PSC 151 - Lab 5

Virtual Momentum Track VPL Grapher PENCIL Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod Rev 12/19/18 Mod: 2/9/19 1 Name: Conservation of Linear Momentum Date: Purpose  To investigate the behavior of objects colliding in elastic and inelastic collisions  To investigate momentum and energy conservation for a pair of colliding carts Equipment Explore the Apparatus Open the Virtual Momentum Lab. A lot should look familiar after having worked with the Dynamics Track. Figure 1 – The Momentum Track Let’s take a trial run with the apparatus. Toss the carts around a bit to see how they interact. You’ll see that they bounce nicely off of each other and lose a bit of speed when they collide with the orange bumpers. Turn on the “Velcro®” and try it again. Hopefully they act as you’d expect. Turn the “Spring Plunger” back on. Start both carts moving. Now click on either cart. The other one stops too. But when you release the mouse button the unclicked cart starts moving again. The best way to stop them both is with the stop carts button. Try adding some mass to one cart. You have to release the mass while it’s over the mast (the rod holding up the flag). Bang the carts around a bit to see how the mismatched carts behave. Now try the launchers. Here’s how they’re operated: Drag a cart to the launcher bumper and continue dragging it until it appears to go behind the bumper. Release the cart. This engages the cart and bumper. Now cock the launcher spring by pulling back the white circle on the side of the launcher. Click the release button to fire. Try again with the launcher spring pulled back different distances. Try launching both at once ( release both ). This would be a good time to try out the “Motion Sensor.” It’s a bit trickier with this lab since you have two carts to work with as well as abrupt changes in speed and direction. Try this. Double the mass of the red cart by adding 250 grams. Attach it to its launcher and pull back the spring about 50%. Put the blue cart at mid-track. Switch to the “Spring Plunger” if you still have the “Velcro®” on. You’ll soon need to change the masses on the carts. You remove masses by double-clicking on the stack of masses. In computer lingo the order is LIFO. “Last in, first out.” The last mass added (the top one) is the first one removed by clicking.

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 2 Rev 12/19/18 Mod: 2/9/19  Turn on the “Motion Sensor” by clicking it.  Release the left launcher.  Once the carts collide, click the “Motion Sensor” to turn it off.  You should see a graph similar to the one shown in Figure 2. Figure 2: Dual x-t Graphs Let’s identify all the parts of this interaction on our graph. When you turn on the “Motion Sensor,” each cart is stationary until you click the launcher release button. During this time each cart has an initial, constant position (zero velocity) as indicated by a horizontal ( t , x ) lines. When the launcher is fired the red cart is given an initial velocity. (We ignore acceleration in these graphs). The red cart collides with the blue cart. The red cart is pushed to the left, slowing it down. The blue cart is pushed to the right with an equal, but opposite force, thus giving it a positive velocity which appears to be somewhat faster than the red cart’s initial velocity. Figure 3: Before and After Collision Let’s analyze our data. You have five velocities, but you’re interested in only four of them. You are only interested in the velocities just before and just after interactions – collisions. The blue cart is at rest before, and traveling at some positive velocity after the collision. The red cart has a positive velocity before and a smaller positive velocity after the collision. The red cart’s initial zero velocity before launch is not related to the collision. You’ll always ignore similar segments. The blue cart’s initial zero velocity is obvious from the graph. Let’s see how to find the other velocities using Grapher. 1. In the momentum apparatus, click Copy Data to Clipboard . 2. Open Grapher. Click in the “paste data” box and use Ctrl+V to paste it into the data table. 3. You should see three columns of data labeled “X”, “Blue”, and “Red.” These hold the data for time, blue cart position, and red cart position, respectively. You should also see two graphs – one position-time graph for each cart. Use manual scaling to make sure that each graph starts at (0, 0) and has the same maximum x and t values. A range of 0.0 m to 2.0 m is good. Label the axes of the top graph “Blue Position (m)” and “Time (s).” Label the bottom graph similarly. Give each graph an appropriate name. 5. Turn on “Linear Fit.” Determine the constant velocities of the carts prior to the collision by finding the four slopes of their ( t , x ) graphs. You should know how to use the “Linear Fit” tool from your kinematics labs or by studying the Lab Guide. You’ll note that when you drag across a certain portion of the graph a pink line of best fit is drawn for that range of points. The data in the linear fit data box also corresponds to that data range. Thus you can determine before and after collision velocities for each cart. The longer the line segment you drag across, the better your results will be.

