Measuring Momentum: Using distance moved after impact to estimate velocity
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1 Case File 6 Measuring Momentum: Using istance move after impact to estimate velocity Explore how the spee of an impacting vehicle causes a stationary object to move. Police Report Last Tuesay night, police officers were ispatche to the remote icy intersection of Elm Roa an Wining Way for a routine collision investigation. The river of a car seems to have lost control of his vehicle on the ice an crashe into a black van sitting ile on the sie of the roa. Investigators took some measurements at the crime scene in orer to etermine how fast the car was going before it hit the van. Since the car skie on an icy roa, there were no tire tracks to measure to etermine its spee. However, the van was parke on a sany shouler, an investigators were able to measure the istance it was pushe when the car hit it. The marks in the san show that the van was pushe 1.6 meters when it was struck by the car. Accoring to the car manufacturer, the car has a mass of 1000 kg. Evaluation copy
2 Measuring Momentum Case 6 OBJECTIVES Establish a relationship between the momentum of a vehicle an the istance a stationary object moves when the vehicle hits it. Accurately gather ata from a collision of a vehicle with a stationary object. Establish a relationship between the istance an object moves after a collision with a vehicle an the momentum of the vehicle. MATERIALS computer clamp or heavy tape Vernier computer interface string Logger Pro masking tape Vernier Motion Detector book, 5 7 cm thick meter stick book, 2 cm thick 1.5 m ramp of strong carboar or woo g cart about 6 cm tall 25 cm support for ramp balance PROCEDURE 1. Use a balance to measure the mass of the cart. Recor the mass in your Evience Recor. 2. Measure the mass of each of the books, an recor each mass in your Evience Recor. 3. Prepare the Motion Detector for ata collection. a. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. a. Open the pivoting hea. If the Motion Detector has a sensitivity switch, set it to Track. b. Prepare the computer for ata collection by opening the file 06 Measuring Momentum from the Forensics with Vernier foler of Logger Pro. 4. Set up the ramp as shown in the figure below. Place the heavier (thicker) of the two books at the base of the ramp. Evaluation copy 5. With the book at the bottom of the ramp, place the cart at the bottom of the ramp against the book. Apply a strip of tape to the ramp at the location of the front wheels of the cart. The tape shoul be about 10 cm long an parallel to the bottom ege of the ramp. 6. Place a meter stick in the center of the ramp with the 0 at the bottom ege of the tape you applie in Step 5. Tape it securely to the ramp at the following istances: 25, 35, 50, 70, an Forensics with Vernier 6-1
3 Case 6 80 cm from the bottom ege of the tape. If the ramp is mae of carboar, the meter stick will provie an aitional support, a guie for the cart, an a way to measure the istance the cart will travel own the ramp. 7. Place the Motion Detector at the top of the ramp. There shoul be at least 25 cm between the Motion Detector an the rear of the cart when the cart is place with its front wheels at the 80 cm mark. 8. Place the cart on the ramp so that it strales the meter stick an has its front wheels at the 80 cm mark. 9. Click an release the cart after ata collection begins. The cart shoul collie with the book. 10. Measure the istance the book was pushe by its collision with the cart. Enter that istance in meters into your Evience Recor. If the book was not pushe parallel to the ramp, measure the istance from its starting point to the ege of the book along its centerline, as shown in the figure below. Once you have measure the istance, return the book to its original position at the base of the ramp. 11. Determine the cart s velocity when it struck the book. Note: Do not be confuse by any unusual reaings that may show up on the graph for times after the cart has collie with the book. a. Click once on the velocity graph to make it active. b. Click the Examine button,. Click the point on the graph corresponing to the time when the car struck the book. Recor the maximum velocity, isplaye in the floating box, in your Evience Recor. 12. Repeat Step 8 11 twice more. Calculate the average of the results an recor it in the Evience Recor. 13. Repeat Step 8 11 for the other istances you have marke off on your ramp (70, 50, 35, an 25 cm). 14. Repeat Step 8 13 for the lighter (thinner) book. 15. Calculate the average momentum of the cart at impact for each average istance the book move. Do this by multiplying the average velocity of the cart by the mass of the cart. Recor the average momentums in your Evience Recor. 16. Click the Next Page button,, to go to the secon page of the file. 6-2 Forensics with Vernier
