic energy changes in relation to work. Since we know that F=k*x and that W=F*d we can see how the change in the kinetic energy of an object is equal to the net work done on the object and thus proves the work-kinetic energy principle.