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 4 Rev 12/19/18 Mod: 2/9/19 Procedure I. Conservation of Momentum in a collision NOTE : In most of this lab you’ll use your data to answer questions. Even non-numerical questions.  Load the blue cart with 500 g, giving it a total mass of 750 g.  Position the blue cart right between the release both and stop carts buttons.  Engage the red cart with its launcher. Cock the launch spring about half-way back.  Turn on the “Motion Sensor.”  Release the left cart.  Somewhat before the blue cart hits the right bumper, turn off the “Motion Sensor.” Your graph should look something like Figure5. There may be additional lines due to collisions with the plungers. Ignore them. Dragging the big white ball below the graph will adjust the time display scale Take screenshot of the Red Cart  Blue Cart elastic collision graph on the Momentum track and paste below. PASTE HERE, RED CART  BLUE CART COLLISION GRAPH Fig. 5P (Personal) x-t Motion Graph of Elastic Collision of Red Cart into Blue Cart: mR = 0.25 kg; vRi = ?; vRf = ? mB = 0.75 kg; vBi = 0; vBf = ? Before finding actual values for the velocities, let’s think about what the graph tells us about the signs of the momenta. 1. What is the sign of the red cart’s initial momentum, m R v R o , its momentum just before the collision? + (+/-) 2. What is the sign of the red cart’s final momentum, m R v Rf , its momentum just after the collision? - (+/-) 3. What is the sign of the change in the red cart’s momentum, Δ(mR v R ) = mR(Δ v R )? + (+/-) 4. The blue cart’s initial momentum, m B v Bo doesn’t have a sign. Its momentum before the collision is? 0 5. What is the sign of the blue cart’s final momentum, m B v Bf , its momentum just after the collision? + (+/-) 6. What is the sign of the change in the blue cart’s momentum, Δ(mB v B ) = mB(Δ v B )? + (+/-) So the red cart had a negative change in momentum while the blue cart had a positive change in momentum. If the total momentum must be constant, then the sum of these changes, the total change, must add to zero. Let’s look at the numbers. Figure 5: A Collision

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 5 Rev 12/19/18 Mod: 2/9/19 Copy/Paste your data from the apparatus into Grapher as before. Using the “Linear Fit” tool determine the carts’ velocities before ( v o ) and after ( v f ) the collision. Record these in the first two empty columns in Table 1. Take screenshots of collision motion graph on Grapher, showing measurement of v R0 , v Rf , & v Bf from slopes of the graphs, and paste below. Replace line fit data below with those from your experiment. ELASTIC COLLISION MOTION GRAPH FROM GRAPHER Fig. 6 x-t graph in Fig. 5P on Grapher Line Fit Data From Grapher Below Initial velocity of Red Cart: v R0 = 0.41706 m/s Final velocity of the Red Cart: v Rf = -0.20406 m/s Final velocity of the Blue Cart: v Bf = 0.20406 m/s Use above data in Table 1 below 7. Fill the mass of each cart into Table 1. The blue cart has a mass of 750 g which you divide by 1000 to get to kg, so the mass of the blue cart is 0.750 kg. The mass of the red cart is 250 g. Record it in kg. 8. The light orange shaded cells should be filled with the values for mass and the velocities that you measured. 9. Fill the next two columns with the initial momentum (p 0 ) and the final momentum (p f ) (4 values) • For each cart, take its mass and multiply by its velocity. • For example, the initial velocity (v 0 ) for the blue cart is 0 and its mass is 0.75 kg. Therefore the initial momentum (p 0 ) for the blue cart is m v 0 or (0.75 kg) x (0 m/s) or 0 • Repeat this for the final velocity for the blue cart and the initial and final velocity for the red cart 10. Add the initial momenta of the carts to determine the initial momentum ( p (sys)o ) of the system. Similarly determine the final momentum ( p (sys)f ) of the system. Record these two values in Table 1. 11. Finally, calculate and record the change in momentum of the system (Δ p sys ) from ( p (sys)f ) - ( p (sys)o ).

