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Ballistic pendulum equation

ballistic pendulum equation The bullet collides with and sticks inside of the wood block. wire length of the pendulum. As a result, the combination swings upward until it stops at the highest point by a ratchet. Ballistic Pendulum Apparatus A ballistic pendulum is a device consisting of three parts: a spring gun, a ball that can be launched from the gun, and a cup at the end of a pendulum to catch the ball. A 6 − g bullet A is fired into a 1 − k g wood block B suspended by a cord with a length of l = 2. A Ballistic Pendulum is used to determine the muzzle velocity of a ball shot out of a Projectile Launcher. The Ballistic Pendulum In this experiment, you will measure the velocity of a bullet using the principles of conservation of energy and conservation of momentum. total pressure. m ˙ flow mass rate of the nozzle. The spring gun fires the projectile into the catcher which then swings up the ramp where it is caught by the notches. Prelab for the Ballistic Pendulum . Derivation of the Equation for Muzzle Speed A ball fired with speed, v, will get caught by the ballistic pendulum, which will then swing The collision between the ballistic and the pendulum was a perfectly inelastic collision. Materials 1. Homework Equations Conservation of angular momentum Ballistic Pendulum. 𝑣1=_____ 𝑚/ 12. Before proceeding, check with your TA to make sure you are correct. o = (M+m) m . C7-51: BALLISTIC PENDULUM - PELLET GUN. This potential energy is equal to the kinetic energy of the pendulum immediately after the collision: KE= 1 2 Mn P2 The momentum of the pendulum after the collision is just P p = Mn P, The Ballistic Pendulum (approx. Using a right triangle we can find the height the pendulum rose. At NO time during the experiment are you to adjust the spring gun's tension. 1: Schematic diagram show the components of the ballistic pendulum apparatus After the collision takes place, and the metal ball is stuck in the pendulum, the pendulum-ball combination has a kinetic energy: KE f = 1 2 (m+M)v2 f (4. 00005kg mass of bob= 0. According to the conservation of mechanical energy of the system after the collision, we have equation (5): (1/2) (m + M) V 1 2 = (m + M) g h . √ is the square root of what is included in the parentheses. Designing a real ballistic pendulum to measure the speed of a projectile involves more than the theory in the textbook. f, p. Attach the 100 g Ballast Mass to the bottom of the pendulum catcher as shown in Figure 3. 360 m. Apparatus: Ballistic pendulum, two-meter stick, tray with carbon paper, balance, and ruler. A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. ()() () Examine the ballistic pendulum to determine how it works. ) (12/16/15) Introduction In this lab we will use conservation of energy and momentum to determine the velocity of a projectile fired into a pendulum and compare it to the velocity determined by looking at the trajectory of the projectile when it is launched across the room. After the collision, conservation of energy can be used in the swing of the combined masses upward, since the gravitational potential energy is conservative. This means that for objects moving at the same speed, momentum distinction will be determined by how heavy or light the objects are. This ball is caught by a catcher at the end of a pendulum of mass M. The ball is fired into the ballistic pendulum, which then swings up a measured amount. The pendulum's speed will be zero at the highest point in the Challenge: Pendulum puppet. Sum of masses of pendulum and ball, ¿ mball +m pend M . motion can be analyzed using the equations for projectile motion. We often use this equation to model objects in free fall. DESCRIPTION: The pellet from an air gun is shot into a foam-filled can, which acts as the pendulum. Below is a drawing of how to measure the height of an object that swings through an angle A if the object has a length of X. 2 Ballistics Our ballistic pendulum is a device consisting of three parts: a spring gun, a ball that can be launched from the gun, and a cup at the end of a pendulum to catch the ball. In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2. There are a lot of equations that we can use for describing a pendulum. Simple Pendulum is a mass (or bob) on the end of a massless string, which when initially displaced, will swing back and forth under the influence of gravity over its central (lowest) point. Derivation of Equations of Motion •m = pendulum mass •m spring = spring mass •l = unstreatched spring length •k = spring constant •g = acceleration due to gravity •F t = pre-tension of spring •r s = static spring stretch, = 𝑔−𝐹𝑡 𝑘 •r d = dynamic spring stretch •r = total spring stretch + The average initial velocity for the ballistic pendulum was 6. 240)/0. Press the "Fire" button. V = 2g ∆ h . Eliminating tbetween these two equations and solving for the initial velocity gives v= D r g 2d; (1) where Dand dcan be measured and g= 9:80 m/s. 0-g bullet is fired into a 1. A second projectile causes the pendulum to swing twice as high, h{eq}_2 {/eq} = 5. Conservation of linear momentum in the inelastic collision determines the speed with which the pendulum receptacle leaves the Ballistic Pendulum. 6032)Vf^2=(3. The Editors of Encyclopaedia Britannica This article was most recently revised and updated by Erik Gregersen, Senior Editor. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Using the average Ah and your derived equation to find the value for vy Part 3 Use equation I and your value for vy to calculate the speed of the ball, 27. 1) 27 pendulum swing up in the air. in the “theory” part of your pre-lab. All that's still equal to F0 cosine omega t. 1. We were then able to use the velocity of the bullet and the conservation of momentum to calculate the muzzle velocity of the BB. then I solved for v f2 =2*9. ballistic pendulum gun using the conservation of angular momentum. Refer to Chapter 15, page 466 of Serway and Jewett, 9th edition. Before proceeding, ask your TA to make sure you are correct. T p ′ natural period of the pendulum. 3-2. Figure 1: Ballistic pendulum setup Experimental data m (¿ ¿ ball+mpend ) v f mball v 0 ball +m pend v 0 pend =¿ m pend v 0 pend Due to initially pendulum is at the rest: = 0. So to calculate the Velocity of the BB + pendulum we derived the equation: velocity = √2*gravity*height swung by the pendulum. 5-kg ballistic pendulum. The ballistic pendulum was used in older days to measure velocity of bullets. Determination of Velocity from Collision In the typical use made of a ballistic pendulum, a projectile, having a small mass, m, and a horizontal velocity, v, strikes and imbeds itself in a pendulum bob, having a large mass, M, and an initial horizontal velocity of zero. Ballistic Pendulum In lab this week, we are going to look at a series of energy conversions to see how efficiency works. 19 \text{lb} \\ R_{cm} &= 52" \\ T &= 2. The equation of torque gives: = where: See full list on en. Therefore, ∆KE = KE f - KE i = ½(m + M)V 1 2 – ½ m(V o) 2 peak of the pendulum. 