Conservation Laws - Fundamentals of Physics I - Lab 4 | PHYS 101, Lab Reports of Physics

Download Conservation Laws - Fundamentals of Physics I - Lab 4 | PHYS 101 and more Lab Reports Physics in PDF only on Docsity! PHYS-101 LAB-04 Conservation Laws (Collisions) 1. Objective The objectives of this experiment are: • Measurement of momentum and kinetic energy in collisions. • Experimentally test the validity of the principles of conservation of momentum and kinetic energy. • Examine the principle of rotational invariance with respect to our conservation laws. 2. Theory Review Chapter 8 in Serway and Jewett. As you have learned, a closed system can be characterized completely, if one knows all the positions r x and their velocities r v of all the objects (particles) within the system, and moreover how these particles interact. By characterized completely, we mean that if one knows the positions and the velocities of every object in the system and how they interact, one can (in principle) determine exactly what will happen to the system any time in the future or has happened to the system anytime in the past. In practice of course, it is difficult to know about every ‘object’ in the system and how they interact as typically our apparatus is made of many (~1023) particles all interacting in complicated ways. Nonetheless, if we can design an experiment that is very close to this idealized system, we can ‘probe’ our experimental setup to test fundamental properties of nature such as the conservation of energy and momentum, as well as invariance principles. All closed systems have certain properties that always hold, no matter how we design these systems. The three properties we will investigate today are two fundamental laws: • The Conservation of Energy • The Conservation of Linear Momentum And more over we will examine the • Rotational Invariance of the fundamental laws. All systems that are closed (this just means you are not exchanging mass or energy with the system) have this property. Since studying any system is quite complicated, we will study a nice simple system where we have particles (hockey pucks in our case) that do not interact unless they “bang” into each other (which will cause them to scatter about). No matter how these particles bounce, our two fundamental laws of physics will always be true. The important thing to remember here, is even though we are studying this simple system, these principles are true in general, for all systems! But first lets review some physics, Suppose I have a hockey puck with mass m and velocity r v . I can associate two quantities with this puck. (1) The kinetic energy of the puck: E = 1 2 mv 2 (1.1) and (2) the linear momentum of the pick: p = mv (1.2) The total linear momentum of the system is just the sum of the individual momentum of each object in your system: p tot = p i = m i v i i ! i ! (1.3) And correspondingly the total kinetic energy of the system is just the sum of the Individual kinetic energies: E = 1 2 m i v i 2 i ! (1.4) To review, the energy of course is a simple number (scalar) and only has positive quantities, while the linear momentum is a vector (three numbers) and each component may have positive or negative quantities) We are designing an experiment such that the potential energy of the system does not change (the objects are not interacting except for the collision and friction may Figure 2 Example of a collision between two equal masses. As the top puck is initially still, there is only a single velocity associated with it. The bottom puck is initially moving upwards at a relatively high rate of speed, upon collision it moves towards the right at a slower rate of speed (with some of the momentum being transferred to the top puck). You should be able to determine the initial and final momentum of each puck by analyzing the above figure. 3. Procedure 1. Level the air table. 2. Set the Spark timer to the desired setting (50 ms, 20 hz) (This is the time interval between each dot placed on the paper). 3. Place a piece of recording paper on the air table and place the 0.2kg puck (P2) near the center of the table. 4. Release the 0.5kg puck (P1) to collide with the stationary puck simultaneously activating the Sparktimer. That’s it! The data you need to do this analysis is all on the paper you just generated! Extra Credit (20 pts) Repeat the experiment and data analysis above, only this time launch both pucks towards each other (both pucks have initial velocities so that they collide with each other near the center of the table). You do not have to perform a rotation of coordinates for this case. LAB-04 Conservation Laws (Collisions) Name:_______________________ Sec./Group__________ Date:_____________ 4. Prelab Read over the lab carefully! a. Why are we asking you to level the table off? What will happen if the table is angled at some slight angle in terms of the observed kinetic energy of the system before and after the collision? b. While the components of the velocity before and after the collisions change, the speed does not. In words, explain why this is the case? c. Suppose you wait 10 minutes after the collision and measure the velocities of the each of the puck? What would you imagine the total kinetic energy of the system would be? Why is the conservation of energy not holding? LAB-04 Conservation Laws (Collisions) Name:_______________________ Sec./Group__________ Date:_____________ Now I want you to rotate your X axis (and Y axis) 45 degrees clockwise and do the exact same calculations: Before the collision: • Velocity of P1: _____i + _____j ______ • Velocity of P2: _____i + _____j ______ After the collision: • Velocity of P1: _____i + _____j ______ • Velocity of P2: _____i + _____j ______ Analysis of the momenta before the collision using the 2nd coordinate system: • Momentum of P1: _____i + _____j ______ • Momentum of P2: _____i + _____j ______ • Total linear momentum: _____i + _____j ______ Analysis of the momenta after the collision using the 2nd coordinate system: • Momentum of P1: _____i + _____j ______ • Momentum of P2: _____i + _____j ______ • Total linear momentum: _____i + _____j ______ LAB-04 Conservation Laws (Collisions) Name:_______________________ Sec./Group__________ Date:_____________ 6. Conclusions Analyze the results you have calculated. Is the linear momentum of the system (in both coordinates) conserved after the collision? Is the total energy of the system conserved after the collision? As a note, in problems in Serway, we exploit the fact that energy and momentum are conserved to predict the velocities of the pucks after the collision! In this case, we are performing the complement experiment. We are analyzing the data representing the pre and post collision velocities to verify the conservations laws. Why is it that I did not ask you to test the rotational invariance principle for the conservation of energy? I did not ask you not because it is not true, but because it must be true! Explain why this is so: LAB-04 Conservation Laws (Collisions) Name:_______________________ Sec./Group__________ Date:_____________ Extra Credit (20 pts) mP1 = ________ mP2 = _________ Let us first define the positive X axis as the initial direction that the first puck (the one your are throwing). Examining the data right before the collision: • Distance between two dots, before of the first puck before the collision? _________________ • The ‘speed’ of the first puck (P1)? (Use the time interval between each mark to calculate this): _________________ Using the “X axis” as we have defined it • Velocity (in components) of P1? _____i + _____j ______ Do a similar analysis to find the same quantities for the 2nd puck (P2): • ‘Speed’ of P2? _________________ • ‘Velocity’ of P2? _____i + _____j ______ Now lets do the same analysis after the collision. Since the pucks are moving in any direction now, to break the velocities into the x and y components remember to draw a right triangle and use trigonometry • Speed of P1: _________________ • Velocity of P1: _____i + _____j ______ • Speed of P2: _________________ • Velocity of P2: _____i + _____j ______