D-2

Tony Xu, Vicki Shopland, and Alanna Smith Scenario 2

Tony Xu: Attorney Vicki Shopland: Police Witness Alanna Smith: Expert Witness



Exhibit A: Exhibit B:

Force of Impact MV1: F = W/32.2*V^2*.5*d F = 189.9/32.2*23.5^2*.5*1.5 F = 2,421.93 lbs

Force of Impact MV2: F = W/32.2*V^2*.5*d F = 189.9/32.2*23.4^2*.5*2 F = 3,256.9 lbs

Approaching Speed MV1:

http://www.e-z.net/~ts/speedch.htm Formula: S= 5.5*sqrt(f)(d) S = 5.5*sqrt (.8*13.75) S = 19.19mph

http://www.e-z.net/~ts/speedch.htm Graph: S = 29 mph

Guest Speaker Method: V = sqrt(2gd) V = sqrt 2(.885)(13.75)(32.2) V = 19.08 mph

Approaching Speed MV2:

http://www.e-z.net/~ts/speedch.htm Formula: S= 5.5*sqrt(f)(d) S = 5.5*sqrt(.885)(11.25) S = 17.35mph

http://www.e-z.net/~ts/speedch.htm Graph:

S = 30mph

Guest Speaker Method: V = sqrt(2gd) V = sqrt(2*32.2*11.25) V = 17.26mph

Point of Impact Speed MV1: Given: v1f=v2f m1v1+m2v2= (m1+m2)v (3140)v+(2685)(24.4)=(3140+2685)(24.4) V=25.26m/s

Point of Impact Speed mv2: GIVEN S = 23.4 mph Post Collision MV1 and MV2: S = sqrt (30*d*f*n) S = sqrt (30*25*.885*1) S = 25.8 mph

Approaching Momentum MV1: P = mv P = 1247.3kg*12.96m/s P = 16170.2kgm/s

Approaching Momentum MV2: P = mv P = 1220.5kg*13.41m/s P = 16355.906

Point of Impact Momentum MV1: P = mv P = 1247.3kg*10.5m/s P = 13103.4kgm/s

Point of Impact Momentum MV2: P = mv P = 1220.5kg*10.4m/s P = 12767.3 kgm/s

Post Collision Momentum MV1: P = mv P = 1247.3kg*11.5m/s P = 14330.1kgm/s

Post Collision Momentum MV2: P = mv P = 1220.5kg*11.5m/s P = 14022.2kgm/s

Time Example: T = v/gf T = 35.77/9.8/.885 T = 6.67s

Exhibit C:

Exhibit D: 66.9 in (1699.3 mm) with roof rails || (from: http://en.wikipedia.org/wiki/Subaru_Forester#USA_specifications ) (from: see bibliography)
 * ~ [|Wheelbase] || 103 in (2616.2 mm) ||
 * ~ Length || 179.5 in (4559.3 mm) ||
 * ~ Width || 70.1 in (1780.5 mm) ||
 * ~ Height || 65.9 in (1673.9 mm)
 * ABS brakes, which shorten stopping distance
 * Force Limiters in seat belts to reduce seat belt-related injury
 * Front side-impact airbags

Exhibit E: Front and rear side airbags
 * Wheelbase || 102.9 in ||
 * Lenth || 168.5 in ||
 * Width || 66.7 in ||
 * Height || 56.8 in ||

Source- []

Exhibit F: The video is too large to be posted, however it shows the scene of the accident from several perspectives.

Exhibit G:

__Lab 1__: Measuring Driver Reaction Time Tony Xu, Alanna Smith, Vicki Shopland 5/2/10

Objective: Determine the reaction time of a person. Materials: 1 meterstick Procedure: Given Data:
 * Alanna ||  ||   ||   ||   ||   ||
 * Trial || Distance (ft) || Initial Velocity (ft/s) || acceleration (ft/s) || time (s) || PRT (s) ||
 * 1 || 0.656 || 0 || 32.2 || 0.2019 || 2.0189 ||
 * 2 || 0.625 || 0 || 32.2 || 0.1970 || 1.9703 ||
 * 3 || 0.620 || 0 || 32.2 || 0.1962 || 1.9620 ||
 * ||  ||   ||   || Average || 1.9838 ||
 * Vicki ||  ||   ||   ||   ||   ||
 * Trial || Distance (ft) || Initial Velocity (ft/s) || acceleration (ft/s) || time (s) || PRT (s) ||
 * 1 || 0.4375 || 0 || 32.2 || 0.1648 || 1.6485 ||
 * 2 || 0.2708 || 0 || 32.2 || 0.1297 || 1.2970 ||
 * 3 || 0.3542 || 0 || 32.2 || 0.1483 || 1.4832 ||
 * ||  ||   ||   || Average || 1.4762 ||
 * Tony ||  ||   ||   ||   ||   ||
 * Trial || Distance (ft) || Initial Velocity (ft/s) || acceleration (ft/s) || time (s) || PRT (s) ||
 * 1 || 0.8333 || 0 || 32.2 || 0.2275 || 2.2751 ||
 * 2 || 0.6667 || 0 || 32.2 || 0.2035 || 2.0349 ||
 * 3 || 0.6146 || 0 || 32.2 || 0.1954 || 1.9538 ||
 * ||  ||   ||   || Average || 2.0879 ||
 * 3 || 0.6146 || 0 || 32.2 || 0.1954 || 1.9538 ||
 * ||  ||   ||   || Average || 2.0879 ||


