INTRODUCTION: Part A: Determination of the Initial Velocity of a Projectile Using a Ballistic Pendulum The linear moment

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Introduction Part A Determination Of The Initial Velocity Of A Projectile Using A Ballistic Pendulum The Linear Moment 1 (60.49 KiB) Viewed 37 times

Introduction Part A Determination Of The Initial Velocity Of A Projectile Using A Ballistic Pendulum The Linear Moment 2 (42.6 KiB) Viewed 37 times

Introduction Part A Determination Of The Initial Velocity Of A Projectile Using A Ballistic Pendulum The Linear Moment 3 (55.6 KiB) Viewed 37 times

Introduction Part A Determination Of The Initial Velocity Of A Projectile Using A Ballistic Pendulum The Linear Moment 4 (58.92 KiB) Viewed 37 times

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Introduction Part A Determination Of The Initial Velocity Of A Projectile Using A Ballistic Pendulum The Linear Moment 9 (54.17 KiB) Viewed 37 times

INTRODUCTION: Part A: Determination of the Initial Velocity of a Projectile Using a Ballistic Pendulum The linear momentum of a body is a vector quantity and is defined as the product of the mass of the body and its velocity. Linear momentum-p-my (1) The importance of momentum is that it is conserved in all collisions in the absence of external forces. In part A of the experiment you will obtain the velocity of a projectile fired from a spring loaded gun (see Figure 1b), by using the law of conservation of linear momentum, as it applies to a completely inclastic collision, and the law of conserva- tion of energy. A projectile of mass mis fired with an initial horizontal velocity of ve into a stationary pendulum of mass M. The pendulum with the projectile trapped inside is given a velocity V. Momentum before collision: mv. Momentum collision (m+M)V. www. (2) As a result of this collision, the pendulum with the projectile trapped inside swings up until the center of gravity rises to a vertical height Ah so that its initial kinetic energy is entirely converted into gravitational potential energy. Stated mathematically, % (M+) V-(M + m) g ab (3) Solving Eq. 3 for V and substituting its value into Eq. 2 will yield the value of the projectile's initial velocity vo
APPARATUS 1. 2. 3. 14 Figure 1b. Position of Ballistic Pandahim before and after the shooting DESCRIPTION OF APPARATUS: The apparatus used in this experiment is a combination of a ballistic pendulum And a spring gun for launching a projectile. 21 Ballistic Pendulum Projectile (metal ball) Quadruple Beam Balance M+m 5. 6. Two metersticks Carbon paper Scotch tape
Figure 2 describes how the ballistic pendulum is used. The pendulum consists of a cylindrical bob C of mass M hollowed out to receive the ball B of mass m and sus- pended by a rod A pivoted at the top. The ball B when shot into the pendulum is held there by the spring S in such a position that its center of mass lies on the axis of the suspension rod A. An index I is attached to the pendulum to indicate the height of the center of mass of the loaded pendulum. When the ball B is shot into the pendulum it swings upward to a height of Ah and is caught at its highest point by a pawl P which engages a tooth on a notched rack R. PART A: Determination of the Initial Velocity of a Projectile Using a Ballistic Pendulum NOTE: Before commencing with the experiment the instructor will explain the precautionary measures that are important to observe in order not get hurt and in order not to damage the equipment. PROCEDURE FOR PART A 1. in your lab notebook, prepare the following list: mass of metal ball: mass of pendulum: height of pointer I before collision: notch readings for 3 trials: average height of pointer I after collision be Set the apparatus near the edge o the table facing into the room. Weigh and record the mass m of the ball used as the projectile. The mass of the pendulum M is stamped on the pendulum
