PCS211 - Lab 5 Report

Lab 5 - Elastic and Inelastic Collisions Introduction: The purpose of this lab is to see how the masses of two objects undergoing a collision affects their initial and final velocities in both the case of an elastic collision and a perfectly inelastic collision. An inelastic collision will be simulated by placing velcro on the front end of cart 1 and

the back end of cart 2, allowing them to remain stuck together after the collision. An elastic collision will be simulated by placing a magnet on the front end of cart 1 and the back end of cart 2, forcing them apart when they approach one another in order to mimic the two objects bouncing off of each other. The two types of collisions will be done thrice each, first with both masses being equal, then with the mass of one cart being greater than the mass of the other for the two subsequent trials. Theory: The conservation of energy, including its momentum and kinetic energy, is demonstrated in the experiment that follows. The loss or gain of energy in the system is proven for both elastic and inelastic collisions using various techniques for the conservation of linear momentum. Kinetic energy is first used in the lab since it is connected to the motion of the moving cart. It might be viewed as the characteristic that distinguishes elastic from inelastic collisions. However, momentum will be taken into consideration in both scenarios. The linear momentum of an item is thus another crucial idea to be examined. In actuality, the linear momentum of a mass-moving object is denoted by the following formula: 𝑝 = 𝑚𝑣 Both collisions in this experiment take place in a single dimension. The rule of conservation of momentum is expressed as follows as a result of the two cart bodies: 𝑚 1 𝑣 1𝑥 + 𝑚 2 𝑣 2𝑥 = 𝑚 1 𝑣' 1𝑥 + 𝑚 2 𝑣' 2𝑥 As was already established, the cart is propelled from rest to its top speed using kinetic energy. The speeds of the carts in both collisions must be determined. The two collisions, elastic and inelastic, must be taken into account for a deeper comprehension. When two or more elastic bodies collide, there is no loss of total kinetic energy when the bodies separate after the collision. The conservation of kinetic energy implies what follows: or 1 2 𝑚 1 𝑣 1 2 + 1 2 𝑚 2 𝑣 2 2 = 1 2 𝑚 1 𝑣' 1 2 + 1 2 𝑚 2 𝑣' 2 2 𝐾𝐸 = 𝐾𝐸' Inelastic collisions include the separation of two bodies after a collision, which causes a partial loss of kinetic energy in the system. However, momentum conservation leads to another equation that may be simplified: 𝐾𝐸' = 1 2 (𝑚 1 + 𝑚 2 )𝑣' 2 It should be noted that, in any collision, it is not possible for both to remain stationary after the collision. Since the two particles' masses must be equal and the collision must be perfectly

elastic, this situation is simply impossible. Using the law of conservation of momentum, it says that the totals of the momentums before and after the collision must be the same. Let's assume m 2 is at rest while m 1 is approaching m 2 at speed v 1 in preparation for a collision. The total momentum before collision using the law of conservation of momentum is: 𝑚 1 𝑣 1 + 𝑚 2 𝑣 2 = 𝑚 1 𝑣 1 ' + 𝑚 2 𝑣 2 ' Substituting the values when one object is at rest before the collision and both objects come to rest after the collision into the equation above: (𝑚 1 𝑣 1 ) + (𝑚 2 × 0) = (𝑚 1 × 0) + (𝑚 2 × 0) 𝑚 1 𝑣 1 + 0 = 0 + 0 𝑚 1 𝑣 1 = 0 ⇑ Since is not zero and cannot be equal to zero after a collision, this equation is incorrect, 𝑚 1 𝑣 1 showing why it is not possible for both of the particles to be at rest after the collision. Inelastic collisions, in contrast to elastic collisions, conserve momentum but not energy. The kinetic energy carried by the moving objects is not always conserved, even though the system's total energy is always conserved. Energy is lost to the environment during an inelastic collision and is converted into other forms, such as heat and sound. Apparatus: - Vernier Computer Interface - Logger Pro Software - Two (2) Vernier Carts (attached with magnets and velcro on either end) - Aluminum track - Two (2) Vernier Motion Sensors - 500g weight Procedure: 1. It is necessary to measure and record the mass of each cart as well as any weights that will be used as attachments. As usual, include an estimate of the measurement uncertainty. 2. SETUP