 * || PRT (s) ||
 * AVERAGE of all three || 1.8493 ||
 * Average of Alanna and Vicki || 1.7300 ||

Calculations: d=vit+(1/2)at^2 d=(1/2)at^2 t=SQRT(2d/a) t=SQRT(2*(0.8333)/(32.2)) t=0.2275 s

PRT=t*10 PRT=(0.2275*10) PRT=2.2751 s

Conclusion:

The reason for the error in this lab is that as shown in our data, not everyone has the same reaction time. To deal with different reaction times we used the average between all of ours giving us a range of data, but this does not mean that the drivers reaction time even has to be in this range. Also, there are many factors that change reaction time such as the use of alcohol or stress levels. The only way to make this lab more accurate would be to make the drivers of the cars perform the lab, and then determine their reaction times. This would give us a more accurate representation of their general reaction time, but even then it would not be perfect since all the factors are not the same. This lab is a real life application in itself, being that we used it for the data to a car crash scenario.

__Lab 2:__ Measuring Drag Factor of a Car Tire Tony Xu, Alanna Smith, Vicki Shopland 4/29/10

Objective: Determine the drag factor of a car tire on a road's surface. Materials: Drag Sled, Force Meter Procedure: Given Data:
 * Mass (kg) || Pulling Mass (kg) ||  ||   ||   || Normal Force (N) || Pull Force (N) ||
 * || 1 || 2 || 3 || Average ||  ||   ||
 * 1 || 0.925 || 0.925 || 0.925 || 0.925 || 9.81 || 9.07425 ||
 * 2 || 2.4 || 2.6 || 2.6 || 2.533 || 19.62 || 24.852 ||
 * 3 || 3.3 || 3.3 || 3.4 || 3.333 || 29.43 || 32.7 ||
 * 4 || 4.1 || 3.9 || 4.1 || 4.033 || 39.24 || 39.567 ||
 * 5 || 4.6 || 4.6 || 4.6 || 4.6 || 49.05 || 45.126 ||

Graph:

Calculations: F=ma N-W=0 N=W N=mg N=(1)*(9.81) N=9.81N

Conclusion:

The reason for the error in this lab has to do with the ground surface that we used and block that we dragged across the ground. Ground surface varies based on wear, temperature, and weather. There is no evidence to support the ground conditions being the same. The same is true for the block, being that the tire may have been more worn down, or the friction might not have been as great. There is no real way of getting better measurements unless you have an actual computer that determines the coefficient of friction on the ground when you slam on your breaks. This is extremely expensive equipment so it is not possible. For more precise data we could have used devices more precise than the springs. This lab is a real life application being that it was used during many crime scenes before the more accurate machine was built to determine the coefficient of friction.

Lab 3: Crush Activity Tony Xu, Alanna Smith, Vicki Shopland 4/27/10

Objective: Estimate the Crush Energy from Damage Measurements on an aluminum soda can. The can will serve as an approximate of an automobile. Materials: Soda can, 1" metal ball bearing, balance, meter stick, small ruler Procedure: 1) Trace the perimeter of the soda can onto a piece of paper (lab journal). 2) Place the 1" metal ball bearing exactly 1 meter above the soda can. 3) Have a partner hold down the soda can so that it doesn't shift during the operation. 4) Commence slaughter and deformation of soda can by dropping the metal ball. 5) After termination of deformation, trace the perimeter of the soda can onto the image of the original soda can to see the areas of dents.

Data: Experiment with can:
 * Height of Ball (in) || M of Ball (g) || Zone || A || B || C (in) || L (ft) || CE (ftlbs) || CE (J) || PEg Actual (J) || % Difference (%) ||
 * 49 || 66 || 1 || 173 || 57 || 0.125 || 0.042 || 11.953 || 16.207 || 0.6468 || 96.009 ||
 * 49 || 66 || 2 || 173 || 57 || 0.156 || 0.042 || 12.189 || 16.526 || 0.6468 || 96.086 ||
 * 49 || 66 || 3 || 173 || 57 || 0.156 || 0.042 || 12.189 || 16.526 || 0.6468 || 96.086 ||
 * 49 || 66 || 4 || 173 || 57 || 0.094 || 0.042 || 11.720 || 15.890 || 0.6468 || 95.930 ||
 * 49 || 66 || 5 || 173 || 57 || 0.063 || 0.042 || 11.489 || 15.577 || 0.6468 || 95.848 ||
 * 49 || 66 || 6 || 173 || 57 || 0.016 || 0.042 || 11.143 || 15.108 || 0.6468 || 95.719 ||
 * ||  ||   ||   ||   ||   ||   ||   || 95.834 ||   ||   ||


