Theory: Impulse is equal to the force of the cart integrated with respect to time, on a graph this can be presented as the area underneath a line on a force vs. time graph. Impulse is also determined by the change in momentum (Pf-Pi), so if we set an apparatus to measure the force of an elastic collision over time, and measure the change in velocity after the collision (P=Mass*Velocity) and compare the two, they should be the same. For an inelastic collision
Procedure:
*Experiment 1: Set up an apparatus of a track, a cart with a force gage on the front and a rubber stopper attached to the gage, a velocity sensor pointing down the track, and another cart fastened to the table with a spring to simulate an elastic collision for the rubber stopper to bounce off of during the collision. Determine mass of the cart. Push the cart so it moves towards the cart with the spring, after the collision, integrate the force graph with respect to time, and find the velocity of the moving cart before and after the collision. Calculate the change in momentum and compare it to the Impulse determined by the integration of the force graph.
*Experiment 2: Repeat Experiment 1 with extra mass added to the moving cart, and note any differences from the results.
*Experiment 3: Replace the cart with the spring with a wood block with clay attached to it, add a nail to the moving cart so it will stick to the clay on collision. Note any difference in impulse determined by integration and change in momentum in comparison to the previous experiments.
Apparatus
Experiment 1
Graph Force vs Time and Velocity vs Time
*The area of the force shape and the horizontal axis (the integral) is 0.8923
*Mass of the cart 0.727 kg
*Velocity before collision -0.61 m/s
*Velocity after collision 0.6019 m/s
*The calculation:
Impulse= Mass*Velocity_After - Mass* Velocity_Before
Impulse= (0.727)*(0.6019)-(0.727)*(-0.61)
Impulse= 0.4376+4435
Impulse= 0.8810 kg*m/s
*The calculated Impulse and the Impulse determined from the force graph ((0.8923-0.8810)/0.8923 * 100%) have only a 1.1% percent error between the two.
Experiment 2
*We added 0.3 kg to the moving cart
Graph
*The area of the force shape and the horizontal axis (the integral) is 0.8530
*Mass of the cart 1.027 kg
*Velocity before collision -0.4680 m/s
*Velocity after collision 0.385 m/s
*Calculation was done as before and Impulse determined to be 0.876031 kg*m/s
* 2.7% difference from impulse of force graph.
Experiment 3
*This will be an inelastic collision due to the nail and clay on the cart and wood block replacing the spring cart
*The area of the force shape and the horizontal axis (the integral) is 0.2715
*Mass of the cart 1.027 kg
*Velocity before collision -0.2647 m/s
*Velocity after collision 0 m/s
*Calculation was done as before and Impulse determined to be 0.2718 kg*m/s
* 0.13 % difference from impulse of force graph.
Conclusion
*The difference between the calculated impulse and determined impulse was minute, so the Impulse momentum theorem seems confirmed.
*The inelastic was a sharp spike that was a smaller value than the elastic collisions, I understand mathematically why this is the case (a zero value for the final velocity resulted in only the initial velocity being considered in determining Impulse), but not fully understanding conceptually why this is. Perhaps because the force that would have "pushed back" on the cart was "lost" into the greater system of the block, the table, and the rest of the Earth.
*Sources of error for the experiment are, it doesn't take into account friction between the cart and track or from air resistance.
No comments:
Post a Comment