Air Track Collisions

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1 PC1141 Physics I Air Track Collisions 1 Objectives Determine the velocity and momentum of each glider before and after the collision from which the total momentum of the system before and after the collision is obtained. Evaluate the extend to which the total momentum of the system before the collision is equal to the total momentum of the system after the collision. 2 Equipment List Air track with two gliders Air track accessory tray consisting of rubber band bumpers, bumper blades on cylinder, wax filled cylinders, needle on cylinder and additional masses for gliders Photogates Laboratory balance Smart Timer and picket fence 3 Theory The momentum of an object of mass m moving with a velocity v is defined to be p = m v Momentum is a vector quantity because it is the product of a scalar (m) with a vector ( v). Forces exerted between particles of a system are called internal forces and they cannot change the momentum of the system. The total momentum of the system can change only if external forces act on the system. Momentum is conserved in a collision between two objects because the forces that the objects exert on each other are internal to the system. If p 1 i and p 2 i stand for the initial momenta of particles 1 and 2, and p 1 f and p 2 f stand for their final momenta after the collision, then p 1 i + p 2 i = p 1 f + p 2 f (1) In the most general case, equation (1) implies that each of the components of the momentum is conserved. In this experiment, two gliders will undergo collisions on a linear air track Page 1 of 6

2 Air Track Collisions Page 2 of 6 and hence these are one dimensional collisions. The vector nature of the problem is specified by writing momenta to the right as positive and momenta to the left as negative. Equation (1) is strictly valid only if there are no external forces on the system. Friction on the gliders of an air track will be an external force. Therefore, frictional effects on the gliders will tend to invalidate equation (1) if the frictional forces are comparable to the forces of collision on the gliders. When two gliders collide with each other, the total momentum of both gliders is conserved regardless of elastic or inelastic collision. Both elastic and inelastic (completely) collisions will be investigated in this experiment. An elastic collision is one in which the two gliders bounce off each other with no loss of kinetic energy accomplished through the use of the rubber band bumper with bumper blade on cylinder on each end of the glider in this experiment. A completely inelastic collision is one in which the two gliders hit and stick to each other accomplished in this experiment using the wax filled cylinder and needle on cylinder at one end of each glider. In this experiment, the measurements will involve determination of the velocities of two gliders before the collision and after the collision. Each of these four velocities is a constant velocity. The value of a velocity will be determined by Smart Timer when the glider passes through the respective photogates (see Figure 1). Figure 1: Apparatus setup. Three different profiles for collision will be investigated in this experiment. These are: Collision I: Place one of the gliders at rest in the middle of the track. Give the other glider an initial velocity toward the stationary glider. Collision II: Start both gliders at one end of the track. Give the first glider a slow velocity and the second glider a faster speed so that the second glider catches the first glider. Collision III: Start both gliders at opposite ends of the track toward each other.

Air Track Collisions Page 3 of 6 4 Laboratory Work Part A: Inelastic Collisions In this part of the experiment, you will investigate completely inelastic collisions between two gliders.

Level the track by setting a glider on the track to see which way it moves.

3 Air Track Collisions Page 3 of 6 4 Laboratory Work Part A: Inelastic Collisions In this part of the experiment, you will investigate completely inelastic collisions between two gliders. Two gliders will hit and stick together after the collision. It is accomplished using the wax filled cylinder and needle on cylinder at one end of each glider. A-1. Level the track by setting a glider on the track to see which way it moves. Adjust the leveling screw at the end of the track to raise or lower that end until the glider placed at rest on the track will not move. A-2. Insert a picket fence in the top surface of each glider. Position the two photogates just far enough apart so the collision can take place between the photogates. Connect the photogates to the Smart Timer (see Figure 3). Figure 2: Smart Timer picket fences. Figure 3: Conneting the photogate to the Smart Timer. A-3. Mount the wax tube at the end of a glider and the needle at the end of the other glider (see Figure 4). Place the gliders on the air track so that the wax and needle face each other. Figure 4: Needle and wax tube. Note: The wax tube is mounted on the end of a glider for an inelastic (completely) collision. The needle is mounted on the end of the second glider. It needs to be positioned so the needle will stick into the wax tube of the other glider once the two gliders collide, causing the gliders to stick together.

Air Track Collisions Page 4 of 6 A-4. Adjust the height of the photogates so the 1-cm flag will block the photogate infrared beams. Figure 5: The photogate head.

