Crumple Zones Gizmo Answer Key

Name: Kamila Townsend Date: 12-28-2022 Student Exploration: Crumple Zones Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. Vocabulary: acceleration, airbag, collision avoidance system, crash test dummy, crumple zone, force, kinetic energy, Newton’s laws of motion, safety cell, seat belt, work, work-energy theorem Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Two burglars run down an alley at night, trying to escape the cops. Jack is carrying a rigid metal safe. Jill is carrying an armful of antique quilts. In the pitch dark, they both collide headlong into a concrete wall. 1. Who do you think will be hurt more in the collision, and why? Jack because since the metal is rigid the safe will not crush but stay solid 2. During a car crash, what features of the car might act like either Jack’s safe or Jill’s quilts? The safe would function as a metal cage or a car, while the blankets would serve as an air bay. Gizmo Warm-up When cars were first invented, the safety of passengers was not a great concern. As vehicles grew larger and faster, accidents became more deadly. Safety features went from being a rare luxury to a legal requirement. In the Crumple Zones Gizmo, you will design cars that will help a crash test dummy survive a collision. 1. To begin, do not make any changes to the DESIGN tab of the Gizmo. Select the CRASH TEST tab, and click Play ( ). After the crash, click Slo-mo replay. What happens? The test dummy goes forward and the car gets crushed 2. Select the RESULTS tab to read about the results of the crash. Do you think a passenger would have survived this car crash? Explain. No, because of the serious body and head injuries. Get the Gizmo ready: Activity A: ● Click Reset ( ). ● On the DESIGN tab, check that Sedan is selected. Surviving a crash Introduction: Modern vehicles contain features designed to keep passengers safe in a crash. The crumple zone in the front of the car slows the car gradually and increases stopping time. The safety cell is a rigid cage that prevents passengers from being crushed. Inside, seat belts and airbags prevent the driver from hitting the windshield, steering wheel, or dashboard. Question: How does a crumple zone help protect a passenger? 1. Make a hypothesis: On the DESIGN tab, look at the parameters you can control. What settings do you think will make the safest car? Set up the Gizmo, and then fill in below. Crumple zone length: 120 Crumple zone rigidity: 100 Safety cell rigidity: Seat belt present? yes If present, seat belt stiffness: 54 Air bag present? yes If present, air bag rigidity: 50 4,000 2. Test: On the CRASH TEST tab, check that the Car 1 speed is 16 m/s, or about 35 miles per hour (mph). Click Play. After the crash, select the RESULTS tab. A. By what percentage did the crumple zone deform? 1.2 B. Did the dummy hit the steering wheel? No C. What was the maximum force on the dummy? 17.01N D. How likely was the dummy to survive? 95% Safety cell? 0.05 In this simulation, forces are measured in kilonewtons (kN). One kilonewton is equal to 1000 newtons, or the force of a 225-pound (102 kg) person standing on your chest. While many factors affect survival, only the maximum force and safety cell collapse are considered here. 3. Experiment: On the DESIGN tab, set the Crumple zone length to 100 cm and the Safety cell rigidity to 2000 kN. Set the Seat belt stiffness to 50 kN/m and turn off the Airbag. For each Crumple zone rigidity setting, run a 16 m/s crash test and enter the results below. Crumple zone rigidity 100 kN 200 kN 300 kN 400 kN Crumple zone deformation 1m 0.93m 0.62m 0.47m Dummy displacement 1.42m 1.21m 1.02m 0.93m Max. force on dummy 20.88 KN 14.25 KN 19.88 KN 23.02 KN Likelihood of survival 87% 100% 89% 82% 4. Evaluate: Look at the results of your experiment. What was the relationship between crumple zone rigidity, crumple zone deformation, and maximum force on the dummy? The rigidity and distortion of the crumple zone aid in lowering the dummy's initial force. 5. Infer: For a 1.00 m (100 cm) crumple zone, how much deformation do you think is needed in order to keep the passenger the safest? 200 KN Explain your answer: The dummy had a 100% survival rate as a result. 6. Explore: In the U.S., all cars are evaluated using a frontal 35 mph (~16 m/s) crash test. Using the variables on the DESIGN tab, try to design a car that produces the lowest possible force on the dummy and does not injure the dummy in a 16 m/s crash. If you like, record your data on the provided blank data tables on the next page. When you have finished, describe your car and your results below. Car parameters (CZ = crumple zone, SC = safety cell, SB = seat belt, AB = airbag) CZ length 120 CZ rigidity 100 SC rigidity 4000 SB stiffness 54 AB rigidity 50 SC deform. 