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29 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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Name
: _____
____

Period______ ID________________ Table______ Date______

Unit 1 Review Packet: Identifying Variables, Average/Uncertainty
, Graphs, and Drawing Conclusions
\

Scenario A:
A construction company gathers data for the following
question

"How does the compression strength of a concrete column depend on the diameter of the column?"

1. Fill out the average and uncertainty columns in the data table.

Diameter of
Column

(m)

Compression
Strength

(lbs)

Measurement

#1

Compression
Strength

(lbs)

Measurement

#2

Compression
Strength

(lbs)

Measurement

#3

Average
Compression
Strength

(lbs)

Compression
Strength
Uncertainty

(lbs)

0.5
±
0.3

2620

2510

2370

2500

100
(round 125)

1.0
±

0.3

4750

5025

5225

5000

200

1.5
±

0.3

7100

7825

7575

7500

400
(round 361)

2.0
±

0.3

9400

10275

10225

10000

400

2.5
±

0.3

11900

12475

13125

12500

600

2.
Plot the data from the
above
table on
graph paper.
Use a ruler to draw the best
-
fit line. Include error bars.

See graph

3.
Which
pattern
from class describes the relationship
between compression strength and diameter?

linear

4. For the experiment, det
ermine the following variables.

a.

Independent variable:

diameter of column

b.

Dependent variable:

compression strength

c.

2 variables that must
be controlled:

material of column,
height of column or weight of column [there may be
others]

5.
Describe the relationship between the variables using a “For Every” statement.

It tells us that the compression strength of the column increases by
5000

pou
nds for every 1 meter increase in
the diameter of column.

4.
Write a conclusion including a prediction for the compression strength of a 1.8 m column.

Because all of the data fits on a best
-
fit line that is _
linear
_,

I conclude that there is a _
linear

_ relationship
between _
the diameter of the column
_ and _
the compression strength
_. This can be represented as a “For
Every” statement as

_
for every 1 m increase in diameter, the compression strength increases by 5000 lbs
. So I
predict with _
high
_ conf
idence based on my data that when the 1.8 m column is compressed with a 8000 lbs
hold
/break, because the best
-
fit line hits near
_
the center of nearly all the data points
_

and this
prediction is
_
within the data range
_

Scenario B:

A physics student gathers the following data
for the friction
a car’s tires require

to safely travel
through a certain corner
.

6
. What kind of relationship
exists between
force of friction and the top safe speed of the car
?

7. Write the math
ematical relationship between force and top safe speed using the appropriate variables.

Force of friction = 3.96*(top safe speed of car)
2

8
.
Write a complete conclusion.

Include a prediction for
the force of friction if the top safe speed of the car is 1
6
m/s
.

Because all of my data fit on a best
-
fit line that is quadratic, I conclude that there is a quadratic relationship
between the force of friction and the top safe speed of the car. This can be represented mathematically as Force
of friction =
3.96*(top safe speed of car)
2
. So I predict with medium
-
high confidence that at 16 m/s, the force of
friction required is 1000 N because my best fit line is near the center of nearly all the data points and the predicted
value is near the data range.

y = 3.9631x
2

0
200
400
600
800
1000
1200
0
5
10
15
20
Force of Friction (N)

Top Safe Speed of Car (m/s)

Relationship Between Force of Friction and Top
Safe Speed of Car

y = 502.74x + 106.44

0
200
400
600
800
1000
1200
0
0.5
1
1.5
2
2.5
Speed other Galaxy is moving away (km/s)

Distance to Other Galaxy (Mpc)

Relationship Between Distance to Galaxy and
Galaxy Speed

Scenario C:
An early 20
th

Century lawyer
-
turned
-
astronomer noticed a relationship between the distances of
nearby galaxies and the speed in which they appear to be moving away and asked the following question.

"How does the distance a galaxy is from our
Milky Way affect the speed at which it is moving away?"

Distance to other Galaxy

(Mpc)

Speed other Galaxy is moving away
(km/s)

0.5 ± 0.3

270 ± 30

0.9 ± 0.3

500 ± 30

1.4 ± 0.3

730 ± 30

1.7 ± 0.3

960 ± 30

2.0 ± 0.3

990 ± 30

9
. Identify variables
for this
experiment.

a.
Independent variable:

distance to other
galaxy

b.
Dependent variable:

speed at which the other
galaxy is moving away

10
. What kind of relationship
exists between the speed of the other galaxy and the distance to the galaxy?

linear

11
. Describe the relationship between the variables using a “For Every” statement.

For every 1 Mpc, the speed of the other galaxy increases by 500 km/s.

12
.

Write a co
mplete conclusion. Include a prediction for the speed of the other galaxy when the distance to the
galaxy is 1 Mpc.

Because all of the data fits on a best
-
fit line that is _
linear
_, I conclude that there is a _
linear
_ relationship
between _
the distance
to the other galaxy
_ and _
the speed at which it is moving away
_. This can be
represented as a “For Every” statement as _
For every 1 Mpc, the speed of the other galaxy increases by 500
km/s
_. So I predict with _
high
_ confidence based on my data that when t
he distance to the galaxy is 1 Mpc, the
speed of the other galaxy_
600 km/s
_, because the best
-
fit line hits near _
the center of nearly all the data points
_
and this prediction is _
within the data range
.

y = 356.95x
-
1.272

0
1000
2000
3000
4000
5000
6000
7000
8000
0
0.5
1
1.5
2
2.5
Force Needed (N)

Distance to Pivot (m)

Relationship Between Distance
From Pivot and Force Needed

Scenario D:
Data for the following question is gather
ed while you are on a seesaw with an old childhood friend.

"How doe
s the distance from the pivot point on the seesaw affect the force needed to support your 600 N friend?"

13
. Fill out the average and uncertainty columns in the data table.

Distance

(m)

Force Needed

(N)

Measurement

#1

Force Needed

(N)

Measurement

#2

Force Needed

(N)

Measurement

#3

Average
Force

(N)

Uncertainty

in Force

(N)

0.1 ± 0.1

6010

6030

5930

5990

50

0.5 ± 0.1

1222

1183

1207

1200

10

(should be 20)

1.0 ± 0.1

611

606

588

602

8

(should be 10)

1.3 ± 0.1

462

470

455

462

8

1.7 ± 0.1

347

366

350

350

10

14
. a. What is the independent variable?

D
istance

b. What is the dependent variable?

Force

c. What are 2 variables that need to be controlled?

____
Use the same seesaw
_
and ______
The weight of the person (600N friend)
____

15
. What kind of
relationship
exists between the force
needed and distance to the
pivot?

Inverse

16
.
Write a conclusion.

Because all of the data fits on a best
-
fit line that is _
inverse
____, I conclude that there is a __
inverse
_
relationship between _
force
____ and __
distance
____. This can be represented as a mathematical relationship
of _
Force
___ = 356.95 x
distance
-
1

. So I predict with
medium
-
high

confidence based on my data t
hat
the force
need to balance my 600 N friend when she is siting 1.8 m away from the pivot point is
200 N
, because the best
-
fit line hits near
the edges of most of my data points

and this prediction is
within my data range
.

Graph for question #2.

Compression Strength = 5000 Diameter

0
2000
4000
6000
8000
10000
12000
14000
0
0.5
1
1.5
2
2.5
3
Compression Strength (lbs)

Diameter (m)

Relationship between Compression Strength and
Diameter of a Concrete Column