30- Sept - 2014 Work and KE Lab

Work and KE Lab

Objective:

 Show that the change in work equals to the value of Kinetic Energy at that point in position.

Set- Up: 

Figure 1a. Our apparatus set up at a top view

 We had a set up with a motion sensor and a force sensor plugged into labber pro for this lab. We also had a cart. aluminum track, a spring, a block for mass, a block for leveling the spring and rods with clamps to hold the force sensor in place as seen in (fig 1a- 1b).

Data Collection:

 After we had set up our apparatus, we reset both sensors to zero when the spring was at a relaxed state. Then, we reversed the motion sensor setting to toward the sensor is the positive direction. We then stretched the spring between 20 cm to 30 cm. When data collection began, the cart was released and the spring pulled the cart away from the sensor. 

Our readings were shown initially as a velocity graph and a force graph. We took the force graph and changed the time axis into position. Using 

KE= (1/2) mass* (velocity)^2

Figure 1b. apparatus set up at a side view

we inserted a kinetic energy graph with a x-axis of position along with the force vs. position graph. Now as seen in (fig 2.)

We integrated our Force graph to find a change in work and compare our integration with our KE values to see if they matched.

Theoretical Value= .413 N*m

Experimental Value= .378 N*m   

.378 * 100% = 91.523%

.413                                

 Apparently the target value for our integral is higher than our KE value at that point in position by approximately 8.477%. 

Conclusion:

 What may be the main source of our 8.477% error is that the spring may not have had a spring constant that applied to the entire spring since some parts are more tightly coiled than other places in a relaxed state, or the spring was not ideal. With that in mind, our results were close enough to show that the concept holds water and completes our lab objective.

Figure 2. Our resulting integral of the change in work in an interval between different points in position.

Figure 3. Our row where our target value of KE is found
unfortunately it does not match our work integral.