0.05m Dummy disp. 1.52m Max. force 17.01 KN Survival % 95% Crash results CZ deform. 1.2m 7. Test: Click Reset. On the CRASH TEST tab, change the Car 1 speed to 22 m/s (about 50 mph). Run a crash test at this speed, then look at the summary data. A. What did you find? Everything increased but the crumple zone deformation. Along with a 0% survival rate B. What is a possible disadvantage of designing a car for only one crash speed? Different parts of the city have different speed limits. Blank data tables for car experiments (make as many copies as you need) Key CZL = Crumple zone length (cm) CZR = Crumple zone rigidity (kN) SCR = Safety cell rigidity (kN) SBS = Seat belt stiffness (kN/m) ABR = Air bag rigidity (kN) CZL 120 85 60 55 85 75 65 100 70 85 Car parameters CZR SCR SBS 100 4000 54 1300 2900 92 3600 1950 63 2700 2450 55 2200 3200 38 4000 4000 50 2800 2950 55 4000 3200 47 2700 2050 52 3500 2850 59 CZL 60 120 120 120 Car parameters CZR SCR SBS 2600 1650 75 4000 4000 100 3200 3200 55 2200 2200 50 CZ def = Crumple zone deformation (m) SC def = Safety cell deformation (m) Dum d = Dummy displacement (m) Max F = Maximum force on dummy (kN) Surv% = Likelihood of survival ABR 50 27 34 30 23 29 32 25 32 36 ABR 26 50 30 27 CZ def 1.2 0.14 0.05 0.07 0.09 0.05 0.07 0.05 0.07 0.05 Crash results SC def Dum d Max F 0.05 1.52 17.01 0.06 0.47 57.12 0.1 0.44 58.46 0.08 0.47 52.06 0.06 0.55 39.2 0.05 0.49 50.99 0.06 0.47 54.32 0.06 0.49 45.55 0.09 0.47 52.58 0.07 0.46 59.79 Surv% 95% 0% 0% 0% 32% 0% 0% 0% 0% 0% CZ def 0.07 0.05 0.06 0.09 Crash results SC def Dum d Max F 0.11 0.43 52.79 0.05 0.4 83.41 0.06 0.47 52.82 0.07 0.5 47.31 Surv% 0% 0% 0% 0% Activity B: Get the Gizmo ready: Modern safety features ● Click Reset. ● On the DESIGN tab, check that Sedan is selected. Introduction: The idea of a crumple zone was conceived by Béla Barényi in 1952 and first used in the 1959 Mercedes W111. Seat belts were also first widely used in the late 1950s. More recently, airbags and collision avoidance systems (CAS) were introduced. Question: How do modern safety features and body types help keep passengers safe? 1. Experiment: Set the Crumple zone length to 90 cm, the Crumple zone rigidity to 1000 kN, and the Safety cell rigidity to 1000 kN. Turn off the seat belt and the airbag. These settings represent a 1950’s car with no crumple zone, seat belt, or airbag. A. On the CRASH TEST tab, set the Car 1 speed to 16 m/s. Click Play. What happened to the dummy? No possibility of survival B. Turn on the seat belt and set the Seat belt stiffness to 100 kN/s. Run another crash. What happened? No injury due to the seatbelt C. Set the Crumple zone rigidity to 250 kN and run another test. What happened? The dummy wasn't hurt, and the survival rate was 95%. D. How did the crumple zone and seat belt work together to keep the driver safe? There was less of an impact. The seatbelt helps the dummy from flying 2. Test: An airbag is designed to quickly inflate on impact, then deflate as the passenger hits the bag. Invented in the early 1970s, airbags did not become widespread until the 1990s. Using the crumple zone and safety cell settings above, experiment with the seat belt to find the lowest possible force on the dummy. Then, experiment with just the airbag. Finally, include both the seat belt and airbag. Report your findings below. Setup Seat belt only Airbag only Seat belt and airbag Seat belt stiffness 100 (No seatbelt) 100 Airbag rigidity (No airbag) 5 5 How did the seat belt and airbag work together to keep the driver safe? They prevent the motorist from suffering a serious collision or flying out. Max. force 16.55 KN 1000KN 20.36 KN 3. Experiment: Another modern safety innovation is the collision avoidance system, or CAS. A CAS will apply the brakes when it senses an imminent collision. The brakes can slow the car by about 8.8 m/s for each second they are engaged. Click Reset. On the CRASH TEST tab, select Enable collision avoidance system (CAS). Drag the car to the far right of the track at the bottom of the Gizmo, then click Play. What were the results of this test? 100% success. Before striking the wall, the automobile came to a stop. 4. Explore: Click Reset. In some cases, there will not be enough time for the car to completely stop before the crash occurs. However, the