I need help with my pre cal project really bad. The teacher wants us to do it on something that interests us, but it has to have calculus related to it. I need the brightest of the bright. I have some books about automobiles that involves math(exp. A-arm suspension, independant rear suspensions, etc.)What other parts of an automobile includes calculus? Also, how can i go about this. Here are the objectives of the project:
1. Presentation must be 5 minutes2. Must include more than one math concept3. What ever it takes to explain4. Visual aids5. Report must be 2pages minimum or 10 pages maximum6. It's a 4 letter grade
Basically, if you dont do this project you fail the semester.I'm not good at pre calculus so i need your help. Give me any formulas , functions, concepts, etc. that help determine certain things about automobiles. Don't disregard this post please!!!! This is not some joke. I will make sure to acknowledge you guys at the end of my presentation.How should i lay out the project? What cars should i focus on?
:help This project is due March 13 :help
Please help me with Pre-Cal project!
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Opposite_Lock
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DonDonati88
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drifter sx
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You could use apparent size.
Say car no1 is 2 miles (10560 ft.) away. It's apparent size is .5 feet.
So with the equation S= (theta)R were S is the arc lenght and R is the radius. And Theta is in radians.
.5=(.0000474848)(10560)
Then if 60 seconds later its apparent size is 1 and Theta is .0001893939
1=(.0001893939)(x)
How far did the car go and how fast is it going?
1=(.0001893939)(5280)
The car traveled 1 mile in 60sec so the car is going 60mph.
I just made up both the apparent size values and radians angles. You could make them anything you want to calculate the distance traveled. And to find how fast it is going. You could make multiply problems like this.
Say car no1 is 2 miles (10560 ft.) away. It's apparent size is .5 feet.
So with the equation S= (theta)R were S is the arc lenght and R is the radius. And Theta is in radians.
.5=(.0000474848)(10560)
Then if 60 seconds later its apparent size is 1 and Theta is .0001893939
1=(.0001893939)(x)
How far did the car go and how fast is it going?
1=(.0001893939)(5280)
The car traveled 1 mile in 60sec so the car is going 60mph.
I just made up both the apparent size values and radians angles. You could make them anything you want to calculate the distance traveled. And to find how fast it is going. You could make multiply problems like this.
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Opposite_Lock
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DonDonatti88- ha ha ha "NO"
Fiznat, Drifter sx - I guess thats what the guys that create those g-tech systems use to get those dyno sheets on their new g-tech system huh. Do you know where i can get books on that, or what should i look for in my pre cal book that relates to dyno sheets
S13KA24E- Wow pretty intersting, since i do need multiple math concepts i'm gonna ask you the same thing, where should i look in my pre cal book for that? Also, is this somehow related to what Fiznat and Drifter sx said about dyno's
Driftaholic- Is that even possible... cause if it were
Fiznat, Drifter sx - I guess thats what the guys that create those g-tech systems use to get those dyno sheets on their new g-tech system huh. Do you know where i can get books on that, or what should i look for in my pre cal book that relates to dyno sheets
S13KA24E- Wow pretty intersting, since i do need multiple math concepts i'm gonna ask you the same thing, where should i look in my pre cal book for that? Also, is this somehow related to what Fiznat and Drifter sx said about dyno's
Driftaholic- Is that even possible... cause if it were
Well, i'm taking precal this year...and while i was looking through my book i saw something about calculating how far a piston was from the top of it's stroke when the spark plug fired at 5 degrees before top dead center, I think it related to applying trigonomitry to calculus or somethin...not sure. Ironiccally enough i'm at school right now but i don't have my book. I'll check back on this thread later tonight and see if we have the same book, and if so i'll give you the page #.
-Jon-
-Jon-
If your in pre-cal then i don't think you will be able to find the area under the curve. Finding the area under the curve involves integrating a function over a closed interval. When i was in pre-cal we never did integrals, only derivatives. Also there isn't really a defined function for a torque or horsepower curve. If you wanted to though, you could teach yourself how to integrate and then learn the fundamental theorem of Calculus and then figure out some way to define the curve as a function.
What you might be able to do though is create functions for your cars postition, velocity and acceleration. Show how the velocity and acceleration functions are derivatives of the postition function. Then you could also show how the graphs of each function relate to each other. That's all i can think of that you could do. I don't really remember pre-cal.
