Free fall is defined as the ideal falling motion of an object that is subject only to the earth’s gravitational field. To prove the law of conservation of energy, the free fall motion of an object can be represented through 3 different analyses; position of the object vs. time, velocity of the object vs. time, and acceleration of the object vs. time. It is observed in this ball toss experiment, at any point during the free fall period, the system contains the same total amount of mechanical energy. This amount is the sum of kinetic and gravitational potential energy.
FREE FALL AND THE CONSERVATION OF ENERGY
The law of conservation of energy states that the total amount of energy remains constant in an isolated system – energy can neither be created or destroyed, but can change from one form to another. In this analysis, a ball is thrown above a motion sensor and data is collected for distribution into 3 graphs; position of the ball vs. time, velocity of the ball vs. time, and acceleration of the ball vs. time. The purpose is to prove the law of conservation of energy during this free fall of the object. It should be understood that to prove this law, the experimental value of ‘g’ (for gravity) as solved in x=v₀t+½gt² should be comparable to the gravitational constant of 9.8 m/s². The law of conservation of energy relates to real-life situations, such as when a tennis ball goes from hitting one racquet to another, or when a construction crane swings a wrecking ball into a building. The total energy in these systems remains constant, even though it seems energy is “lost” – in which it is not lost, but changed from kinetic to potential or vice versa.
* Computer (MAC OS)- Vernier Computer Interface- LoggerPro Software * Vernier Motion Detector- Basketball
1. Connected the Vernier Motion Detector to the DIG/SONIC I channel of the interface, and set the detector to Normal. 2. Set up the data collection interface using the LoggerPro software experiment “06 Ball Toss” 3. Held the ball directly above the Motion Detector and started the data collection 4. Listened for Motion Detector response and tossed ball directly upward, immediately moving hands away from the motion detector. 5. Caught ball above Motion Detector.
6. Ended data collection and stored graph.
7. Repeated steps 3-6, four more times to obtain a total of 5 different analyses. 8. Weighed ball
9. Analyzed graphs using software to determine best curve fit, best linear fit, best statistics
OBSERVATIONS – Experimental Data
Trial 1:Trial 2:
Trial 3:Trial 4:
OBSERVATIONS – Graph Analysis
Initial Values for Position, Velocity and Acceleration (taken from graph) | ‘y’-Position (m)| ‘v’-velocity (m/s)| ‘a’-acceleration (m/s2)| Trial 1| 0.223m| 0m/s| 0m/s2|
Trial 2| 0.279m| 0m/s| 0m/s2|
Trial 3| 0.229m| 0m/s| 0m/s2|
Trial 4| 0.285m| 0m/s| 0m/s2|
Trial 5| 0.255m| 0m/s| 0m/s2|
*** The ball had very minimal values for acceleration and velocity before it was tossed – Therefore the values are assumed to be zero. Values for Position, Velocity and Acceleration (as per determined points A, B and C on graphs) Trial| yA (m)| yB (m)| yC (m)| vA (m/s)| vB (m/s)| vC (m/s)| aA(m/s2)| aB(m/s2)| aC(m/s2)| 1| 0.331m| 0.350m| 0.333m| 0.606m/s| 0m/s| -0.576m/s| -9.576m/s2| -9.625m/s2| -9.284m/s2| 2| 0.590m| 0.700m| 0.591m| 1.471m/s| 0m/s| -1.412m/s| -9.409m/s2| -9.403m/s2| -8.915m/s2| 3| 0.728m| 0.855m| 0.725m| 1.573m/s| 0m/s| -1.587m/s| -10.113m/s2| -10.183m/s2| -9.775m/s2| 4| 0.710m| 0.847m| 0.689m| 1.623m/s| 0m/s| -1.741m/s| -10.229m/s2| -9.903m/s2| -9.808m/s2| 5| 0.466m| 0.605m| 0.449m| 1.636m/s| 0m/s| -1.700m/s| -9.726m/s2| -9.555m/s2| -9.168m/s2| *** - The values of position for A & C are...