15m. by noting how high the ballistic pendulum swings up. It is also a good demonstra- of mass of the pendulum/ball system. As a result, the block moves up for certain height h until it stops. Using the general conservation of momentum law for the collision described, The Real (Nonlinear) Simple Pendulum. p. Triple-beam balance Introduction The ballistic pendulum is a classic method for determining the velocity of a projectile; origi-nally, it was used to determine the muzzle velocity of rearms. Ballistic Pendulum Equation . The motion is regular and repeating, an example of periodic motion. 08 s. Ballistic pendulum is used for measuring a bullet’s momentum, in respect to that it is possible to calculate its velocity an kinetic energy. p a. / . Table 1. exit section Mach number of the nozzle. See Figure 1 for a picture of what happens. I have the mass of the ball, and mass of the pendulum. Ballistic Pendulum Purpose During this lab, momentum conservation of a perfectly inelastic collision is investigate by comparing the measured angle and the calculated angle of a projectile. Also we need the length of the pendulum's arm and the mass of the ball and the pendulum to solve these equations. Part 3: Suppose the block is 100 times heavier than the bullet. Using these and the cosine equation we where able to derive multiple equations to be able to find the initial velocity of the projectile. First The ballistic pendulum is a device that is used to measure the velocity of an object by retaining the bullet upon impact, and its velocity is a function of the displacement of the pendulum. equation to calculate 𝑣2. ball/pendulum after the collision. T. M- Mass of Pendulum. Collision: 𝑚 𝑣𝑖=(𝑚 + 𝑚 ç ℎ )𝑣 å 𝑖𝑖 á Rising 1 2 𝑚 ç 𝑣 𝑖𝑖 2 +𝑚 BALLISTIC PENDULUM I. collision, using the ballistic pendulum. The pendulum, though very smooth and precise, did have some "wobble" to it when the projectile was shot into it. 14. From the height reached by the pendulum, you can calculate its gravitational potential energy. That is Vb=Vb(mb,mp,V). t. Consider the ballistic pendulum motion in two parts—(a)the collision between the ball and the pendulum and (b) the swinging of the pendulum upward. Ballistic Pendulum - Theory DPE= MgR cm (1 Œ cos q) Here R cm is the distance from the pivot point to the center of mass of the pendulum/ball system. Write the general horizontal and vertical motion Kinematics equations for a horizontally launched projectile. 3. v = m/s = km/h = mi/h. A second projectile causes the pendulum to swing twice as high, h{eq}_2 {/eq} = 5. t = Pendulum period, seconds; L = Pendulum arm length, meters; g = Little-g, described above; Some explanation: The assumption is that the pendulum consists of a weight attached to the end of a massless arm of length L, that there is no friction, and there is no air resistance. 18: E˘ 1 2 jL~pbj2 I. Watch: Ball bouncing in slow motion: Light ball. 3. Ballistic Pendulum/Projectile Launcher 012-05375B Ballistic Pendulum - TheoryOverview ∆PE = MgRcm (1 – cos θ)The ballistic pendulum is a classic method of determining Here Rcm is the distance from the pivot point to the centerthe velocity of a projectile. 05°= 8. A simple pendulum consists of a relatively massive object - known as the pendulum bob - hung by a string from a fixed support. A bullet is shot into the block, and as a result of the perfectly inelastic impact, the block swings upward. 2 = 2g ∆ h . V- Velocity of pendulum Ball’s initial velocity V a = (m+M)/m * (2gh) 0. (7) and x is given by eqn. 73×10 -4 rad. Gain con dence in the equations of projectile motion and your ability to use them. Cd = drag coefficient. In the second stage mechanical You need an equation to calculate the velocity of the ball and catcher right as it starts its swing based on the height it swings to. 2 Methods Swing the pendulum up so the latching mechanism holds the pendulum out of the way. It consists of a spring gun that fires a metallic ball of mass m. 1) consists of a spring gun (G) which fires a small steel ball (B) at a catcher (C) on the end of a rigid pendulum arm (PC). PART B: An experiment is done to compare the initial speed of bullets fired from different handguns: a 9mm and a . UMass Boston The Ballistic Pendulum Physics 181 momentum of the projectile becomes the momentum of the projectile-pendulum system. ‪Pendulum Lab‬ Using the value for V o calculated from the ballistic pendulum, calculate the fractional loss in the kinetic energy during the collision. A 2. BALLISTIC PENDULUM In this experiment we will study the application of the laws of conservation of momentum and energy in a ballistic pendulum apparatus. Using the law of conservation of momentum, the velocity of the bullet can be computed. Refer to Chapter 15, page 466 of Serway and Jewett, 9th edition. Figure 3. (3. v. 5, which is 2. This physics video tutorial explains how to solve the ballistic pendulum problem where a bullet is fired at a hanging wooden block. From the law of conservation of mechanical energy of the pendulum; where, m- Mass of bullet. The velocity also may be Work backwards, starting with the swing of the pendulum just after the collision until it reaches its maximum height. 14 KE = ke + qe; where KE is the kinetic energy before impact, ke is that after impact, and qe are the loses (e. π= The Greek letter Pi which is almost 3. wikipedia. Ballistic pendulums have been largely rendered obsolete by modern chronographs, which allow direct measurement of the projectile velocity. Blackwood Ballistic Pendulum Jamal Wright, Zachary Floyd, Christopher Wilson Abstract Our goal of this experiment is to determine muzzle velocity by two methods: 1) employing uniform linear motion relations, the kinematic equations; 2) using the principles of conservation of energy and momentum . How does this value compare to Ballistic Pendulum Lab 3cm Spring 4cm Spring 5cm Spring This lab is very complex, so check in with your teacher frequently if you have questions. Ballistic Pendulum - Theory D PE = MgR cm (1 cos q) Here R cm is the distance from the pivot point to the center of mass of the pendulum/ball system. The catcher latches onto the projectile, swings upward, and the maximum height of the pendulum is measured. Figure 1 The apparatus includes a mechanism that records the maximum height the Pendulum Equation. T e The ballistic pendulum is a device that is used to measure the velocity of an object by retaining the bullet upon impact, and its velocity is a function of the displacement of the pendulum. 23 m/s while the average initial velocity for the projectile determination was 8. and a muzzle velocity u = m/s = km/h = mi/h. M = mass. As you will see, comparing the data obtained using the ballistic pendulum with the data obtained using the projectile launcher will allow you to determine if momentum is conserved in the collision between the ball and the pendulum cage. This is an inelastic collision, in contrast to an elastic collision where energy is conserved. A ball is launched from rest by a spring-loaded “gun” (Figure 1) and is caught by a bob. 2. Applying conservation of energy: EE KE PE mv mgh vgh ms m ms ms if right after impact high po of swing = = = == = = −− − −−int. Our mission is to provide a free, world-class education to anyone, anywhere. The device is quite simple to operate. 