EGG 131L, Lab 6 Manual, 80 points Law of Momentum Conservation Name: 1. Objective Study the momentum conservation and energy conservation law by using a ballistic pendulum. 2. Apparatus Ballistic pendulum apparatus, triple beam balance, meter stick, and plain paper. 3. Theory A ballistic pendulum is a device used to measure the velocity of a projectile fired into an initially stationary pendulum with a mass of M. In this lab a ballistic pendulum will be used to measure the velocity v of a ball with a mass of m projected from a spring gun. The fast moving ball strikes the pendulum, and the pendulum will gain a velocity of V. According to the principle of conservation of momentum, if there are no external forces acting on a system of several particles, then the total momentum of the system remains constant. We have: mv = (M + m )V (1) The pendulum block will be raised a vertical distance h due to its initial velocity V. According to the energy conservation we have: % (m +M)V' = (m + M)gh. (2) Combining equation I and equation 2 we have: D = (m+M) V2gh (3) Thus the velocity of the fast moving ball can be found by measuring m, M, and h. The same velocity v also can be measured by using the projectile-motion theory. Let the ball be fired without hitting the pendulum. It will travel a horizontal distance x, and simultaneously fall a vertical distance y. Thus we have: x= vt (4) and y= 1/ gt (5) 1EGG 131L, Lab 6 Manual, 80 points Combining equation 3 and equation 4 we can get: x zy (6) TI 4. Preparation 4.1 Read the following references: https://vlab.amrita.edu/?sub=1&brch=74&sim=202&cnt=1 1 1-EXPERIMENT 8.pdf (sjsu.edu) 4.2 Watch the following videos to see some demonstrations for this lab. https:/www.youtube.com/watch?v=6F6deDoKLoE https://www.youtube.com/watch?v=PUNKqLkELbQ 5. Procedure 5.1 Ballistic Pendulum Measure the mass of the ball, m, the mass of the pendulum block M, and the initial vertical position 2EGG 131L, Lab 6 Manual, 80 points of the pendulum block ho. Fire the ball, and measure the final vertical position of the pendulum block hi. Make sure to take the measurement from the center of the block. Find h by using (hi - ho). Repeat the same procedure for three more times. Record your data, then find the average of h. 5.2 Projectile Motion Measure the vertical distance y that is from the ball to the floor. Fire the ball without hitting the pendulum block. Measure the traveling distance x by the ball. Repeat the same procedure for three more times. Record your data, and find the average of x. Lab Report 1. Purpose (12 points) 2. Data 2.1 Ballistic Pendulum (4 points) The mass of the ball, m: The mass of the pendulum block, M: The initial height of the block, ho: The first trial, hi: ; the second trial, h12: The third trial, him: ; the fourth trial hi4: The average value for hi is "/4(hut hiz + his + hid) : The average value for h is equal to: hi - ho = 3EGG 131L, Lab 6 Manual, 80 points 2.2 Projectile Motion (4 points) The vertical position of the ball, y: X1 = X1= X3 = X4 = The average value for X: 3. Computation 3.1 Use the mass of the ball, the mass of the block, and the average value of h to calculate the velocity of the ball. (24 points) 3.2 Use the value of y, and the average x to calculate the velocity of the ball. (24 points) 4. Conclusion: (12 points) Find the percentage difference between computation 1 and computation 2. 4