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PHYS 1401 Lab-4: Conservation of Momentum Name: _____________________________ Objectives: 1) To study the types of Collision in one dimension between two balls by using PHET Simulation. 2) To determine the kinetic Energy and the linear momentum of each ball before and after the collision. 3) To conclude the main difference between the elastic collision and the inelastic collision. 4) To explore conservation of momentum in one-dimensional collisions. Introduction The general formula of Newton’s Second Law is where is the external force acting on the object, is the linear momentum of the object and t is the time, when the external force equal to zero the linear momentum becomes constant because p = 0, so the linear momentum is conserved regardless to the type of collision. The simplest explosion is when two objects, originally at rest, push away from each other because of only a force between the two (a force completely internal to the system). When only internal forces are exerted, the total momentum of a system is conserved. Because the system is initially at rest, its initial momentum, pi, is zero. The final momentum of the system, pf, must still be zero. The final momentum of each object, therefore, must be equal in magnitude and opposite in direction. Therefore, the ratio of the final velocities of the two objects is equal to the negative inverse ratio of their masses: The velocity ratio is a negative number because v1 and v2 are in opposite directions. When two objects collide, either elastically or inelastically, the total momentum of both objects is always conserved. The sum of the initial momentum of the two objects is always equal to the sum of their final momentum. The total kinetic energy of both objects, however, is not always conserved. An elastic collision is defined as one in which the total kinetic energy is conserved, i.e., they bounce off each other with no net loss of kinetic energy. An inelastic collision, of course, is one in which the kinetic energy of the system is not conserved. In an inelastic collision, some of the initial kinetic energy goes into deforming the objects. In most inelastic collisions, the deformed objects separate after the collision, but in a perfectly inelastic collision, they stick together. A collision is one dimensional when the direction of one object’s initial velocity passes through the other object’s center of mass. After such a collision, the objects move away from each other along this same line. If the initial velocity does not pass through the center of mass, the objects will move away in different directions, making the collision two dimensional. Being a vector quantity, momentum can be resolved into components. For a system’s total momentum to be conserved, each of its components must be conserved. If a moving object has a collision with a stationary object, the initial momentum of the system is equal to that of the moving object. The vector sum of the final momentum of both objects will be equal to this initial value, whether the collision is elastic or inelastic, and whether it is one-dimensional or two-dimensional. Activity-1: Elastic Collisions Go to PHET simulation and find collision lab or type in https://phet.colorado.edu/sims/html/collision-lab/latest/collision-lab_all.html 1) Click Explore 1D 2) Select (Elasticity 100%) by dragging the blue rectangle to the right 3) Uncheck “reflecting border”. 4) Click on more data at the bottom. This will give mass as well as velocity and momentum values. 5) You can click on the ball and drag it to change its position. Also, you can click on position x box under more data and type in the number. 6) Control the balls velocity by changing the length and the direction of the velocity vector. Press on the circle at the tip of the velocity vector and then drag to change its magnitude and direction. You can also click on the velocity vx box and type in the number. 7) Set up your page as shown in the figure below. Question-1: With the current set-up, what will happen after the collision? Question-2: What will each object’s velocity and momentum be prior to and after the collision? Hit the “Play” button, Click “Pause” just after collision, and record the data in Table-1. Table-1 m1 (kg) v1i (m/s) p1i (kgm/s) m2 (kg) v2i (m/s) p2i (kgm/s) v1f (m/s) p1f (kgm/s) v2f (m/s) p2f (kgm/s) 0.50 0.50 0.25 2.0 -0.50 -1.00 Key: m = mass, v = velocity, p = momentum, 1 = object 1, 2 = object 2, i = initial (prior to collision), f = final (post collision) Add your two initial momenta and your two final momenta pi = ________________________________ pf = ________________________________ Question-3: What can you observe about the total momentum before and after the collision? Activity-2: Elastic Collisions – Equal masses (m1 = m2) 1) Choose both masses to be equal. Perform several experiments with different values for mass and velocity, but in each case choose m1 = m2. 