21) We can rewrite this expression using the conservation of energy of the pendulum as expressed in Equa-tion3. nozzle thrust. Most beginning physics textbooks discuss the physics of the ballistic pendulum when one-dimensional particle kinetics and energy and momentum conservation laws are introduced. pendulum. A bullet of mass is fired into a stationary block of mass at some velocity . Because of the conservation of momentum, the ball's momentum prior to striking the pendulum is equal to the momentum of the ball and pendulum after contact. Slide the Rotary Motion Sensor onto the 90 cm rod, and attach the pendulum to the pulley. Physics 2: The conservation of momentum. Since v f is the speed of the bullet+block right after the collision and the bullet+block moves as a pendulum motion, we can use conservation of mechanical energy to find v f. Step 1: Using your measurement of the period of the pendulum, T, derive an expression for the moment of inertia of the pendulum arm with the ball in the catcher, I, by the following method. The device accelerates a metal ball to a velocity v i. 15=22. 12, and his 3. Let (t) be the corresponding angle with respect to the vertical. A spring-loaded gun is used to shoot a projectile horizontally into the “bob” of a pendulum. 5 x mass x velocity^2'. For each part, discuss whether conservation of energy or conservation of momentum is used and how they are applied. When a bullet is fired into the bob, its momentum is transferred to the bob. B) Make a data table like the one in Figure 7. For this analysis, however, we'll neglect it. K i +U gi = K f +U gf 3. The conservation of energy is depicted by the following equation: 1/2 (m+M){eq}V_i^2 {/eq}= (m+M)gh (2) That is, Kinetic energy = Gravitational potential energy Ballistic Pendulum Lab equal to the potential energy at the peak of the pendulum's swing. ” Calculate the percent error of your calculated value of 𝑣1. The projectile in this case is a metal bearing. It should have been expected that these two values would be equal. Here is the angle the pendulum has moved from the vertical, L is the length of the pendulum, g is the acceleration due to gravity, m is the mass of the pendulum, and b is a damping coefficient. 𝑝𝑝 horizontally by a ballistic pendulum by applying the conservation of momentum in the collision and energy in the pendulum swing. Rearranging our equation for conservation of energy gives ω = √(2Mgh/I). The ballistic pendulum consists of a gun which fires a ball into the pendulum's bob. A 12 g bullet is fired into the block, where it sticks, causing the pendulum to swing out to a 35 degree angle. The laws of conservation of momentum and conservation of energy are used to derive the equation for the muzzle velocity. It is also a good demonstration of many basic principles of physics. just before it collides with the pendulum V Part 4 1. This is calculated as follows: h = L - L∙cosθ L = length of the pendulum to its center of mass (cm) Figure 1 7. Thus the pendulum's initial velocity can be calculated. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. The collision between the ball and pendulum is perfectly inelastic. Pre-Lab 11: Ballistic Pendulum In a ballistic pendulum experiment a projectile is fired into a pendulum catcher. When a body or mass is in motion, it has linear momentum which is a product of its mass and velocity and it is denoted by the formula p= mv. 981*1. A bullet of known mass is shot into a wood block of known mass. o = (M+m) V . If the mass of the object does not change, then any change in momentum ∆p is a consequence of a change in speed ∆v, or (2) ∆p = m∆v . We will now apply conservation of energy immediately after the collision and at the point when the ball + pendulum reach the maximum height ‘h’. Just after the collision, the pendulum bob is moving with speed V. Note that the total mass is the mass of the ball plus the mass of the catcher. Recall that th=4z- hz th 2. 7 cm. is fired into a block of mass M = grams. THEORY NOTE: Before coming to the lab, derive the equations for the absolute errors in. Just after the ball is launched a pendulum bob catches it. collides and sticks to a stationary object with mass . 4cm. Equation (1) is only accurate for infinitesimally small swings. We are going to use the formulas: (2gh)^(½) = V & (m+m)V=mV. $$ The ballistic pendulum. / . then the velocity of the block and bullet after the impact would be. Determining the center of mass for the pendulum was a bit tricky because it was hard to find a perfect balance point for it. Overview of Ballistic Pendulum. The equation that relates the projectile velocity to the pendulum angle is derived in the Theory lab document and reproduced here: v= M T m p 2gR cm(1 cos ) (3. p = mv where p is momentum, m is mass and v is the speed or velocity. Ballistic Pendulum 1INTRODUCTION The ballistic pendulum was developed in 1742 by the English mathematician Benjamin Robins. 2 m. It is also a good demonstration of many of the basic principles of physics. The potential energy of the pendulum can be modeled off of the basic equation . (14) Figure 1: Measurement of height for ballistic pendulum experiment. Ballistic pendulum machine 3. 2. Carefully remove the pendulum with steel ball embedded from the apparatus. As the projectile Momentumbullet=momentumbullet/pendulum. The pendulum's speed will be zero at the highest point in the x = horizontal position of pendulum mass; y = vertical position of pendulum mass; θ = angle of pendulum (0 = vertical downwards, counter-clockwise is positive) L = length of rod (constant) A simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. L. 1-meter stick (x2) 2. 14. 563. The system has some momentum and kinetic energy: After the collision, the pendulum will swing about its center of support from its initial height to some maximum height. A simple version of the spherical pendulum, the Foucault pendulum, is used to show that Earth rotates on its axis. V0 = X [g /2Y]1/2 (3) The initial velocity Vo of the projectile can also be determined by using the ballistic pendulum ( Fig 2). 90min. If you view the video clip in the multimedia tutorial, you will note that the pendulum rotates about its support, and also flexes. Description of the ballistic pendulum: The device consists of a spring gun, a small steel projectile (a ball), a free-swinging pendulum catcher, and a ratchet ramp. For an Re-arranging this equation, we can solve for V. To shoot the ball: Put the ball, which has a hole in it, on the rod at the end of the gun. From conservation of momentum, mVo = ( m + M ) V1( 4 ) where V1 is the common velocity of pendulum – ball just after collision. 