Release the pendulum from the Ratchet R by lifting up the Pawl P and allow it to hang freely without swinging. Measure the height h, of the Pointer 1 above the base surface. With one hand press down on the base of the pendulum to minimize recoil and fire the ball into the freely hanging stationary pendulum and note the notch at which the Pawl P stops on the Rachet R. 7. Remove the ball from the pendulum bob by pushing up on Spring S so as not to damage the spring. Repeat the procedure at least two more times. Place the Pawl in the notch on the Ratchet R corresponding to the average position and measure the height h, of the Pointer I from the base surface used for the h, measurement. ANALYSIS FOR PART A Calculate Ah: Ah-he-h 2 Use Eq.3. to find VA 2g Ah Use Eq. 2, mive (M+m)V to find v - PART B: Determination of the Initial Velocity Va of a Projectile Using Kinematics In Part B of this experiment, the initial velocity of the same projectile fired from the same gun, used in Part A. will be determined by using the equations of kinematics. as depicted in Figure 3, the projectile is shot horizontally from the gun and allowed to fall freely toward the y = 1 gt³²
earth. The horizontal range of the projectile, x, and its vertical fall, y, in time t are given by x = Vol y - 1/2gt² (5) The value of ve obtained in Part B should equal to ve obtained in Part A. PROCEDURE FOR PART B Part B of the experiment is performed ONLY from the table in the front of the blackboard. DO NOT DO THIS PART FROM ANY OTHER TABLE IN THE LAB. 1. Without changing the spring tension in the gun, place the Pawl P of the pendulum on the Rack R 2. Bring your pendulum to the desk in the front of the room and place it in the frame that is clamped to the table top. (NOTE: For this part of the experiment the Pawl P must be on the Rack R.) Make sure that the range in front of the apparatus is clear. Cock the gun, press down on the gun with one hand, fire he gun, and note the place where the ball strikes the floor. 3. Use scotch tape to attach a piece of carbon-paper at this position. Shoot the ball three more times and mark the average position of the three impressions on the carbon paper. 4. Measure the horizontal range x of the ball along the floor from the point immediately below the projection point to the average position of the points at which the ball struck the carbon paper, and record x in your notebook. 5. Measure the height y from the bottom of the ball as it rests on the gun to the floor, and record y in your notebook
ANALYSIS: FOR PART B 1. Use equations (4) and (5) to obtain the initial velocity vs of the ball. 2. Compare the values of vo found in Part A and in Part B and find the percent difference. QUESTIONS: 1. What conservation laws are involved in he computation of the initial velocity of a projectile using the ballistic pendulum? 2. After the projectile leaves the gun what are the accelerations in the x and y directions? 3. Use the value of ve obtained in Part A to calculate the kinetic energy of the ball just before impact. BP 5
4. Calculate the kinetic energy of the pendulum bob and ball just after impact from the value of their common velocity V and of their masses. 5. Using the results of questions 3 and 4, calculate the loss of energy during the inelastic impact. What became of the energy lost? 6. a) A 20 gram bullet is fired horizontally into a 400 gram block of wood suspended like a ballistic pendulum. The bullet strikes the block and becomes imbedded in it. The impact causes the block and bullet to swing so that its center of mass rises 15 cm. Find the velocity of the bullet just before the impact. 7. Compare the momentum and the kinetic energy of an automobile weighing 2500 lb. and moving with a velocity of 70 miles per hour, with the momentum and the kinetic energy of a projectile weighing 100 pounds and moving with a velocity of 2000 feet per second.
Data for Part A mntramom usmil to noisvisenos towalsuomire Mass of metal ball: m= 69.3 g vols lanim sdt ni Mass of pendulum: M= 273.4 g des out of seq of a tamsab to anosups.or bree boboot Height of pointer 1 before collision: h1= 6 cm Notch readings for 3 trials: 24, 24, 25 visiolamoon of 29ilges til to nomivisen 201 Average height of pointer 1 after collision: h2= 13.1 cm & mot be it alapoing to bolov od vitor. To noituvasario bad Data for Part B Range x for 3 trials: 277.5, 282.5, 285 cm Notre-Damainams Me Average range x: 281.67 cm son notalo soladining to god mulubog tozesm Height y=104.6 cm noisilloo oftest log 30 usion sandvi