2) This collision will take place between blue ball (m1) and pink ball (m2) of the equal masses (m1 = m2 = 2kg), with (m2) initially at rest (v2i = 0). The blue ball (m1) will collide with pink ball (m2) and essentially stops, then m2 will move in the same direction of m1 before collision. 3) Click on Play, then just after collision Pause. 4) Record the values of v1f and v2f after collision in Table-2. 5) Calculate the values of pi and pf, record them in Table-2. 6) Choose any mass for Trials 2 and 3, but in each case choose m1 = m2. Table-2 m1 (kg) v1i (m/s) p1i (kgm/s) m2 (kg) v2i (m/s) p2i (kgm/s) v1f (m/s) p1f (kgm/s) v2f (m/s) p2f (kgm/s) Trial 1 2.00 1.00 2.00 2.00 0.00 0.00 Trial 2 Trial 3 For trial#1 above: Calculate the total initial kinetic energy and total final kinetic energy. Show equations and substitutions. Initial: Final: Question-4: What do you observe about the total kinetic energy before and after the collision? Question-5: When the collision is elastic and the masses are the same, what happens with the velocities? Activity-3: Elastic Collisions – Unequal masses (m1 m2) Choose m1 = 0.1 kg and m2 = 3.0 kg. Perform the following experiment and record the data in Table-3 Table-3 m1 (kg) v1i (m/s) p1i (kgm/s) m2 (kg) v2i (m/s) p2i (kgm/s) v1f (m/s) p1f (kgm/s) v2f (m/s) p2f (kgm/s) Trial 1 0.10 1.00 3.00 0.00 Trial 2 0.10 1.00 3.00 -1.00 Trial 3 0.10 1.00 3.00 -2.00 Trial 4 0.10 2.00 3.00 0.00 Trial 5 0.10 2.00 3.00 -1.00 Question-6: What do you observe about the final velocity of the heavier object? Question-7: What do you observe about the final velocity of the lighter object? Comment on the magnitude and direction. Question-8: What do you observe about the total kinetic energy before and after the collision? Activity-4: Inelastic Collisions – Unequal masses (m1 m2) 1) Click Explore 1D 2) Change Elasticity to 0% by dragging the blue rectangle to the left. 3) Uncheck “reflecting border”. 4) Choose m1 = 3.00 kg and m2 = 1.00 kg. 5) Click on “Play”, then after collision click “Pause”. 6) Record the value of vf into Tables 4 and 5. 7) Calculate the values of pi, pf, pf/pi, Ki, Kf and Kf/Ki and record them into Tables 4 and 5. Table-4 v1i (m/s) v2i (m/s) (kg.m/s) vf (m/s) Experimental pf (kg.m/s) Calculated (kg.m/s) 2.00 0.00 2.50 0.00 3.00 0.00 Table-5 v1i (m/s) v2i (m/s) vf (m/s) (J) (J) 2.00 0.00 2.50 0.00 3.00 0.00 Question-9: What is the difference between elastic and inelastic collision? Question-10: In a collision between two unequal masses, which mass receives a greater magnitude impulse? a) the smaller mass b) the larger mass c) They receive equal impulses. Question-11: Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. The person in the front throws a very massive ball toward the back, and the person in the back catches it. After the ball is caught, the canoe is a) stationary. b) moving forward. c) moving backward. Question-12: A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true? (There could be more than one correct choice.) a) The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball. b) The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball. c) The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball. d) Both balls lose all their momentum since the collision is inelastic. e) The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball. Question-13: In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is a) completely inelastic. b) perfectly elastic. c) partially inelastic. d) characterized by an increase in kinetic energy. e) not possible because momentum is not conserved. Question-14: In the figure showing an isolated system, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is a) perfectly elastic. b) completely inelastic. c) partially inelastic. d) characterized by an increase in kinetic energy. e) not possible because momentum is not conserved. Question-15: Show your calculation, but you may use any shortcuts identified in this experiment. a) A 2.0 kg mass traveling at 3.0 m/s strikes another 2.0 kg mass traveling at -1.0 m/s. They collide and have a completely elastic collision. What are the velocities of each after the collision? b) A 2.0 kg mass traveling at 4.0 m/s collides elastically with a 1.0 kg object traveling at 1.0 m/s. The final speed of the 2.0 kg mass is 2.0 m/s. What is the final speed of the 1.0 kg object? 4