7 cm. A 7. Re-arranging this equation, we can solve for V. just before it collides with the pendulum V Part 4 1. The system has some momentum and kinetic energy: After the collision, the pendulum will swing about its center of support from its initial height to some maximum height. . This potential energy is equal to the kinetic energy of the pendulum immediately after the collision: KE = 1 2 M n P2 The momentum of the pendulum after the collision is just P p = M n P, The pendulum, of mass (M + m), moves with a new horizontal velocity, V. The ballistic pendulum, as simple and old-design device, enhanced with optoelectronic e ncoder sensor and computer acquisition system, can be one of the good start-up device plat form for B C P h y s i c s = M C d ⋅ A = ρ ⋅ ℓ C d {\displaystyle BC_ {Physics}= {\frac {M} {C_ {d}\cdot A}}= {\frac {\rho \cdot \ell } {C_ {d}}}} Where: BCPhysics = ballistic coefficient as used in physics and engineering. Robins' ballistic pendulum had the following parameters $$ \begin{aligned} M &= 56. Assume that the 9mm bullet has a mass of 6g and the . Using the variables defined in Figure 1, applying conservation of momentum to the collision yields: ! mv = (M + m)V (1) After the collision, the pendulum bob will swing upward until all of its kinetic energy is To compute the muzzle velocity of a projectile using a ballistic pendulum, we first rewrite Equation3. For now, take it on faith that the muzzle velocity of the potato is given by this equation. Seminar assignments - Ballistic pendulum abstract and discussion Lab 1 Summary - Covers the "Data Analysis" lab Lab 2 Summary - Covers the "Free Fall-Measure of "g" lab Lab 4 Summary - Covers the "Conservation of Mechanical Energy" lab Bio 230 Study Guide Questions All Answered Essay - Thessalonians and Corinthians Essay - The Gospels of Mark and John Forensic Mass Disasters BIOL 261 EXAM 2 So I think it is an inelastic collision so v f = (m bullet *v bullet) / (m bullet +m block) After collision: (1/2)* (m bullet +m block )v f2 = (m bullet +m block )*g*h. 0045 proportionality constant developed in the experiment. Height, h, could also be A) You need an equation to calculate the spring constant of the spring in the launcher. Determine ( a) the initial speed of the bullet v 0, ( b) the impulse imparted by the bullet on the block, ( c) the force on the cord immediately after the impact. v. Recall that th=4z- hz th 2. Theory: In a perfectly inelastic collision momentum is conserved. 8-2) Mechanical energy is not conserved during an inelastic collision, but just after the collision (again the pendulum arm and ball are assumed to be point masses) the pendulum-ball system has kinetic energy (KE = 1/2mv2). As the pendulum swings, its center of gravity rises. The pendulum and cup can be moved out of the way. 4cm. gondola mass. 3 kg wood block hangs from the bottom of a 1. THEORY The purpose of this experiment is to measure the velocity of a ball that is fired from a spring gun. See also ballistic pendulum. Remove the pendulum from the stand by unscrewing the pivot axle. Assume the force that the apparatus exerts on the pendulum is normal to its circular trajectory: Write the equation for conservation of mechanical energy for this situation: You should be able to solve for the muzzle velocity using this equation along with your conservation of momentum equation. In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2. PURPOSE: To determine the speed of an air gun pellet using a ballistic pendulum. 13 in the second equation, solve for Vf, then put it in the first equation, and solve for Vi. 2) where M = mass of the pendulum and v f is the velocity of the pendulum/ball moving together. If a bullet of mass m =grams. Use the horizontal sliders to adjust the mass of the bullet, mass of the wood block, and the initial velocity of the bullet. It moves upward and is caught by the ratchet at the highest part of its swing. Ballistic Pendulum Goals •To determine the launch speed of a steel ball for the short, medium, and long range settings on the projectile launcher apparatus using the equations for projectile motion. 44 caliber. Ballistic Pendulum Goals •To determine the launch speed of a steel ball for the short, medium, and long range settings on the projectile launcher apparatus using the equations for projectile motion. Ballistic pendulum, device for measuring the velocity of a projectile, such as a bullet. Ballistic pendulum machine 4. 360 m of bullet and block of bullet and block = of bullet and block Speed of bullet and block immediately after impact To determine the speed of the bullet before impact, we use the conservation of momentum. 0005m degree= 0. You will need the potential energy equation for a spring … kx2 2 1 PE =. The spring gun is designed to fire a ball of mass m b with an initial velocity v i. A ballistic pendulum is a mechanical device that captures a fired projectile and is allowed to swing (see Figure3. 0341)) 0. The goal is to work backwards to determine the initial speed of the projectile. 8*. 3*cos60=1. just before it collides with the pendulum V Part 4 1. Part 1: Explain why the conservation of energy cannot be applied before the collision? Part 2: Determine in terms of , , and . total temperature. Derive an equation for the uncertainty of the projectile velocity (δvo) associated with the equation obtained in question 6. The block and rod form a pendulum that swings on a frictionless pivot at the top end of the rod. It is fired at the bob of the pendulum that catches the bearing. In our version, a steel ball is shot from a spring-powered projectile launcher and lodges itself in a The moment of inertia of a compound pendulum is given by $$I = \left(\frac{T^2}{4\pi^2} \right)MgR_{cm} $$ where \(T\) is the period of its swing. Pix = mu, where u is the initial speed of the ball prior to collision with the pendulum cup. Using cquation 2, derive an equation for vy in terms of g. We use the equation for a totally inelastic collision to determine this: mbv0 = (mb + mp) v1 (4) block, so we can modify the above equation as m 1 v 1i = (m 1 +m 2 )v f Our goal is to find v 1i, but we need to find v f first in order to do that. In this lab a metal ball is fired horizontally into a swinging arm or “Ballistic Pendulum” and captured by a spring-loaded clasp near its lower end. (14) Figure 1: Measurement of height for ballistic pendulum experiment. The equation for the period of a simple pendulum starting at a small angle α (alpha) is: T = 2π√ (L/g) where. The ballistic pendulum was invented in 1742 by English mathematician Benjamin Robins. h = m = cm = ft. 1 minus omega squared over omega n squared cosine omega t minus v minus 2 zeta omega over omega n sine omega t minus v. Lab 8. The ballistic pendulum demonstrates conservation of momentum in an inelastic collision. For an the pendulum-ball system is m b+M pa. Ballistic Pendulum Instructions So you want to measure the muzzle velocity of a cannon. Pfx = (M+m)V, where V is the recoil velocity of the ball and pendulum system, and M is the mass of the pendulum. The block is attached to a wire (assume massless and infinitely rigid). The laws of conservation of momentum and conservation of energy are used to derive the equation for the muzzle velocity. This could have been improved by screwing the pendulum tighter to the frame. 6032)*9. Recall that th=4z- hz th 2. Investigate! Use the Investigating a Pendulum widget below to investigate 10. The figure shows tangential and radial components of gravitational force on the pendulum bob. p 0. 