CAS can still be useful. On the CRASH TEST tab, set the Car 1 speed to 23 m/s (about 50 mph). Play a crash without the CAS, and then run another test with the CAS on. What did you find? The car needs more time to halt. 5. Challenge: You work in the safety engineering department for a large auto manufacturer. Your job is to create the safest possible vehicle given each of the following design criteria. Using the Gizmo, try to create a vehicle that meets each description. ● ● ● Design the safest possible SUV with a crumple zone length of 85 cm, no CAS, and a speed of 20 m/s (45 mph). (Note: Injuries such as broken legs are not allowed.) CZL CZR SCR SBS ABR Max. F Surv% 85 cm 2700 2500 91 0 31.47 60% Design the safest possible subcompact (no injuries) with a crumple zone length of 80 cm, no CAS, and a speed of 18 m/s (40 mph). CZL CZR SCR SBS ABR Max. F Surv% 80 cm 750 2050 76 0 30.84 62% Design a sedan with a crumple zone length of 110 cm that can give passengers a greater than 50% chance of surviving a 27 m/s (60 mph) crash and give passengers a greater than 80% chance of surviving a 16 m/s (36 mph) crash. (Note: Crumple zone length in both experiments is 110 cm.) Speed CZR SCR SBS ABR 27 m/s 16 m/s 500 550 100 0 Max. F Surv% 21.65 65% 21.65 85% Activity C: Get the Gizmo ready: Force and acceleration ● Click Reset. ● On the DESIGN tab, select the SUV. Introduction: To understand the physics of a car crash, it is helpful to consider Newton’s laws of motion: ● ● ● First law: An object in motion will stay in motion unless acted on by an unbalanced force. Second law: The acceleration (a) of an object is directly proportional to the net force (F) on the object and inversely proportional to its mass (m). In equation form: F = ma. Third law: For every action there is an equal and opposite reaction. If object A exerts force F on object B, then object B exerts force –F on object A. Question: In a car crash, how are force, mass, acceleration, and velocity related? 1. Observe: On the DESIGN tab, check that SUV is chosen. Turn off the seat belt and airbag. On the CRASH TEST tab, set the Car 1 speed to 10 m/s and click Play. Observe the crash, then observe the dummy in slow motion by clicking the Slow-mo replay button. How does Newton’s first law explain the motion of the dummy? The dummy is at rest until anact at force is acted 2. Select the TABLE tab. On the table, scroll down to where the Dummy v changes. The velocity change occurs when the dummy hits the steering wheel. A. What maximum force did the steering wheel exert on the dummy? 10.0 Notice that this force is negative. In this Gizmo, the positive direction is right to left. A negative force pushes the dummy from left to right, opposite its velocity. B. According to Newton’s third law, what force did the dummy exert on the steering wheel? -10.0 3. Calculate: On the DESIGN tab, set the Crumple zone length to 100 cm, the Crumple zone rigidity to 200 kN (200,000 N), and the Safety cell rigidity to 4000 kN. These settings will result in the crumple zone exerting about 200,000 N of force on the wall during the crash. A. If the crumple zone exerts +200,000 N of force on the wall, how much force will the wall exert on the crumple zone? -200.000N B. The SUV has a mass of 2,000 kg. According to Newton’s second law, what will be the acceleration of the SUV during the crash? 4. Test: Select the TABLE tab and click Play. Look at the Car a column. Note where the SUV hits the wall and starts to slow down. What is the acceleration of the SUV? You may notice that the acceleration of the car is not exactly what you predicted. The SUV’s acceleration depends on the rigidity of the crumple zone and the safety cell. If the safety cell were perfectly rigid, the acceleration would only depend on the rigidity of the crumple zone. 5. Predict: On the DESIGN tab, select the Subcompact. A subcompact has the engine in the back, so the entire front of the car is part of the crumple zone. (Engines do not compress easily, so having the engine in the front of the car reduces the length of the crumple zone.) Set the Crumple zone length to 80 cm, the Crumple zone rigidity to 190 kN, and the Safety cell rigidity to 4000 kN. Turn off the seat belt, turn on the airbag, and set the Airbag rigidity to 15 kN. A. Based on the crumple zone rigidity, approximately what force will the wall exert on the car during the crash? 190 N B. Based on the mass, estimate the acceleration of the car: C. Like the crumple zone, the airbag in this Gizmo exerts a constant force on the dummy. What force, in newtons, does the airbag exert? 