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 7 Rev 12/19/18 Mod: 2/9/19 Fig. 7a Fig. 7b Fig. 7a x-t Motion Graph of Elastic Collision of Red Cart into Blue Cart: m R = m B = 0.25 kg Fig. 7b x-t graph in (a) on Grapher, determining v Ri = 0.87010 m/s. v Rf = 0; v i-blue = 0; v Bf = 0.86836 m/s b. If this is an elastic collision (and it is), then momentum and energy should be conserved. Why did the red cart stop after the collision? The momentum and energy are being affected every time the carts hit each other as well as the end of the track. Kinetic energy can be lost as heat on the track . 2. Move the red cart to the far left with the plunger depressed. Move the blue cart to the far right with the plunger depressed. a. Start the sensor and release both carts. What do you observe? The carts start off moving quickly toward each other before bouncing off of each other and moving to the opposite ends of the track. As they bounce off each other and the ends of the track, they start to lose speed. 3. Take screenshots of the head-on  elastic collision graph on the momentum track (MT) and from the Grapher, showing measurement of v R0 , v Rf , & v Bf from slopes of the graphs, and paste below. Change line fit data below with those from your own Grapher. RED CART   BLUE CART ELASTIC COLLISION GRAPHS FROM MT & GRAPHER Fig. 8a Fig. 8b

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 8 Rev 12/19/18 Mod: 2/9/19 Fig. 8a x-t Motion Graph of Elastic Head-on-collision of Red and Blue Carts: m R = m B = 0.25 kg Fig. 8b x-t graph in (a) on Grapher, determining v Ri = 0.86945 m/s; v Bi = -0.86949 m/s; v Rf = -0.86831 m/s; v Bf = 0.86836 m/s a. How does what you physically observe with the carts compare to what you see on the x-vs-t graph? What I observed and what the graph show are the same. They each start fast before bouncing off of each other and the ends. They have the same slopes . III. Totally Inelastic Collisions In the previous section we observed carts making elastic collisions. Our carts can have another type of collision. The springy bumpers between them can be replaced by sticky “Velcro®” bumpers. In this case we would have a totally inelastic collision, one where the carts stick together after the collision and share a common speed. 1. Repeat II.1 but with the “Velcro®” bumpers selected instead of the “Spring Plunger.” a. Release both carts. What do you observe? The red cart starts moving quickly before it attaches to the blue cart. The two carts then start moving towards the right end slower than the red cart was moving. Both travel together, bounce off the end and continue to move. 4. Take screenshots of Red Cart  Blue Cart inelastic collision graps on the momentum track and from the Grapher, showing measurement of v R0 , v Rf , & v Bf from slopes of the graphs, and paste below. Change line fit data below with those from your own Grapher. RED CART  BLUE CART INELASTIC COLLISION GRAPHS FROM MT & GRAPHER Fig. 9a Fig. 9b Fig. 9a x-t Motion Graph of Inelastic Collision of Red Cart into Blue Cart: m red = m blue = 0.25 kg; Fig. 9b x-t graph in (a) on Grapher, determining v Ri = 0.81884 m/s; v Rf = v Bf = 0.41678 m/s

Physical Science Laboratory: PCS 151 LR 5 VPL Lab - Conservation of Momentum – mod 1 Rev 12/19/18 Mod: 2/9/19 c. Intuitively, part b should make sense. Two identical objects moving with identical speeds hit each other and stick together. Therefore, they “cancel out” and end up at rest. d. You will discuss Kinetic Energy in the next lecture section. At this point, it should suffice to note that KE = ½ m v 2 . It may seem very similar to momentum and that’s true, but v 2 vs v has one important distinction. We found in 2.b that even though the carts are initially moving, the total momentum is zero. This happens because 10 m/s + (-10 m/s) = 0. For kinetic energy, however, the same result would be (10 m/s)^2 + (-10 m/s)^2, and you would end up with 200 m 2 /s 2 if kinetic energy was conserved. Instead, we see that the final velocity is 0, therefore kinetic energy is NOT CONSERVED in inelastic collisions.