a. The two motion sensors should be placed in the CH-1 and CH-2 slots on the Vernier Computer interface. b. Put a sensor at either end of the track. Rotate the articulating head of the sensor until it is parallel to the table. Make sure that each sensor has the "cart" mode option selected. c. Open Logger Pro on the computer. The sensors should be recognised automatically. d. The sampling rate must be adjusted to 10 samples per second under Experiment → Data Collection , (0.1 seconds per sample). Additionally, it needs to be set that it will take 5 seconds in total. The Done button must be selected following these changes. e. Try clicking ▶ to gather data on the LoggerPro software. As the sensors gather data, move the cart back and forth with your hand. Verify that the graphs behave as you would anticipate. If you are not obtaining the desired answer, try repositioning the sensor(s), and if necessary, get assistance from your TA. 3. PERFECTLY INELASTIC COLLISION a. To ensure that the two carts will stick together in the case of a collision, the velcro pads on each cart should be facing one another. Don't add extra weight to either cart. Guide the two slowly moving carts to roll in the same direction so they may collide and stick together. One of your team members needs to be ready to stop the two carts before they crash with the sensor at the end of the track. b. Click ▶ (Collect) to begin data collection after you are confident in your method, and then send carts "1" and "2" toward one another on route to colliding. c. You should be able to observe from the graph cart "1"'s velocity prior to and following the collision once data collecting is complete. Try collecting data again if the collision's location is not immediately apparent. d. Measure the final velocity of both carts after the collision and the velocity of cart "1" before the collision using the LoggerPro software. How to do it: i. To choose the range of data you wish to fit, click and drag on the position graph, then click Analyze → Linear Fit . ii. You will be prompted to choose the data column you want to fit. Based on the curve you are utilizing, select Latest:Position 1 or Latest:Position 2 . Click Cancel if the software only offers you the choice of fitting Velocity

1 or Velocity 2 . The ability to match the position data should then be available in a new popup. iii. On the graph, a best fit equation will be displayed. Please take note that by clicking and dragging the black [] brackets, you may change the data range that is being used for the fits. e. Store the most recent data run by choosing Experiment → Store Latest Run . f. Mass is added to cart "1". The amount of mass you should add should be sufficient to increase cart "1"'s overall mass by at least 50%. Take note of each cart's updated mass before returning to step 3b and repeating your steps to determine the masses' initial and final velocities. Keep in mind that you may choose whether to display or hide certain data sets on the graph by clicking Data → Show Data Set (or) Hide Data Set . g. To make cart "2" heavier than cart "1," remove the mass from cart "1" and add it to cart "2." Take note of each cart's updated mass before returning to step 3b and repeating your steps to determine the masses' initial and final velocities. h. The three data sets for the three different mass carts should now be included in a single Logger Pro file. Save your Logger Pro file with a descriptive name, such as PCS211_Firstname_LastName_Inelastic.cmbl, to the computer's desktop. Export your data in .txt format as well, and then send it to your Lab 5 submission folder on D2L. After that, email or transfer the files to a USB key. When you log off, all files on the computers will be removed. 4. NEARLY ELASTIC COLLISION a. Start a new LoggerPro file by selecting " Data → Clear All Data " after saving your "inelastic" data to a secure location (or emailing it to yourself). Save the file to your desktop with a new name, such as PCS211_Firstname_LastName_Elastic.cmbl, once the data has been cleared. b. Position the magnets on the ends of the two carts so that they face one another. Make sure the carts repel one another when they are near to one another. Don't load either cart with extra weight. Roll cart "1" gently in the direction of cart "2" until the two bounce off one another but do not come in contact. c. Click ▶ (Collect) to begin data collection after you are confident in your method, and then send carts "1" and "2" toward one another on route to colliding. d. The velocity of cart "1" before and after the collision, as well as the velocity of cart "2" after the impact, should be shown on the graph once data gathering is