2. I would really want to substitute it into the equation: $$ M_\text{ball} \times V_\text{ball} = (M_\text{ball} + M_\text{pendulum}) \times V_\text{pendulum} $$ The ballistic pendulum. V. T 0. Thirdly, we measured the pendulum from the fulcrum at the top to the center of mass near the bottom in order to find l, or length. Substituting the value of g into this equation, yields a proportionality constant of 2Π/g 0. Khan Academy is a 501(c)(3) nonprofit organization. A bullet of mass m is fired at a block of mass M hanging from a string. ½(M+m) V. derive the equation for the muzzle velocity. In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2. Develop con dence in your ability to use the equations of motion to predict the results of an experiment. Because the bullet lodges in the pendulum’s body, we can say that the collision was inelastic. . A bullet of known mass is shot into a wood block of known mass. 3, College Physics, Serway and Vuille The law of conservation of momentum is a universal law that applies to all interactions Kf / Ki = m1 / ( m1 + m2 ) Some basic mathematical analysis will allow you to look at the expression m1 / ( m1 + m2) and see that for any objects with mass, the denominator will be larger than the numerator. We are going to use the formulas: (2gh)^(½) = V & (m+m)V=mV. Determine this equation using conservation of energy. The first method will use horizontal projectile motion while the second method will use conservation of momentum and conservation of energy. (ballistic pendulum). h=2. 12, and his 3. time. A second projectile causes the pendulum to swing twice as high, h{eq}_2 {/eq} = 5. Note that the projectile, a ball, is launched from a launcher and will immediately be caught up in the ballistic pendulum arm where it is held in place by jaws tensioned with a rubber band. At NO time during the experiment are you to adjust the spring gun's tension. The Ballistic Pendulum. 2 = (M+m) g ∆ h . 𝑒 = _% Conservation of Energy and Momentum During L = length of the pendulum to the center of mass. m p. ambient pressure. Masking tape a steel ball and a ballistic pendulum. T is the period in seconds (s) π is the Greek letter pi and is approximately 3. The bullet of mass m is fired into that block. 4. The kinetic energy of a system is equal to '. M. Combining equations (4) and (6), we can solve for the initial velocity of the launcher. , through heat and deformation). If yes, then write out the procedure and equation for your experiment. 1. 0 cm for this one). The ball brings in energy of course. We evalutate a loss of almost half a Joule of Kinetic Energy- accounted for by the heat and sound produced by the collision. The development of the ballistic pendulum was a significant event in the history of ballistics, allowing this field of study to advance significantly. Ballistic Pendulum Austin Glass (Lab partner: Jack McElligott) 2/15/ ABSTRACT The design of the experiment was set up in order to test the theories of conservation of energy and momentum which state that energy and momentum are conserved during a collision. A second projectile causes the pendulum to swing twice as high, h{eq}_2 {/eq} = 5. Solve the equation for v 0. In this experiment we will use a ballistic pendulum to determine the initial horizontal launch velocity of a brass ball. Further develop an appreciation of analysis of errors in physical measurements. 00005kg length of arm shooter= 0. Using cquation 2, derive an equation for vy in terms of g. Using the average Ah and your derived equation to find the value for vy Part 3 Use equation I and your value for vy to calculate the speed of the ball, 27. After impact, the bob with the ball inside swings up to a maximum height (Figure 2). If the UMass Boston The Ballistic Pendulum Physics 181 momentum of the projectile becomes the momentum of the projectile-pendulum system. Show your work below. A ballistic pendulum is a device used to determine the speed of a bullet. If the projectile is particularly fast, such as a bullet, then the pendulum bob needs to be massive and there has to be a way to prevent it from swaying from side-to-side after the collision. There In this lab, the purpose is to use the maximum angle of the pendulum to determine the initial velocity of the projectile. Blackwood ballistic pendulum, metric balance, meter stick, carbon paper, wire restraint loop, heavy wire or cable, high range spring balances. Find the initial speed of the bullet. Use this online simple pendulum calculator to calculate period, length and acceleration of gravity alternatively with the other known values. We measure it in seconds. 3. The pendulum plus bullet (P+b) is on a circular trajectory which requires a centripetal force F c, provided by the tension in the rope: F c = (m + M) v 2 r = (m + M) g cos ballistic pendulum ) originally invented for determining the speed of a bullet. 12, and his 3. 2: Ballistic Pendulum The ballistic pendulum is used to explore the trans-fer and conservation of energy and momentum in a collision of two objects. See also ballistic pendulum. The result of this is: m b v b=(m b+M pa)V pab (Eq. Step 1: Using your measurement of the period of the pendulum, T, derive an expression for the moment of inertia of the pendulum arm with the ball in the catcher, I, by the following method. In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2. 12 in terms of the angular momentum of the pendulum given in Equation3. With the following information, we can conclude that the total momentum of the isolated system of the two particles remains constant and can be written as in an equation: Newton's second law of motion states that the sum of the forces acting on an object is equal to the product of the mass times the acceleration of the object. Mass of ball plus pendulum m bp= _____(kg) 10. A simple version of the spherical pendulum, the Foucault pendulum, is used to show that Earth rotates on its axis. When a projectile is shot into the wood, the block begins to swing in a pendulum-like motion. Weigh the pendulum support containing the steel ball on a top-loading balance. M e. L = length of pendulum bob . That is V=V(g,h). Ballistic Pendulum. 80665m/s 2 The velocity at the bottom of the swing is: v = √ 2g * L * (1-cos(a)) Where: v: The velocity at the bottom of the pendulum a: The angle from the vertical Thus the momentum of the ball just before the collision is equal to the momentum of the ball- catcher system immediately after the collision: mballvo= Mv(1) where v is the speed of the catcher-ball system just after the collision, and M is the combined mass of ball + catcher. In the case of the ballistic pendulum, a projectile is launched from a spring loaded gun and is trapped in the base of a pendulum. The masses mb and mp will be measure directly. The Editors of Encyclopaedia Britannica This article was most recently revised and updated by Erik Gregersen, Senior Editor. By applying Newton's secont law for rotational systems, the equation of motion for the pendulum may be obtained , and rearranged as . Use the average angle value in the calculation. The bullet embeds itself in the block. 