 * Velocity Determined by Crush Energy (m/s) || Velocity Determined by Kinetic Energy (m/s) || Percent Difference (%) ||
 * 53.889 || 4.427 || 1117.237 ||

Data for Crush Energy on Vehicles:
 * MV1 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Zone || A || B || C (in) || L (ft) || CE (ft*lb) || CE (J) ||  ||   ||   ||
 * 1 || 140 || 67 || 16 || 1 || 10962.26866 || 14862.84062 ||  ||   ||   ||
 * 2 || 140 || 67 || 21 || 1 || 17859.76866 || 24214.59493 ||  ||   ||   ||
 * 3 || 140 || 67 || 15 || 1 || 9783.768657 || 13265.00916 ||  ||   ||   ||
 * 4 || 140 || 67 || 15 || 1 || 9783.768657 || 13265.00916 || velocity (m/s) || km/min || miles/hour ||
 * ||  ||   ||   ||   || Sum || 65607.45387 || 9.5983 || 0.5759 || 21.4708 ||
 * MV2 ||  ||   ||   ||   ||   ||   ||   ||   ||   ||
 * Zone || A || B || C (in) || L (ft) || CE (ft*lb) || CE (J) ||  ||   ||   ||
 * 1 || 173 || 57 || 8 || 1 || 3470.535088 || 4705.413768 ||  ||   ||   ||
 * 2 || 173 || 57 || 18 || 1 || 12610.53509 || 17097.58983 ||  ||   ||   ||
 * 3 || 173 || 57 || 20 || 1 || 15122.53509 || 20503.40452 ||  ||   ||   ||
 * 4 || 173 || 57 || 12 || 1 || 6442.535088 || 8734.904715 ||  ||   ||   ||
 * 5 || 173 || 57 || 9 || 1 || 4128.035088 || 5596.86407 || velocity (m/s) || km/min || miles/hr ||
 * ||  ||   ||   ||   || Sum || 56638.17691 || 9.6442 || 0.5786 || 21.5734 ||
 * 5 || 173 || 57 || 9 || 1 || 4128.035088 || 5596.86407 || velocity (m/s) || km/min || miles/hr ||
 * ||  ||   ||   ||   || Sum || 56638.17691 || 9.6442 || 0.5786 || 21.5734 ||

Calculations: Velocity from Kinetic Energy: PEg=KE mgh=(1/2)mv^2 gh=(1/2)v^2 (9.8)(1)=(1/2)v^2 v=4.427 m/s

Velocity from Crush Energy on soda can: CE = (A2/2B)(L) + ACL + (BC2/2)(L) CE= (173^/(2*57))(0.042)+(173*57*0.042)+((57*0.125^2)/2)(0.042) CE=11.953 ft*lbs ft*lbs * 1.35581795= Joules CE= (11.953)*(1.35581795) CE=16.207 J CE total= 16.207+16.526+16.526+15.89+15.577+15.108 CE total= 95.834 J

CEtotal=KE 95.834=(1/2)mv^2 v=SQRT(95.834*2/0.066) v=53.889 m/s

Percent Difference: % Difference= ABS((PEg velocity-CE velocity)/PEg velocity)*100 % Difference= ABS((4.427-53.889)/4.427)*100 % Difference= 1117.237%

Crush Energy on Vehicles: CE = (A2/2B)(L) + ACL + (BC2/2)(L) CE=(140^2/(2*67))(1)+(140*67*1)+(67*16^2/2)(1) CE=10926.26866 ft*lbs ft*lbs * 1.35581795= Joules CE= (10926.26866)*(1.35581795) CE=14862.84062 J CE total= 14862.84062+24214.5949+13265.0092+13265.0092 CE total= 65607.4539 J

CEtotal=KE 65607.4539=(1/2)mv^2 v=SQRT(65607.4539*2/1424.28) v=9.5983 m/s

Conclusion: On this lab, we had an enormous percent error of over 1000%! With a percent error that large, it's difficult to assess the validity of our results. However, if we had used the correct tools and eliminated the chance of human error inflicted by tracing the soda can onto the paper, our results would have been closer to a car accident situation. But for all intents and purposes, this lab was a great way to reenact the crush of a car accident.

__**Bibliography (work in progress)**__ [|http://www.e-z.net/~ts/physics.htm] [|http://www.e-z.net/~ts/speedch.htm] http://www.internetautoguide.com/crash-tests/09-int/2005/ford/focus/index.html http://www.internetautoguide.com/crash-tests/09-int/2002/subaru/forester/index.html [] http://www.nhtsa.gov/cars/problems/Equipment/absbrakes.html http://hypertextbook.com/facts/2004/YuriyRafailov.shtml http://www.caraccidentattorneys.com/ http://www.science.org.au/nova/058/058key.htm http://auto.howstuffworks.com/car-driving-safety/safety-regulatory-devices/seatbelt5.htm