What is the volume of the counter table in 131?
We want the volume in ft3
??
Which conversion factor do we use?
1
What is the area of
this circle in ft2 ?
r
2
miles per gallon
3
4
Order-of-Magnitude Calculations
There are many occasions when one must figure out a
rough approximation to some quantity when the exact
value is not crucial.
It may be sufficient to know the value to an accuracy
of 10%, 25%, or a factor of 2, or even a factor of 10!
In such cases, being able to make a quick, simple
order of magnitude estimate is valuable skill .
For example you may carry out a long elaborate,
complex calculation, which SHOULD yield the proper
value accurately but that calculation may have an
error in one of it’s steps.
By doing a quick order of magnitude estimate as a
check, you may catch the error.
How long will it take to fill a Olympic size
swimming pool with an ordinary garden hose?
an hour?
a day ?
3 days ?
a week ?
Don’t be afraid to estimate
An Olympic swimming pool is roughly 50m long, 25m wide and ~2m deep.
V=50m x 25m x 2m = 2500m3
1000 liters = 1m3
V~ 3x106 Liters
Garden hose delivers 1 gallon in 10 seconds Rate of water volume discharged per time R ~ 3 liters in 10 sec ~ 0.3 liters/sec Time t = V/R = 3x106 Liters/ 0.3 liters/sec=107 seconds
3 liters ~ gallon
What is number of seconds in one day?
It would take several months to fill
the pool with a garden hose!!!
How many truck-stops between Nashville and Memphis on I-40?
Just left Nashville on I40 heading toward Memphis with 200 miles to ride,
out of boredom you began to count the number trucks going in the
opposite direction and on the average 50 trucks are counted every 10 miles.
estimate
Assuming the density of trucks are uniform, this would imply there are roughly
5 trucks / mile or 1000 trucks on I40 between Nashville to Memphis.
Also assume the truckers time on the road is 8hrs per 24hrs so one could estimate 1/3
of trucks in transit are on the road and the remainder are located at a Truck-stop.
If average maximum capacity is 50 for each Truck-stops, what is expected minimum
number of Truck-stops between Nashville and Memphis?
If only 1/3 of the trucks are on the road, this would imply there are 2000 trucks intransit but off the road and likely staying at a truck stop. If we assume the max
capacity is 50 Trucks per Truckstop, this would imply roughly 40 Truck Stops.
Scalars and Vectors
Scalar – a numerical value. May be positive or negative.
Examples: temperature, speed, height, area
Vector – a quantity with both magnitude and direction.
Examples: displacement (e.g., 10 feet north), force,
magnetic field, velocity
Oh yeah
Problem Solving in Physics
No recipe or plug-and-chug works all the time, but here
are some guidelines:
1. Read the problem carefully
2. Sketch the system
3. Visualize the physical process
4. Strategize
5. Identify appropriate equations
6. Solve the equations
7. Check your answer
8. Explore limits and special cases
One-Dimensional Kinematics
Position, distance, and displacement
Speed and velocity
•Average
•Instantaneous
•Constant
Acceleration
•Average
•Instantaneous
•Constant
Equations of motion with constant acceleration
Free fall
11
Finish Line
12
In the game of Football, is the goal to maximize distance or displacement?? http://www.youtube.com/watch?v=NvZdu3RLeLU
13
Displacement
Xi
Xf
14
Distance
Displacement
Xi
Xf
15
Displacement is the change in position. If you drive from your house to the
grocery store and then to your friend’s house, your displacement is 2.1 mi and
the distance you have traveled is 10.7 mi.
The distance is the total length of travel; if you drive from your house to the
grocery store and back, you have covered a distance of 8.6 mi.
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Clicker Quiz
You have 30 seconds to provide an answer
a) yes
You and your dog go for a walk to the
b) no
park. On the way, your dog takes many
side trips to chase squirrels or examine
fire hydrants. When you arrive at the
park, do you and your dog have the same
displacement?
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