lab report 12.docx

Principal Investigator: Morgan Green Assistant Investigator: Sean H. Experiment 12 The Ballistic Pendulum Objective: To measure the velocity of a projectile Apparatus: Cenco ballistic pendulum apparatus, Ohaus triple beam balance, meter stick Theory: The velocity of a rifle bullet or other projectile may be measured by shooting into a block which is suspended as a pendulum provided to conditions are met. The collision must perfectly inelastic, and the collision must be completed in a time interval which is very short when compared to the period of the pendulum. Before the collision the projectile has mass m and velocity v, and the pendulum has mass M and velocity V=0. After the collision the pendulum has mass (m+M) and velocity V?. Solving for v gives us the equation: v= (m+M)/m*V? To measure the velocity of the system after the collision we can make use of the fact that kinetic energy which is transferred to the pendulum is converted to gravitational potential energy as the pendulum swings away from the equilibrium position. ½ (m+M)V? =(m+M)g(H-h), or V?= 2g(H-h) and V= (m+M)/m* 2g(H-h) Where h is the height of the center of mass of the pendulum-bullet system before the collision and H is the height of the center of mass of the system after the collision. The position of the venter of mass is marked approximately by the tip of the pointer which is screwed to the side of the pendulum. Both H and h must be measured relative to the same reference datum, namely the top of the table. Procedure: Level the apparatus, measure the mass, m, of the spherical steel ball projectile. Remove pendulum from the apparatus and measure its mass, M. measure the position to the center of the mass inside the pendulum cavity. Measure the height, h, of the tip of the pointer relative to the apparatus base. Load the projectile onto the gun and cock it. Pull the trigger. The ball should lodge itself in the pendulum cavity. If the collision is satisfactory, the pendulum will swing away from the collision point and will be caught at the maximum of its swing by the ratchet mechanism. Measure the height, H, of the tip of the pointer relative to the apparatus base. Compute v from the equation and record data in a table. Repeat the procedure at least 12 times. Calculate the average velocity of the projectile and its standard deviation. h=.057 (m+M)/m=4.997 Average v= 4.421 .354 Discussion: Overall we were able to achieve our goal of measuring the velocity of a projectile in this experiment. Error in this experiment could have been caused by inaccuracy in measuring tools, or by the fact that it is hard to measure h without some error. Repeating the procedure 12 times, however, adds to the accuracy of the experiment, and leads us to believe that our results are more accurate than if we were to have only done a few trials. The experiment was a success overall, and we achieved our goal, despite the possibility of error. Trial Number H (cm) (H-h) (cm) 2g(H-h) v 1 11 5.3 1.02 5.09 2 10.7 5.15 .9905 4.949 3 8.8 3.1 .7799 3.897 4 9.5 3.8 .8635 4.315 5 9.5 3.8 .8635 4.315 6 9.6 3.9 .875 4.372 7 9.4 3.7 .852 4.257 8 9.8 3.9 .875 4.372 9 9.7 4.0 .886 4.427 10 9.5 3.8 .8635 4.315 11 9.6 3.8 .895 4.372 12 9.6 3.9 .875 4.372