Purpose:
The purpose of this lab is to determine the relationship between work and kinetic energy based on measurements of force and distance traveled.
Theory:
Work is represented by the equation W=Fx where a force F acts parallel to some displacement x. Work is also a measure of the change in the internal energy of an object where work done on an object increases its internal energy and work done by and object decreases its internal energy. If the gravitational potential energy of an object is held constant by maintaining the same height relative to its initial position, the work done on an object can be assumed to approximately equal the change in kinetic energy if losses in energy due to non-conservative forces are minimal. In a similar way, work is also equal to change in spring potential energy where if gravitational potential energy and kinetic energy are held constant, the work done on a spring is equal to the change in spring potential energy.
Apparatus:
- Low friction cart and track
- Low friction pulley
- String
- Force sensor
- Motion detector
- Digital scale
- 100g mass (1)
- Small spring
Procedure:
Attach the force sensor to the cart and point the motion detector towards the cart's direction of motion. Zero the force sensor. Simulate a constant force by hanging a 100g mass from a string attached to the force sensor and produce graphs of force and velocity over time. Calculate values for kinetic energy according to the equation KE=1/2mv^2 and layer a graph of kinetic energy over a graph of force. Taking the integral of the force graph should produce the calculated value of kinetic energy at the given time interval. Conduct this setup and graphical analysis again for a system where instead of the 100g mass, a spring is attached to the force sensor and anchored at the other end and the cart is slowly pushed at a constant velocity. Again, the integral of the graph of force vs time should equal the predicted spring potential energy. The third setup will be identical to the second, however instead of slowly moving the cart, the cart is to be pulled to some distance, stretching the spring, and is then to be released. Repeat the same process of graphical analysis.
Data and Graphs:
Mass of the cart: 0.667kg
Photo of first experimental setup
Photo of data collected from first experiment
Graphical analysis using integrals of force as a function of time
Experimental setup for 2nd and 3rd experiments
Graphical analysis of data from 2nd experiment
Data Analysis:
Graphical analysis was carried out as described in procedures. Integrals of force vs time were taken and compared to calculated values for kinetic energy.
Conclusion:
In the first experiment, calculated kinetic energy and integral of force were taken at two different times. For the first selected time, the integral of force was 0.141J while the calculated kinetic energy was 0.130J. At the second selected time, the integral of force was 0.219J while the calculated kinetic energy was 0.196. This difference is most easily explained by the presence of friction forces which were assumed negligible for our experiment. This is because while the total force acting on the object remains mostly constant, some energy is lost as heat due to friction and thus lowers the actual velocity and kinetic energy of the object. For this experiment, a value of kinetic energy produced by the integral of force is considered the "true" value of kinetic energy if our system satisfied our assumptions. The value of kinetic energy calculated from position vs time is then the actual value which accounts for friction and any other counteracting forces. Similar results were obtained for both other experiments. Based on the overall results, work appears to be directly related to change in kinetic energy under conditions where all other internal energies of the object are held constant.
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