Last comment for this thread and then we can let it die...
In case anyone wants to see how Markcb750 got his answer (and how to do this problem), here's how it goes:(Anyone not interested, read no further (
you've been warned).)
Original problem:
In 1989, Shirley Muldowney set a new record for the fastest 1/4 mile by a wheel-driven car.
If I told you that the coefficient of static friction between her tires and the road was mu = 3.34, what was her best possible time?
We're looking for the
absolute best time she could possibly have. We are given the coefficient of friction between her tires and the road as 3.34. We also know she's traveling a quarter mile, that is, the distance.
The best she could do is to have her car accelerate constantly at the best rate it's capable of. The key word is
constant, and that allows us to use some simple equations - the equations of
uniformly accelerated motion. There are about 5 of these equations, but the one we need is:
x = v
0t + (1/2)at
2,
where x is the distance (1/4 mile),
v
0 is the initial velocity (which is zero since she starts from rest),
t = time to get down the track (her best possible time),
and a = her acceleration.
Since v
0 = 0 (she starts from rest), the equation simplifies to
x = (1/2)at
2.
We need to solve this for t (we want to know her best time). A little algebraic shuckin' and jivin' (that is, we manipulate this equation) gets us:
t = (2x/a)
1/2, (
Equation 1)
where the 1/2 exponent is another way to say the square-root.
We know
x (1/4 mile), but we need to do something about the acceleration,
a, since it is not instantly obvious what to do.
We haven't made use of the coefficient of friction yet. Friction is a force, and the equation for it is
f = mg(mu),
where m is the mass of the car,
g = the acceleration of Earth's gravity (more specifically, in the location where Shirley's at),
and mu, (a Greek letter commonly used for this quantity) = 3.34 (we were told this, in real life, we'd have to experimentally determine it).
(The quantity
mg is the mass times gravity, or the weight, FYI.)
Since friction is a force, we can equate it to Newton's 2nd law:
f = mg(mu) = ma,
where you might recognize this as the famous, "Force equals mass times acceleration."
Solving this for the acceleration,
a, (the thing we need in Equation 1) we get:
a = g(mu) = g(3.34). (
Equation 2)
Plugging Equation 2 into Equation 1 we get:
t = (2x/3.34g)
1/2.
The acceleration of gravity on Earth is 32.2 ft/s
2, and 1/4 mile is 1320 feet.
Thus,
x = 1320 ft,
g = 32.2 ft/s
2,
and plugging this all in we get
t = (2*1320/3.34*32.2)
1/2 = 4.9545 seconds.
That is her best
possible time.
Shirley's actual time in 1989 was 4.97 seconds with a top speed of 284mph/457kph.
Note that we were not trying to calculate her actual time, only the best possible time. I believe the current record is 4.437 seconds by Anthony Schumacher.
And again, notice that:
1. You can calculate this with very little information (distance and a coefficient of friction), and
2. The limiting factor when trying to break a speed record is how good your tires grip the road.