3. Hence, mv =(m+M)V; (1) You now need to calculate vand vfor the three range settings. proof mass. Projectile (metal ball) 5. A second projectile causes the pendulum to swing twice as high, h{eq}_2 {/eq} = 5. Reference: Section 6. v- Velocity of the bullet. δ Height= H * ( ( δL /L) 2 + ( (sin° * δ ° )/ (1-cos°)) 2) . Subsequently, the pendulum swings up to a certain height or angle to Figure 1: Ballistic pendulum setup Experimental data m (¿ ¿ ball+mpend ) v f mball v 0 ball +m pend v 0 pend =¿ m pend v 0 pend Due to initially pendulum is at the rest: = 0. just before it collides with the pendulum V Part 4 1. Taking the value of T from (1) and substituting in (2) we get equation (3) as. Dividing both sides of this equation by eqn. The second part deals with the elastic and inelastic collisions and the momentum and energy conservation in both bases. The potential energy of a system is equal to 'mass x height x gravity'. 53 \text{ sec} \end{aligned} $$ yielding $$R_{co} = 62. Theory: In your lab book, clearly derive an expression for v b the launch speed of the ball, in terms of the height the center of mass of the pendulum rises, h, the acceleration due to gravity g, the mass of the ball, m b, and the mass of the pendulum, m p. Use the conservation of momentum equation to calculate 𝑣1. shot time. Determine The speed of the bullet before impact When it swings upward it has a height of 0. For many years, police laboratories used ballistic pendulums to measure the muzzle velocities of firearms. 8) (0. In order to determine the height we need to examine the ballistic pendulum more closely. where g is the acceleration due to gravity and h is the height. The equation formed by setting potential energy equal to kinetic energy UMass Boston The Ballistic Pendulum Physics 181 momentum of the projectile becomes the momentum of the projectile-pendulum system. This is a simulation of a ballistic pendulum. The momentum of the system is now: (2) Since the two momenta are equal, we can solve for U: (3) Finally, the system acts like a simple pendulum. Triple-beam balance Introduction The ballistic pendulum is a classic method for determining the velocity of a projectile; origi-nally, it was used to determine the muzzle velocity of rearms. Conservation of mechanical energy applies here, so: ½(m+M)vf2= (m+M)gh. If no, then what equipments are we missing? Querying for equation is a suitable end-of-chapter problem for an introductory physics course, possibly as a follow-up to a conventional ballistic pendulum problem, while the full energy analysis leading to equations and is a slightly more challenging exercise. It was the first accurate way to determine the muzzle velocity of a bullet. m. Since the pendulum bob catches the ball, they move off with the same velocity (→v 1f = →v 2f) (v → 1 f = v → 2 f) and the kinetic energy of the system is cannot be conserved during the collision. The ballistic pendulum is a tool for measuring the launch speed of a usually small and fast projectile. h- Maximum height reached by the pendulum. Connect the sensor to the interface. Using your measurement data for the ballistic pendulum, calculate the uncertainty (δvo) for v o. Pushing back the spring-loaded piston on the projectile section stores potential energy that can A ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. A ballistic pendulum is a device that can be used to determine the velocity of a bullet. 066) * (2 (9. Recall that th=4z- hz th 2. (8). Using the average Ah and your derived equation to find the value for vy Part 3 Use equation I and your value for vy to calculate the speed of the ball, 27. 44-caliber bullet has a mass of 12g. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. We also measured the pendulum for mass M and the projectile for mass m. Ballistic Pendulum. 66+0. The pendulum string is massless. t 0. 12, and his 3. The bullet-block system swings to a height . Derivation for height, which will be used later Here, r represents the distance from the pivot point to the center of balance, h represents the height the system rose to, and theta is the angle of the system; note that the center of mass is found with the total mass of pendulum and projectile combined. Below is the equation that will be used to find out V1. n. It is also a good demonstration of many basic principles of physics. 2g ∆ h Let s (t) be the distance along the arc from the lowest point to the position of the bob at time t, with displacement to the right considered positive. The spring gun is designed to fire a ball of mass (mb) with an initial velocity (vi). 5. The pendulum bob behaves like a mass point. Conservation of Linear Momentum: the Ballistic Pendulum I. The second object is a pendulum that is initially stationary. m. The preset scrollbar value for 𝑣1 is the “accepted value. The Blackwood pendulum (Fig. Sum of masses of pendulum and ball, ¿ mball +m pend M . The first method will use horizontal projectile motion while the second method will use conservation of momentum and conservation of energy. Weigh the pendulum support containing the steel ball on a top-loading balance. Recall that th=4z- hz th 2. Thus the period equation is: T = 2π√(L/g) Over here: T= Period in seconds. Theory Part 1 The setup for the ballistic pendulum is shown in Error! Reference source not found. Using the average Ah and your derived equation to find the value for vy Part 3 Use equation I and your value for vy to calculate the speed of the ball, 27. However, the pendulum is constrained by the rod or string and is not in free fall. mv. 4cm. 7 cm. The initial velocity of the projectile can be determined from the vertical rise of the ballistic pendulum using momentum and energy conservation principles. The ballistic pendulum is a device used to catch a ball fired from a spring-powered gun. Expt 3 – PHY400 – Ballistic Pendulum 2 (b) By applying the conservation of energy just after the bullet hits the pendulum until it moved a maximum vertical distance h, write down an equation v in terms of m, M, h and g (acceleration due to gravity). PE = mgh. Figure 1: Ballistic Pendulum After the ball is caught in the catcher and the swing-arm starts to move, momentum is no longer conserved because there is a net external force (the force of the swing-arm and gravity are no longer parallel). The bullet’s momentum can be determined from the amplitude of the pendulum swing. Again m is the mass of the ball measured above. Blackwood Ballistic Pendulum Jamal Wright, Zachary Floyd, Christopher Wilson Abstract Our goal of this experiment is to determine muzzle velocity by two methods: 1) employing uniform linear motion relations, the kinematic equations; 2) using the principles of conservation of energy and momentum. Determine this equation using conservation of energy. AP Physics 1: Momentum 8: Impulse Problem 1: Force as a Function of Time Graph. The Ballistic Pendulum Lab Report By: Edgar Avalos, Elysa Chapa, Elyse Chapa, and Michael Foster Objective Our objective during this experiment was to accurately calculate the speed and distance that a ball would travel after being shot from a ballistic pendulum by using the law Using the ballistic pendulum apparatus, I am going to estimate the velocity of the ball to get up to 45°. After the collision, the bullet is embedded in the wood block and the wood block swings upward. On the equation sheet provided during the free response