What you might be able to do though is create functions for your cars postition, velocity and acceleration. Show how the velocity and acceleration functions are derivatives of the postition function. Then you could also show how the graphs of each function relate to each other. That's all i can think of that you could do. I don't really remember pre-cal.
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Mayhem_J30
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Opposite_Lock
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94teggy- My book is called "Precalculus, a graphing approach" the fourth edition one. I also have the third edition somewhere in my room.
Ratm- Could you give me an example of what you described at the end of your suggestion, you know.. where you talk about making a function about a cars position,velocity, and acceleration. this sounds really promising if i can actually get how to do it
Also, I found a couple of concepts that could be related to cars. Newton's law of cooling. Lets say an s13 with an sr20 at a track has ran 2 laps. The engine is at 96 degrees celsius. It's aftermarket radiator lowers the temperature by 16 degrees celsius. Four minutes later the engine is at 45 degrees celsius. Use newton's cooling law to determine when the engine will be 20 degrees celsius.
Model= We know from the given information thatT_o= 96, the initial temperature of the engine,T_m= 16, the temperature of the medium.
Substituting into T(t)= T_m+ (T_o - T_m)e -kt, we haveT(t)= 16 + (96-16)e -kt.
To find the value of k we use the fact that T= 45 when t= 4
45 = 16 + 80e -4k
45 -16= 80e -4k
29/80= e -4k
1n 29/80= -4k *change to logarithmic form*
k= 1n(29/80) ----------- 4k~ 0.254
A modeling equation, then, for the temperature T of the egg at a time t is T(t)= 16 + 80e -0.254t. To find t when T = 20 degrees celsius, we must solve the equation 20 = 16 + 80e -0.254t
Solve algebraically20 = 16 + 80e -0.254t
4/80 = e -0.254t *subtract 16, then divide by 80*
1n 4/80 = -0.254t *change to logarithmic form*
1n 0.05 = -0.254t
t = 1n 0.05 --------- -0.254
t ~ 11.794
InterpretThe temperature of the SR20 will be 20 degrees celsius after around 11.8 minutes( 11 minutes 48 seconds)
I'm probably going to use this concept to explain engine cooling, but i need somebody to explain how to change to logarithmic form.
Ratm- Could you give me an example of what you described at the end of your suggestion, you know.. where you talk about making a function about a cars position,velocity, and acceleration. this sounds really promising if i can actually get how to do it
Also, I found a couple of concepts that could be related to cars. Newton's law of cooling. Lets say an s13 with an sr20 at a track has ran 2 laps. The engine is at 96 degrees celsius. It's aftermarket radiator lowers the temperature by 16 degrees celsius. Four minutes later the engine is at 45 degrees celsius. Use newton's cooling law to determine when the engine will be 20 degrees celsius.
Model= We know from the given information thatT_o= 96, the initial temperature of the engine,T_m= 16, the temperature of the medium.
Substituting into T(t)= T_m+ (T_o - T_m)e -kt, we haveT(t)= 16 + (96-16)e -kt.
To find the value of k we use the fact that T= 45 when t= 4
45 = 16 + 80e -4k
45 -16= 80e -4k
29/80= e -4k
1n 29/80= -4k *change to logarithmic form*
k= 1n(29/80) ----------- 4k~ 0.254
A modeling equation, then, for the temperature T of the egg at a time t is T(t)= 16 + 80e -0.254t. To find t when T = 20 degrees celsius, we must solve the equation 20 = 16 + 80e -0.254t
Solve algebraically20 = 16 + 80e -0.254t
4/80 = e -0.254t *subtract 16, then divide by 80*
1n 4/80 = -0.254t *change to logarithmic form*
1n 0.05 = -0.254t
t = 1n 0.05 --------- -0.254
t ~ 11.794
InterpretThe temperature of the SR20 will be 20 degrees celsius after around 11.8 minutes( 11 minutes 48 seconds)
I'm probably going to use this concept to explain engine cooling, but i need somebody to explain how to change to logarithmic form.
In order to do the suggestion i gave you, you will have to know who to differentiate. That shouldn't be that much of problem though if you don't know how because the equations are pretty easy to differentiate.
