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Nothing is missing. All the informations are there. Please answer all the questions. PHYSICS 111 Experiment # Ballistic Pendulum Name: Grade: Instructor: Partners: Date Performed:

Nothing is missing. All the informations are there. Please answer all the questions.

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PHYSICS 111 Experiment # Ballistic Pendulum Name: Grade: Instructor: Partners: Date Performed: Comments: Date Submitted: OBJECTIVE: A ballistic pendulum is used to determine the muzzle velocity of a ball shot out of a Projectile Launcher. The laws of conservation of momentum and conservation of energy are used to derive the equation for the muzzle velocity. EQUIPMENT: hitp://physics.bu.edu/~duffy/HTML 5/ballistic_pendulum.htm] THEORY: The ballistic pendulum has historically been used to measure the launch velocity of a high speed projectile. In this experiment, a projectile launcherfiresasteelball (of m assmy.1) at alaunch velocity, V. The ball is caught by a pendulum of mass myp..q. After the momentum of the ball is transferred to the caicher-ball system, the pendulum swings freely upwards, raising the center of mass of the system by a distance h. The pendulum rod is hollow to keep its mass low, and most of the mass is concentrated at the end so that the entire system approximates asimple pendulum. During the collision of the ball with the catcher, the total momentum of the system is conserved. Thus the momentum of the ball just before the collision is equal to the momentum of the ball-catcher system immediately after the collision: M1V = Mv Eq. 1 where visthe speed of the catcher-ball system just afterthe collision, and M = Mt + Mypeny Eq. 2 During the collision, some of the ball's initial kinetic energy is convertedintothermal energy. But afferthe collision, asthe pendulum swings freely upwards, we can assume that energy isconserved and that all of the kinetic energy of the catcher-ball system is converted into the increase in gravitational potential energy. Lo MvZ = Mgh = MgL(1-cos 0) Eq. where g=9.8 m/s?, andthe distance h isthe vertical rise of the center of mass of the pendulum-ball system. Combining equations (1) through (3), to eliminate v, yields My, + Mg v, = fogh Fq. 4 My and from Figure 1 we have h=L (1-cos ), Eq. 5 with 1. being the distance between the center of mass and the axis the rod rotates around, and @ is the angle the rod rotates through before stopping. In the explanation video.I went over how to computethe speeds heforeand afterthe collision. To completethetableb elow, you will need the equation to computethe velocity AFTER the collision, which is actually asked in the procedure, but justin case: v=./29L(1 cosB) EQUIPMENT SETUP: t=081s Angle = 36.60 deg. Bullet mass =30.0 g Mass of target =820 g @ Bullet speed = 80.0 m/s Pendulum length = 2.00 m i) Piay | [Pause | [> ] [Resat A ballistic pendulum The simulation will allowyou to vary the bullet speed and mass, the pendulum length and mass of the target. You willrun the simulation a few times to check which is a range of speeds and masses you want to choose for your experiments. This setup is simple, but it can be a bit difficult at the beginning, so make sure you familiarize with it at first. PROCEDURE PART 1: 3. Compute the energy BEFORE and AFTER the collision and calculate the following value, Q = 1 Eafter 1. Choose a value for the speed of the bullet, mass of the bullet Ebefore and mass of target that allows the ballistic experiment to achieve an angle of at least 35 degrees. 4. What does the value of Q represent? 2. Make sure the length of the pendulum stays constant at a length 5. What can you conclude from the calculation of these energies? of, L = 2.0 meters. 3. Fill in the tablesprovided in this lab manual. You willperform 5 different trials where you will record the angle and will calculate the angle as specified in the background of the lab (page 1 and 2). 4. Use conservation of energy and momentum to derive the velocity of the target and bullet right afterthe perfect inelastic collision. 5. Use a full theoretical analysis to derive the speed of the target and bullet right after the collision and perform a % error. (Just use conservation of linear momentum ) 6. Repeat the steps above for a different set of values of speed and masses, this time reduce the length of the pendulum and adjust values, so the angle is not to steep. Record again all those values in tables like the ones in the DATA section and perform analytical calculations and % errors. PROCEDURE PART 2: 1. Once you concluded part 1, make sure you have the data for velocities organized. 2. You will be using the experimental velocity calculated by using the simulations.DATA: 3 ) Discuss the value of the experiment. 1) Fill in and create the charts below in Excel. Mass al Trajectil Mas al Length al Average Pendulum / ml Velacity al Isl Pendulum Isl Launcher | m/3 Canslants End of documen To calculate the velocity in this table, make sure you use equation (4), where h = L (1-cos 0). Trial Angle (deg) Height of swing(m) Velocity(me) %% Eror Hererage QUESTIONS: 1 ) How well does the initial speed, vo, calculated from Equation 4 agree with the value measured directly using the photogates? What does this show? 2 ) Why is error analysis important

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