section of the AP Physics B exam, the letter " J " is used for impulse: J = F ∆t = ∆ p. Foreword The momentum p of a body is defined as the product of its mass m and velocity v , or (1) p = mv . / 1 2 2 2 98 0595 11662 341 2 ch 222b g We can now substitute this value for vfinal into our conservation of momentum equation. (3. In this experiment we will use a ballistic pendulum to determine the initial horizontal launch velocity of a brass ball. When the bob is displaced from equilibrium and then released, it begins its back and forth vibration about its fixed equilibrium position. The initial velocity of the ball is determined in terms of the masses of the ball and the bob and the height to which the bob rises after impact. By plugging the velocities found and the masses found into the derived equation, we can find the final velocity, v'. A large wooden block suspended by two cords serves as the pendulum bob. 8. Theory If a shot of mass m is ¯red from a gun into a heavy pendulum bob of mass M so that the shot is lodged in the bob, total momentum of the shot and the bob is conserved immediately after impact. org this as an equation for x components: Pix = Pfx. The system has some momentum and kinetic energy: After the collision, the pendulum will swing about its center of support from its initial height to some maximum height. From conservation of momentum, we can calculate the velocity which the pendulum will move after trapping the ball. One of these objects is a small projectile of mass mthat is projected at a certain speed vby a launcher. Additionally, the change of KE into PE between the moments of the pendulum at its lowest and highest points can be used (see work below). Timing the swing of the pendulum (with ball) gives a period of about 1. In order to efficiently design any gun system the internal ballistics should be understood to minimize energy losses and correctly define design parameters. o = (M+m) V . SIMULATION: For the last part of this laboratory you will use a commercial Once we add the equation for cosine will allow us to make an equation to find the initial velocity of the ball. In the first stage momentum is conserved and therefore: where v is the initial velocity of the projectile of mass m P. Therefore, ∆KE = KE f - KE i = ½(m + M)V 1 2 – ½ m(V o) 2 ballistic pendulum gun using the conservation of angular momentum. g. So, the speed of the system immediately after the collision is: vf= (2gh)½. The system has some momentum and kinetic energy: After the collision, the pendulum will swing about its center of support from its initial height to some maximum height. R. 4cm. When the ball and the pendulum begin to move together energy is conserved from that point to the point where the pendulum reaches its maximum angle. Carefully remove the pendulum with steel ball embedded from the apparatus. The ball then enters and is caught in a metal cylinder suspended from a fixed axle. To make it somewhat less hazardous we will be using a bean shooter as our cannon. The height it rises is A compound pendulum (or physical pendulum) is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body swinging by a pivot. The ballistic pendulum consisted of a large block, suspended by cords. The height to which the block (plus embedded projectile) rises is a measure of the speed achieved Figure 1: The ballistic pendulum Figure 2: A ball of mass, m, and speed, apparatus v, is caught by the pendulum, which swings up to an angle q. This height can be measured experimentally. 3 kg, 1. The ballistic pendulum is a classic method of determining the velocity of a projectile. 5 =. A ballistic pendulum is a device which is used to arrive at the kinetic energy and velocity of a bullet. 𝑣2=_____ 𝑚/ 11. The purpose of this lab is to investigate an example of a perfectly inelastic collision using a ballistic pendulum, specifically looking at the velocity of the projectile. 9. 1. Using cquation 2, derive an equation for vy in terms of g. Show your work in the empty space provided below. and the combination of block and bullet would swing above its original height by an amount. The bullet becomes imbedded in the wood and the pendulum rises to a vertical height of 0. Using the equation above, we can conclude that the time derivite of the total momentum ( P) is equal to zero or P = p1 + p2 = 0. Write the relevant Conservation of Momentum equation for a case where a moving object with mass . In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2. 75 m/s. i, V. 7 cm. Figure 2 shows a picture of the ballistic pendulum that we will use in this activity. After the collision, the bullet is embedded in the wood block and the wood block swings upward. 6032*Vf Now you can consider energy after the collision 1/2 (3. displacement θ of the pendulum can be recorded To calculate the maximum height h reached by the pendulum relative to the position of the collision, you will use the formula devised in the pre-lab In this formula you will use the length L of the pendulum arm measured to its center of mass when the ball is the catcher Also measure the mass of the ball m b and the mass m p . A ballistic pendulum is used to measure the speed of high-speed projectiles. so as far as simple harmonic oscillators go masses on Springs are the most common example but the next most common example is the pendulum so that's what I want to talk to you about in this video and a pendulum is just a mass M connected to a string of some length L that you can then pull back a certain amount and then you let it swing back and forth so this is going to swing forward and then 35A Ballistic Pendulum 35A - Page 2 of 6 Written by Jon Hanks Figure 2: Mounting Launcher 4. Later in the Cenco document: ERRORS: Part of the momentum of the impact will be transmitted to the pendulum frame through imperceptible flexing and energy will be lost through windage and bearing Express the dependence of the height h, through which the pendulum rises, on the pendulum’s length and on the angle of deflection: \[h=L-L\cos \alpha=L(1-\cos \alpha)\tag{1}\] Hint 2 - momentum. Partners: Mary Schaude, Kyle Collins, and Hunter McCabe Date: 2/11/15-2/20/15. Uncertainties for: Mass of ball= 0. Ballistic pendulum machine 4. v’ is the velocity of the block and embedded projectile (both of mass m P + m B) just after the collision, before they have moved significantly. In this case the pendulum's period depends on its moment of inertia I around the pivot point. L is the length of the rod or wire in meters or feet. Ballistic pendulum lab report for chapters in a thesis corporate strategy case studies essays » naruto speech » about parts of speech » Ballistic pendulum lab report The highest praise he offered his female nudes fuse observation with a portrait ofantonio bruni through knoedler & co extinction curtailing the performance gains divisions Interior ballistics are the events in a gun system that determines the performance of any gun design. pendulum impulse. wire tension. Theory In order to calculate the velocity of the projectile, an equation needs to be derived. The system has some momentum and kinetic energy: After the collision, the pendulum will swing about its center of support from its initial height to some maximum height. Using the average Ah and your derived equation to find the value for vy Part 3 Use equation I and your value for vy to calculate the speed of the ball, 27. This pendulum is a massive block of mass M suspended on the rope. 2. f. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 10. Let’s write out the equations describing each of the two events (collision and rising). 6%. The block then swings through a maximum angle of θ = 60 ∘. 0071, very similar to the 2. 2. m . The ballistic pendulum has historically been used to measure the launch velocity of Lab 7. p e. Mass of the steel ball (m ball ) = kg Mass of the steel ball +pendulum (m ball+pendulum ) = kg Length of pendulum (L) = m Pendulum height (h) = L (1-Cos ) = m Initial velocity (V 01 ) = m/s Experiment 2. 4cm. 12, and his 3. The guns are fired into a 10kg pendulum bob of length L. The formula for cosine is that 'cos(theta) = adj/hyp'. Discussion a. i, and. A = cross-sectional area. This was the first way to find out how fast a bullet was going. g = accel due to gravity. The simple pendulum equation is: T = 2π * √ L/g Where: T: Period of the simple pendulum L: Length of the pendulum g: g: Acceleration due to gravity, the standard gravity of Earth is 9. Finally perform your experiment and test the value of the initial velocity you obtain from your experiment with that of the ballistic pendulum. The system is frictionless. Ballistic Pendulum¤ Object To determine the accuracy of a ballistic pendulum in measuring the muzzle velocity of a gun. Using the value for V o calculated from the ballistic pendulum, calculate the fractional loss in the kinetic energy during the collision. A ballistic pendulum is a device that can be used to determine the velocity of a bullet. Using cquation 2, derive an equation for vy in terms of g. (c) Write down u in terms of m, M, h and g by substituting the equation in part (a) For a physical pendulum, the period, T, equals 2π√(I/MgR), where R is the distance from the pivot to the center of mass of the pendulum (27. But to use that equation and to find the muzzle velocity of the metal ball we need to find how high the pendulum rose at its highest angle. When the angular displacement amplitude of the pendulum is large enough that the small angle approximation no longer holds, then the equation of motion must remain in its nonlinear form $$ \frac{d^2\theta}{dt^2} + \frac{g}{L}\sin\theta = 0 $$ This differential equation does not have a closed form solution, but instead must be solved numerically using a UMass Boston The Ballistic Pendulum Physics 181 momentum of the projectile becomes the momentum of the projectile-pendulum system. and Ball Bouncing in slow motion: tennis ball. We also need to remember that potential energy equals mass times gravity times height and kinetic energy equals one half the mass times velocity squared. Sadistic Extension: 7. Momentum descriptive name Ballistic Pendulum. A Ballistic Pendulum is used to determine the muzzle velocity of a ball shot out of a Projectile Launcher. See Figure 1 for a picture of what happens. When the projectile collides with the pendulum bob, the projectile remains embedded in the pendulum bob - a completely inelastic collision. Sandbags have been used as pendulums for bullets. The pendulum bob and ball move off together after the collision (see Figure 1). Record this value below. Firstly, we have the period equation which helps us calculate how long the pendulum takes to swing back and forth. 0032*Vi=3. The instructions here will let you figure it out. The potential energy of the pendulum is taken to be zero when the pendulum is at its equilibrium point, which is located at the bottom of the pendulum's swing. Rearranging this gives I = (T 2 MgR/4π 2). The bullet remains embed Experiment 8 Ballistic Pendulum Conservation of linear momentum (Before and immediately after the collision) Conservation of energy (During the swing of the pendulum arm) m p b m b v 0 =()m p + m b v r 1 2 ()m p + m b 2v r =()m p + m b gh cm initial velocity v 0 = ()m p + m b v r m b recoil velocity v r = 2gh cm Procedure: 1. 5. Using cquation 2, derive an equation for vy in terms of g. In its simplest form, the ballistic pendulum is a block of wood, hanging freely on ropes or wires and initially at rest. Using a ballistic pendulum that is assumed to have little energy lost, we can use equations to find velocity as the bullet embeds itself into the pendulum hammer. 3 meter long rod. projectile and the maximum angle of the pendulum deflection. UMass Boston The Ballistic Pendulum Physics 181 momentum of the projectile becomes the momentum of the projectile-pendulum system. general index. As the pendulum swings, its center of gravity rises. Just after the collision, the pendulum bob is moving with speed V. This is a percent difference of 33. Measurement of experimental launch velocity (V 02 ) Procedure 1. υ. (7), we nd the simple result: x x = y 2y + h 2h: (8) Thus, we predict the projectile will land at range values of x + x and x − x, where x is given by eqn. gas constant (air) S. There was no deformation of either object and momentum was conserved. Figure 4. Equations governing the ballistic pendulum. 3. The ballistic pendulum A ballistic pendulum takes the horizontal motion of a ball and turns it into the swinging arc of an arm around a pivot: You can break the action into two pieces: A ball of mass m moving at speed v1 slams into an arm of mass M. exit section pressure of the nozzle. The pendu-lum and cup can be moved out of the way. 6 cm. 20) Solving for L~pb we obtain: jL~pbj˘ p 2I E. Any objects that collide in this way will reduce the total kinetic energy (and total velocity) by this ratio. So this equation can be rewritten in this form. 1). Both of these motions store some kinetic energy, as we'll discuss in Rotation. In effect, the plane of the pendulum’s oscillation rotates freely. This is done by using derived equations such as the one below to calculate the height the pendulum rises to. Projectile (metal ball) 5. 65". See the figure below. p = m v p = mv. Ballistic Pendulum Lab The Conservation of Angular Momentum is probably the least familiar of the three great conservation laws for most people. The pendulum will then swing upward where it will be caught by a trip mechanism. 5 = ( (0. Therefore when measuring the swing of the pendulum one needs only take into account the mass of the catcher in the equation for the pendulum swing. v0 = ((mb + mp) / mb ) (7) This equation shows that by measuring the masses of the pendulum, the ball, and the height of the pendulum swing, we can determine the initial speed of the ball before the collision. The goal of this computational model is to develop a ballistics model to aid in gun design. Thus: mu = (M+m)V, or V = mu / (M+m). In effect, the plane of the pendulum’s oscillation rotates freely. 7 cm. This will allows to find an expression for V in terms of g and h. just before it collides with the pendulum V Part 4 1. According to the conservation of mechanical energy of the system after the collision, we have equation (5): (1/2) (m + M) V 1 2 = (m + M) g h . ballistic pendulum equation