First you will have to define the position of the car as a function of time. For motion in a straight line it should be:X = Xo + Vo*(T)+A*(T)^2. Where Xo is the initial position, Vo is the initial velocity, A is the acceleration, and T is the time. The acceleration will have to be constant for this to work. Then to find the velocity function you take the derivative of the position function. Then to find the acceleration function you take the derivative of the velocity function.
Make the graphs for the functions. The velocity at a point is the slope of the line of the position function at that point. Same thing with acceleration and velocity. using y=mx+b you can solve for the equation of the line at that point. m is the slope and (x,y) are the values from the postition equation at that time.
Ex:
x(t)=2+6t+4t^2 v(t)=6+8t a(t)=8
X(1)=2+6+4=12 v(t)=6+16=22 a(1)=8
y=mx+b 12=22(1)+b b=-10
therefore the equation of the line for x(t) at x=1 is y=22x-10, the position is 12, the velocity is 22 and the acceration is 8.
If you have any questions feel free to ask. Also i thought of something else you could do using these equations although i doubt you'll ever do it in pre-cal. It's not really that complicated but i don't think it is taught until calculus. If you want to know i will tell.
First you will have to define the position of the car as a function of time. For motion in a straight line it should be:X = Xo + Vo*(T)+A*(T)^2. Where Xo is the initial position, Vo is the initial velocity, A is the acceleration, and T is the time. The acceleration will have to be constant for this to work. Then to find the velocity function you take the derivative of the position function. Then to find the acceleration function you take the derivative of the velocity function.
Make the graphs for the functions. The velocity at a point is the slope of the line of the position function at that point. Same thing with acceleration and velocity. using y=mx+b you can solve for the equation of the line at that point. m is the slope and (x,y) are the values from the postition equation at that time.
Ex:
x(t)=2+6t+4t^2 v(t)=6+8t a(t)=8
X(1)=2+6+4=12 v(t)=6+16=22 a(1)=8
y=mx+b 12=22(1)+b b=-10
therefore the equation of the line for x(t) at x=1 is y=22x-10, the position is 12, the velocity is 22 and the acceration is 8.
If you have any questions feel free to ask. Also i thought of something else you could do using these equations although i doubt you'll ever do it in pre-cal. It's not really that complicated but i don't think it is taught until calculus. If you want to know i will tell.
Ok, sorry i didn't get back to you last night but i stayed at my friend's house. Sounds like we have the same series of books (Precalculus with Limits a graphing approach published by Houghton Mifflin?), except i have the second edition. Hopefully they're pretty close to the same thing. Ok, in my book it's in section 6.1, Law of Sines on page 468. The question is:
Engine Design, The connecting rod in an engine is 6 inches in length and the radius of the crankshaft is 1.5 inches. Let d be the distance the piston is from the top of it's stroke for the angle "theta"
Part a: Use a graphing utility to complete the table - then you have to give the distance from top dead center when the angle of the crankshaft (theta) =0, 45, 90, 135, and 180 degrees.
Part b: The spark plug fires at theta = 5 degrees before top dead center. How far is the piston from the top of it's stroke at this time? and it has a little drawing of an engine.
Hope that helps or at least you'll be able to find something similar in your book.
Also, the links that Cory gave to team-integra.net are very good. I'm a member there and they have some very good general engine information...definately worth signing up for.
and i don't know if this site will help because i haven't read through it all the way but you can try http://autozine.kyul.net/techn...x.htm
Good Luck,-Jon-
Engine Design, The connecting rod in an engine is 6 inches in length and the radius of the crankshaft is 1.5 inches. Let d be the distance the piston is from the top of it's stroke for the angle "theta"
Part a: Use a graphing utility to complete the table - then you have to give the distance from top dead center when the angle of the crankshaft (theta) =0, 45, 90, 135, and 180 degrees.
Part b: The spark plug fires at theta = 5 degrees before top dead center. How far is the piston from the top of it's stroke at this time? and it has a little drawing of an engine.
Hope that helps or at least you'll be able to find something similar in your book.
Also, the links that Cory gave to team-integra.net are very good. I'm a member there and they have some very good general engine information...definately worth signing up for.
and i don't know if this site will help because i haven't read through it all the way but you can try http://autozine.kyul.net/techn...x.htm
Good Luck,-Jon-