15 N D. The dummy has a mass of 50 kg (110 lb). When the dummy hits the airbag, what will be the acceleration of the dummy? 6. Test: On the CRASH TEST tab, set the Car 1 speed to 16 m/s. Click Play. Select the TABLE tab. What is the car’s acceleration and the dummy’s acceleration during the crash? Car acceleration during crash: 9.7 m/s Dummy acceleration during crash: How do these values compare to your predictions? The dummy slows down more slowly than the automobile. 7. Summarize: How do Newton’s laws help to explain the acceleration of the car and dummy during a crash? The formulas make relationships easier to understand. Activity D: The work-energy theorem Get the Gizmo ready: ● Click Reset. ● On the DESIGN tab, select the SUV body type. Introduction: In designing a safe vehicle, the goal is to minimize the force on the passenger during a crash by maximizing the stopping time and distance. In this process, it is helpful to know the minimum force that is possible. One way to find this force is to consider how the kinetic energy of the dummy relates to the work done in stopping the dummy. Question: How can you determine the minimum possible force that acts on a passenger? 1. Calculate: The energy of a moving object is described by its kinetic energy, in which KE = ½ mv 2. Work is the product of force and distance: W = Fd. The work-energy theorem states that work changes the kinetic energy of an object: W = ΔKE. This means that the work required to stop an object is equal in magnitude to the kinetic energy of the object. A. Work is equal to Fd, and work is also equal to ΔKE. Combine these relationships to write an equation that relates force and distance to the change in kinetic energy. Then, rearrange this equation to solve for force. B. If the goal of a safety system is to minimize the force, should the distance the dummy moves during the car crash be very large or very small? Explain your answer. It needs to be large for least impulse C. Suppose a car has a 1.00 meter crumple zone. The distance from the dummy to the steering wheel is 0.50 m (50 cm). After impact, if the crumple zone collapses completely, how far could the dummy go before hitting the steering wheel? Maximum distance dummy could be displaced: 0.50 D. The dummy has a mass of 50 kg (110 lb). If the dummy is traveling 16 m/s at the time of the crash, what is the dummy’s initial kinetic energy? 16 E. ΔKE = KEfinal – KEinitial. If the dummy comes to a stop, what is ΔKE? 0 joules (J) F. The work-energy theorem can be rewritten as F = ΔKE ÷ d. If the distance and kinetic energy change are known, you can solve for the force. Based on your answers to questions C and D, what constant force will stop the dummy? F= G. 16 N Convert the force to kilonewtons. F = 0.016 kN 2. Test: In the Gizmo, set the Crumple zone length to 100 cm. On the CRASH TEST tab, set the Car 1 speed to 16 m/s. Click Play, wait for the end of the crash, then look at the Summary data on the RESULTS tab. A. What is the lowest possible maximum force on the dummy? 4.27 KN B. The RESULTS tab shows the magnitude of the force on the dummy. (Since magnitude does not deal with direction, it has no sign.) How does the magnitude of this force compare to the magnitude of the force you found in question 1G? I failed to take the seatbelt or airbag into consideration, hence it is larger. C. Suppose the dummy had a velocity of 24 m/s before the crash and the crumple zone had a length of 1.20 m. What is the lowest possible force on the dummy in this case? Show your work and check your answer with the Gizmo. Minimum force on dummy: 8.47 kN 3. Calculate: In the simplified situation shown in the Gizmo, the exact design of the crumple zone is not considered. Instead, the crumple zone is modeled as a semi-rigid structure that exerts a constant force on the car as it collapses. (This model is similar to how real-world crumple zones act.) The more rigid the crumple zone, the greater this constant force will be. You can use the work-energy theorem to determine the ideal constant force the crumple zone exerts. On the DESIGN tab, select the SUV body type and set the Crumple zone length to 100 cm. Note the mass of the SUV is 2,000 kg. On the CRASH TEST tab, set the starting speed to 16 m/s. A. What is the kinetic energy of the SUV, in joules? 15 B. How far can the crumple zone collapse, in meters? 1m C. What force (in kN) must the crumple zone exert in order to stop the car as it collapses completely? 15 joules Check your answer in the Gizmo.