Homework answers / question archive / Ballistic pendulum-Lab 7 Fact-checking the Mythbusters Purpose One purpose of this lab is to explore the concepts and mathematics associated with the ballistic pendulum

Ballistic pendulum-Lab 7 Fact-checking the Mythbusters Purpose One purpose of this lab is to explore the concepts and mathematics associated with the ballistic pendulum

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Ballistic pendulum-Lab 7 Fact-checking the Mythbusters Purpose One purpose of this lab is to explore the concepts and mathematics associated with the ballistic pendulum. An understanding of conservation of energy and angular momentum will be needed. The other purpose of this lab is to explore the use of scientific reasoning and peer review. This replicates, the use of the scientific method in a professional setting when someone wants to publish a paper in a scientific journal or try to reproduce an experiment. Procedure For this lab you will need pencil, paper, and the Mythbusters video provided to you in the link on Canvas. Please also make sure to read up on Chapters 10 and 11 on conservation of energy and angular momentum . You will notice that not all television or movie scenarios are accurate. These scenarios are often what the Mythbuster often attempt to either con firm or debunk. In this case, the question is how deadly a rock flung by a lawnmower blade would be. In testing this they are comparing the energy of a lawnmower blade to that of a .357 Magnum. You will be double checking their conclusions and analyzing their setup. Ballistic pendulum (constraint conditions) 1) Consider the fact that we are approximating angular momentum more than angular momentum, since in the video they use a stiff rod as their pendulum. It takes 1/3 the energy to rotate a rod about one axis than to move a standard block of the same mass connected by strings. This concept should be included in your energy conservation derivation of vbullet+pendulum , vrock+pendulum to get a more accurate result. Also, the height must be based around the center of mass for the rod, which is simply approximately 1/2 Lpendulum . 2) Assume the following: Lpendulum =1m, mbullet =7g, mrock = 100g, and mpendulum =2kg 1 3) The remaining givens, vbullet , vrock , along with values of θbullet and θrock , are provided in the video. Lab deliverables–Visualize a) Draw two before and after impact diagrams of the situation you see in the video. Draw one of the rock being launched and another of the bullet fired, with all of the variables and givens labeled in the diagram. The diagrams should consist of height h, mbullet ,mrock , vbullet , vrock , Mbullet+pendulum , Mrock+pendulum , vbullet+pendulum , vrock+pendulum , mpendulum , length Lpendulum ,and θbullet or θrock . You may abbreviate subscripts as needed. b) Derive an expression for the height h that the pendulum achieves using the Lpendulum and θ. c) Derive an expression for the before-and-after conservation of angular momentum in an inelastic collision using the masses involved. d) Derive an expression for the before-and-after conservation of mechanical energy during the pendulum’s rise upward to it’s final height. HINT: refer to problem 12.21 in your book. Lab deliverables–Analysis I) Calculate the energy before the collision for both the rock and bullet given the velocities provided in the video of each and the masses given in this lab. Which object has more initial energy. II) Calculate the energies of the rock+ pendulum and bullet+pendulum after the collision with your derived expression for vbullet+pendulum and vrock+pendulum from conservation of mechanical energy that used the constraints provided above. III) Compare both initial energies and final energies from the calculations above (I and II). Does the result make sense? Why or why not? IV) Plug these velocities back into your expression for conservation of angular momentum. Do you get the same values for vbullet , vrock provided in the video? Does the result make sense? Why or why not? V) Calculate the speed of the tip of the mower blade assuming that it rotates at a standard 3600rpm and has a diameter of 24 inches. Considering the velocity calculated of a rock flung by the mower was 400ft/s, Does the mower blade tip speed make sense? Why or why not? 2 VI) Based on these estimations and calculations, overall do you believe the Mythbuster’s final assessment is accurate? Why or why not? VII) What are a few possible sources of error in the Mythbuster’s setup? (You may also explore previous videos like part 6 to assess this part).