PC1141 Physics I Conservation of Momentum in Collisions

Transcription

1 PC1141 Physics I Conservation of Momentum in Collisions 1 Purpose Determination of the velocity and this momentum of each glider before and after the collision from which the total momentum of the system before and after the collision is obtained Evaluation of 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 Air track, air blower, two gliders, fork with rubber band, holder with plate, wax and needle Smart Timer and picket fence Photogates Various weights Laboratory balance 3 Theory The momentum of an object of mass m moving with a velocity v is dened to be p = m v Momentum is a vector quantity because it is the product of a scalar (m) with a vector ( v). It can be shown for a system of particles that the total momentum of the system is constant if there are no external forces acting on the system. The forces exerted between the particles of the system are called internal force and they cannot change the momentum of the system. A collision between two objects is an example of a case in which momentum is conserved because the forces that the two objects exert on each other are internal to the system. If p i 1 and p i 2 stand for the initial momenta of particles 1 and 2 and p f 1 and p f 2 stand for their nal momenta after the collision, then p i 1 + p i 2 = p f 1 + p f 2 (1) Page 1 of 5

2 Conservation of Momentum in Collisions Page 2 of 5 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 and hence these are one dimensional collisions. The vector nature of the problem is specied 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 eects 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 o of each other with no loss of kinetic energy accomplished through the use of the fork with rubber band and holder with plate 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 and needle on one end of each glider. Three dierent proles for collision will be investigated in this experiment. There 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 rst glider a slow velocity and the second glider a faster speed so that the second glider catches the rst glider. Collision III: Start both gliders at opposite ends of the track toward each other. Figure 1: Apparatus setup 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 the photogate.

3 Conservation of Momentum in Collisions Page 3 of 5 4 Experimental Procedure 1. Level the track by setting a glider on the track to see which way it rolls. Adjust the leveling screw at the bottom of the track to raise or lower that end until a glider placed at rest on the track will remain at rest. 2. Put a picket fence into the slots in the top of each glider and place the collision gliders so the wax and needle face each other. Position the two photogates just far enough apart so the collision can take place between the photogates. Adjust the height of the photogates so the 1-cm ag will block the photogate infrared beams. Connect the photogates to the Smart Timer. Figure 2: Conneting the photogate to the Smart Timer Figure 3: Smart Timer picket fences 3. Setup the Smart Timer to measure Speed: collision (cm/s). Press Start/Stop to activate the Smart Timer. Note: If the ag does not go through the photogate beams twice, the Smart Timer will not complete the timing cycle and display velocities automatically. You will need to press Start/Stop to stop timing manually. 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, nal speed 1 2: Input Jack 2, initial speed 2, nal speed 2 The rst number represents the input jack and the following two numbers indicate the initial and nal 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.

4 Conservation of Momentum in Collisions Page 4 of 5 4. Equal Masses. Perform each of the following completely inelastic collisions FIVE times. (a) Collisions I. Record your data in the Data Table 1. (b) Collision II. Record your data in the Data Table 2. Note: M 1, M 2 are the respective masses of the gliders and u 1, u 2 are the respective initial velocities (positive if moving towards right). v is the nal velocity of the gliders. 5. Unequal Masses. Put the weights on the steel pegs mounted on the sides of the gliders so that the mass of one glider (2M) is approximately two times the mass of the other glider (1M). Perform each of the following completely inelastic collisions FIVE times. (a) Collisions I. Let 1M be the stationary glider at middle of the track. Record your data in the Data Table 3. (b) Collision II. Let 1M be the rst glider and 2M be the second glider. Record your data in the Data Table 4. (c) Collision III. Record your data in the Data Table Set up the gliders so the fork with rubber band and holder with plate face each other, so the gliders will repel each other when they collide. 7. Equal Masses. Perform each of the following elastic collisions FIVE times. (a) Collisions I. Record your data in the Data Table 6. (b) Collision III. Record your data in the Data Table 7. Note: M 1, M 2 are the respective masses of the gliders, u 1, u 2 are the respective initial velocities (positive if moving towards right) and v 1, v 2 are the respective nal velocities. 8. Unequal Masses. Put the weights on the steel pegs mounted on the sides of the gliders so that the mass of one glider (2M) is approximately two times the mass of the other glider (1M). Perform each of the following elastic collisions FIVE times. (a) Collisions I. Let 2M be the stationary glider at middle of the track. Record your data in the Data Table 8. (b) Collision II. Let 2M be the rst glider and 1M be the second glider. Record your data in the Data Table 9. (c) Collision III. Record your data in the Data Table 10.

5 Conservation of Momentum in Collisions Page 5 of 5 5 Data Analysis D1. Enter your data in the Data Table 15 into the Excel spreadsheet. For each of the cases, calculate the the momentum for each of the gliders before and after the collision in the spreadsheet. Let momenta to the right be positive and momenta to the left be negative. D2. For each case, calculate the total momentum of both gliders before and after the collision in the spreadsheet. Note that momentum is a vector quantity. D3. Calculate the percentage dierence between the total momentum before the collision and the total momentum after the collision for each of the cases in the spreadsheet. Hint: The percentage dierence is dened as Percentage dierence = p i p f ( p i + p f )/2 100% D4. Calculate the best experimental value of the percentage dierence between the total momentum before the collision and the total momentum after the collision as well as its corresponding uncertainty. Do your results indicate that momentum is conserved for inelastic collision? D5. Enter your data in the Data Table 610 into the Excel spreadsheet. For each of the cases, calculate the momentum for each of the gliders before and after the collision in the spreadsheet. D6. For each case, calculate the total momentum and total kinetic energy of both gliders before and after the collision in the spreadsheet. D7. Calculate the percentage dierence between the total momentum before the collision and the total momentum after the collision for each of the cases in the spreadsheet. Perform the similar calculations for the percentage dierence between the total kinetic energy before the collision and the total kinetic energy after the collision in the spreadsheet. D8. Calculate the best experimental values of the percentage dierence between the total momentum and total kinetic energy before the collision and the total momentum and total kinetic energy after the collision as well as their corresponding uncertainties. Do your results indicate that momentum and kinetic energy are conserved for elastic collision?