4 Measuring Momentum 17. Enter the average momentum an istance ata, calculate in Step 15 for the heavy book, in Logger Pro to create a graph of istance vs. momentum. a. Click on the first cell in the Average Momentum column in the table. Type in the momentum of the first incline istance recore in the Evience recor. Click on the next cell own an enter the next momentum value. b. Continue in this manner to enter ata for all the remaining average momentums recore in the Evience recor. c. Click on the first cell in the Distance Move column. Type in the istance move for that calculate momentum. Click on the next cell own an enter the next istance move.. Continue in this manner to enter ata for all the average istances recore in the Evience recor. e. Your screen shoul now show a graph of the cart s momentum on the x-axis an the istance it pushe the book on the y-axis. 18. Use Logger Pro s Linear fit tool to etermine if the relationship between momentum an istance is linear. A linear regression is a mathematical formula that can be use to calculate how closely a set of ata is to a straight line. a. Click once on your graph to make it active. b. Select Linear Fit from the Analyze menu. c. The equation for the linear fit is isplaye in a floating box.. Recor the isplaye equation an the correlation value to three ecimal places in the Evience Recor. The correlation value tells you how well the line fits the ata. The closer the correlation value is to 1, the better the fit. e. Sketch the graph of istance vs. momentum in the Evience Recor. 19. Repeat Steps for the lighter book. EVIDENCE RECORD Using the Heavy Book Mass of cart kg Mass of book kg Forensics with Vernier 6-3
5 Case 6 Distance Cart Travele Before Colliing with Book Velocity of Cart v (m/sec) Distance Book Move Distance Cart Travele Before Colliing with Book Average Velocity of Cart v (m/sec) Average Distance Book Move Average Momentum of Cart at Impact p (kg m/sec) 6-4 Forensics with Vernier
6 Measuring Momentum Linear fit (Heavy Book) Sketch of graph of istance vs. momentum ata mx + b m b correlation Using the Light Book Mass of cart kg Mass of book kg Distance Cart Travele Before Colliing with Book Velocity of Cart v (m/sec) Distance Book Move Forensics with Vernier 6-5
7 Case 6 Distance Cart Travele Before Colliing with Book Average Velocity of Cart v (m/sec) Average Distance Book Move Average Momentum of Cart at Impact p (kg m/sec) Linear fit (Light Book) Sketch of graph of istance vs. momentum ata mx + b m b correlation CASE ANALYSIS 1. Is the linear regression a goo fit to the ata for the heavy book? For the light book? Explain your answers. 2. For the heavy book, write the equation for the graph of the istance the book move versus the momentum at impact. The equation will be in the form y = mx + b. The y is the istance the book move, m is the slope of the best fit line for your ata, x is the momentum at impact, an b is the y-intercept (where the line crosses the y-axis at x = 0). 3. Using your equation, calculate how far the book woul move if its momentum at impact were kg m/sec. Show your work. Don t forget that your answer has units. 4. If the book move 0.2 m after impact, what woul the momentum of the cart be when it hit the book? Show your work. 5. Repeat questions 3 an 4 for the light book. 6. The equation for the istance, y, the van move versus the momentum, x, of the car is y = x The units of y are meters, an the units of x are kg m/s. What was the momentum of the car just before impact? Hint: You nee to rearrange the equation to solve for x. Show your work. 7. What was the impact velocity of the car in meters per secon? Show your work. Hint: You nee to rearrange the momentum equation an then substitute for momentum an mass of the car. The momentum equation is p = m v where p = momentum, m = mass, an v = velocity. 6-6 Forensics with Vernier
8 Measuring Momentum 8. If the spee limit on the roa was 50 mph, was the car speeing just before it hit the van? Show your work. (Hint: 1 m/s = 2.24mph) Forensics with Vernier 6-7
9 Vernier Lab Safety Instructions Disclaimer THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB. This copy oes not inclue: Safety information Essential instructor backgroun information Directions for preparing solutions Important tips for successfully oing these labs The complete Forensics with Vernier lab manual inclues 14 labs an essential teacher information. The full lab book is available for purchase at: Vernier Software & Technology S.W. Millikan Way Beaverton, OR Toll Free (888) (503) FAX (503)
Measuring Momentum: Using distance moved after impact to estimate velocity
Case File 6 Measuring Momentum: Using distance moved after impact to estimate velocity Explore how the speed of an impacting vehicle causes a stationary object to move. Police Report Last Tuesday night,
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