4 Air Track Collisions Page 4 of 6 A-4. Adjust the height of the photogates so the 1-cm flag will block the photogate infrared beams. Figure 5: The photogate head. Note: The Photogate Timer uses narrow-beam infrared photogate (see Figure 5) to provide the timing signals. An LED in one arm of the photogate emits a narrow infra-red beam. As long as the beam strikes the detector in the opposite arm of the photogate, the signal to the timer indicates that the beam is unblocked. When an object blocks the beam so it does not strike the detector, the signal to the timer changes. A-5. Setup the Smart Timer to measure Speed: collision (cm/s). Press Start/Stop to activate the Smart Timer. Note: If the picket fence of both gliders do not go through the photogate beams twice, the Smart Timer will not complete the timing cycle and display velocities automatically. You will need to push Start/Stop to stop timing. The completed timing measurements will be displayed and the uncompleted measurements will be registered as 0. The display will present the results in the following format: 1: Input Jack 1, initial speed 1, final speed 1 2: Input Jack 2, initial speed 2, final speed 2 The first number represents the input jack and the following two numbers indicate the initial and final speeds respectively. If the glider passes through the photogates just once, take the non-zero reading as the velocity of the glider when the glider passes through the corresponding photogate. Press 1 or 2 to scroll back and forth between the registered velocities from respective photogates. Press Start/Stop to reactivate the Speed: collision (cm/s) mode. A-6. Collision I. Perform each of the following completely inelastic collisions and record your data in Data Table 1. Let m 1 be the mass of the stationary glider and m 2 be the mass of the moving glider. u is the initial velocity of the moving glider and v is the final velocity of the gliders. The velocity is positive if moving towards right and negative otherwise. Case C: m 1 = M, m 2 = m where m < M Note: Masses must always be added symmetrically (the same number on each side) or the glider will not function properly.

Air Track Collisions Page 5 of 6 A-7. Collision II. Perform each of the following completely inelastic collisions and record your data in Data Table 2.

5 Air Track Collisions Page 5 of 6 A-7. Collision II. Perform each of the following completely inelastic collisions and record your data in Data Table 2. Let m 1 be the mass of the first glider and m 2 be the mass of the second glider. u 1 and u 2 are respective initial velocities (positive if moving towards right), and v is the final velocity of the gliders. Be sure that the collisions take place between the photogates. A-8. Collision III. Perform each of the following completely inelastic collisions and record your data in Data Table 3. Let m 1 be the mass of the left glider and m 2 be the mass of the right glider. u 1 and u 2 are respective initial velocities (positive if moving towards right), and v is the final velocity of the gliders. Be sure that the collisions take place between the photogates. with u 1 > u 2 Case B: m 1 m 2 = m with u 1 < u 2 Case C: m 1 = m, m 2 = M where m < M with u 1 > u 2 Case D: m 1 = M, m 2 = m where m < M with u 1 < u 2 Part B: Elastic Collisions In this part of the experiment, you will investigate elastic collisions between two gliders. It is accomplished through the use of the rubber band bumper with bumper blade on each end of the glider. B-1. Mount the rubber band bumper at the end of a glider and the bumper blade at the end of the other glider (see Figure 6). Place the gliders on the air track so that the bumper and blade face each other. Figure 6: Rubber band bumper and bumper blade. Note: The rubber band bumper provides a soft collision, eliminating any vibration of the glider as it collides with another glider or an end stop. The bumper blade is mounted on the end of the glider and is designed to collide with the rubber band bumper.

6 Air Track Collisions Page 6 of 6 B-2. Collision I. Perform each of the following elastic collisions and record your data in Data Table 4. Let m 1 be the mass of the stationary glider and m 2 be the mass of the moving glider. u is the initial velocity of the moving glider, and v 1 and v 2 are respective final velocities of the gliders. Case C: m 1 = M, m 2 = m where m < M B-3. Collision II. Perform each of the following elastic collisions and record your data in Data Table 5. Let m 1 be the mass of the first glider and m 2 be the mass of the second glider. u 1 and u 2 are respective initial velocities, and v 1 and v 2 are respective final velocities of the gliders. Be sure that the collisions take place between the photogates. B-4. Collision III. Perform each of the following elastic collisions and record your data in Data Table 6. Let m 1 be the mass of the left glider and m 2 be the mass of the right glider. u 1 and u 2 are respective initial velocities, and v 1 and v 2 are respective final velocities of the gliders. Be sure that the collisions take place between the photogates. with u 1 > u 2 Case B: m 1 m 2 = m with u 1 < u 2 Case C: m 1 = m, m 2 = M where m < M with u 1 > u 2 Case D: m 1 = M, m 2 = m where m < M with u 1 < u 2 Part C: Explosive Collisions In this part of the experiment, you will investigate explosive collisions between two gliders. It is accomplished through the use of two rubber band bumpers on each end of the gliders. C-1. Mount one rubber band bumper at the end of each glider. Place the gliders on the air track so that the bumpers face each other. C-2. Explosive collision is accomplished by pressing the rubber band to each other and letting the gliders go simultaneously. Perform each of the following explosive collisions and record your data in Data Table 7. Let m 1 and m 2 be the masses of respective gliders. v 1 and v 2 are respective final velocities of the gliders. Case B: m 1 = m, m 2 2m Case C: m 1 = m, m 2 4m Last updated: Wednesday 24 th September, :49am (KHCM)

7 CONSERVATION OF LINEAR MOMENTUM II

7 CONSERVATION OF LINEAR MOMENTUM II MEASUREMENTS AND CALCULATIONS OBJECTIVE To measure momentum before and after collisions as a way of investigating momentum conservation. INTRODUCTION ACTIVITY 1 This