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Composition Setup
 Excerpt
hiddentrue
Explore the kinematics of constant power (as opposed to constant force).
Image Added
Photo by Lt. Col. Derik Crotts, courtesy of U.S. Army
...
Top-fuel 
...
 dragsters 
...
 like 
...
 the 
...
 one 
...
 shown 
...
 above 
...
 accelerate 
...
 from 
...
 rest 
...
 at 
...
 a 
...
 tremendous 
...
 rate. 
...
 They 
...
 race 
...
 on 
...
 a 
...
 straight 
...
 1/4 
...
 mile 
...
 long 
...
 track. 
...
 From 
...
 a 
...
 standing 
...
 start, 
...
 they 
...
 complete 
...
 the 
...
 quarter 
...
 mile 
...
 in 
...
 about 
...
 4.5 
...
 seconds 
...
 and 
...
 reach 
...
 a 
...
 speed 
...
 of 
...
 about 
...
 330 
...
 mph 
...
 by 
...
 the 
...
 finish 
...
 line. 
 Deck of Cards
idbigdeck
 Card
labelPart A
Part A
Show that the statistics given in the problem introduction are inconsistent at the 10% level with the assumption that the dragster produces constant acceleration as it moves down the track.
Solution
 Toggle Cloak
idsysa
 System: 
 Cloak
idsysa
 Dragster as .
 Toggle Cloak
idinta
 Interactions: 
 Cloak
idinta
External influence from the ground (friction) assumed to produce constant acceleration.
 Toggle Cloak
idmoda
 Model: 
 Cloak
idmoda
One-Dimensional Motion with Constant Acceleration.
 Toggle Cloak
idappa
 Approach: 
 Cloak
idappa
 Card
labelPart B
Part B 
Using the fact that a top-fuel dragster will typically weigh 2200 lbs (equivalent to a mass of 1000 kg), show that the assumption that the dragster moves down the track with a constant value for the power delivered to the car in the form of kinetic energy is consistent at (approximately) the 10% level.
Solution
 Toggle Cloak
idsysb
 System: 
 Cloak
idsysb
 Dragster as .
 Toggle Cloak
idintb
 Interactions: 
 Cloak
idintb
 Friction interacts with the dragster in such a way as to deliver constant  to the dragster's kinetic energy.
 Toggle Cloak
idmodb
 Model: 
 Cloak
idmodb
.
 Toggle Cloak
idappb
 Approach:
 Cloak
idappb
  

Part A

Show that the statistics given in the problem introduction are inconsistent at the 10% level with the assumption that the dragster produces constant acceleration as it moves down the track.

System:  Dragster as [point particle].

Interactions:  External influence from the ground (friction) assumed to produce constant acceleration.

Model:  [One-Dimensional Motion with Constant Acceleration].

Approach:  We are asked to prove that the model we are examining _does not_ fit the data.  To do so, we look for a contradiction.  In this case, we have several ways to find the acceleration, since we have a large number of givens.  Choosing our coordinates such that the race begins at x_{i} = 0 and proceeds in the positive _x_ direction, we have:

{panel:title=Givens}{latex}\begin{large}\[ t_{i} = 0\]\[t_{f}=\mbox{4.5 s}\]\[ x_{i} = 0\]\[x_{f} = \mbox{402 m} \]\[v_{i}= 0\]\[v_{f} = \mbox{148 m/s}\]\end{large}{latex}{panel}