Lab 11: Work-Kinetic Energy Theorem; Lab Partner: Jamie Lopez; 10-14-16

2) In these two experiments of Work-Kinetic Energy Theorem, we will measure the work done when an object attached to a spring stretched goes through a measured distance and how the work done by the spring is related to the kinetic energy of the object.

3) First we will begin the experiment of what Work is. Work is a quantity measurement of how far an object travels from an external force. It is the product of the force magnitude F and the displacement s or x.  The unit of work is measured in Joules (J) or N*m.  In order to graph this to get an intuitive understanding, let's demonstrate Force vs Displacement graph and how it equals to work.
The shaded region under the equation is the quantity of Work done by an object.

4) In our experiment, our apparatus will be set up with a ramp, cart, motion detector, force probe, and a spring. The spring will be our force apparatus to find how much work is done while the cart moves from its' initial position to its' final position. The force probe sensor attached between the spring and the cart will give our software a reading of how much force was used over a distant interval. The motion detector reads the object's movement of how far or close the object is.

5) For a better understanding of our data point, imagine the force vs displacement graph is similar to y vs x graph. The graph represents a linear equation of y=mx+b. The slope of the graph is the spring constant from our spring apparatus. The data shows the slope is 8.108N/m. The y-intercept should be zero and is close to zero, but of course, due to human error of our response time when the test experiment starts, the y-intercept is 0.05671N. Here is another demonstration why the spring constant graph is a linear slope. 

6)

7) The pink shaded region under the graph is the area of work done to the cart. The work done to the object from the spring is 0.8191 J or N*m. Another way to find work done to the cart is integrating the force and the distance. .

8) Our prediction of finding work done to the object is 0.8209 J or N*m. Our prediction was pretty close of finding Work comparing to the results the software read. Our percentage error is off by 1 percent, so its pretty close.

9) On the next experiment, we will demonstrate how the work done is related to the change of kinetic energy. Kinetic energy is a scalar quantity, it depends on the particle's mass and speed. We convert the force that is applied on the object to mass and acceleration. Here is the conversion using kinematic equations and assuming acceleration is constant.

So with the formula provided, we will prove the work done on the cart will be equal to the change of kinetic energy.

10) We used the same apparatus to in this experiment except our initial position of the cart will be close to the motion sensor with the spring stretched 0.6 meters. When we let go of the cart, the kinetic energy will be greater than zero because the force of the spring is pulling back to its' equilibrium state. After the spring reaches equilibrium state, it will then become compress and the force will now push the cart to the opposite of its direction.

11) According to the data, here is what our assumption our results will be. 
The area of work done will be equal to the change of kinetic energy.

12) After recording our experiment, the graph represents the work done to the cart and the kinetic energy during the object's movement. We chose an area between the points to see if it matches our calculations. Our initial position will start at 0 meters and final position will be 0.379 meters. The spring constant is still the same value according to the past experiment.

13) Our assumption came close to the answer we received. The kinetic energy the lab read is 0.675 Joules. Our spring constant was suppose to be 8.108 N/m. Perhaps a human error was caused during the test but still pretty close. After all, our experiment proves how the work done to an object is related to the change of kinetic energy.