Post on 30-Dec-2015
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PHYS 30 LESSONS
Unit 3: Electromagnetism
Quiz #1: Graphical AnalysisCurve Straightening
UNIT 3: QUIZ #1
Take this quiz only after you have done Lessons 1 and 2.
This quiz will only be valuable to you if you do the questions entirely on your own first.
Do not look at the answer until you have completed the question to the best of your ability.
Good Luck!
Problem #1
In a circular motion experiment, the radius is varied and the responding centripetal acceleration is measured.
The known equation for this experiment is
rTac22 4
Show that ac and r have a direct relationship.
If the relationship between ac and r was graphed,what would be the significance (and units) for the slope?
rTac22 4
MV: r
RV: ac
Control: T
2
24
T
rac
Always get the RV (y)
by itself.
rTac22 4
MV: r
RV: ac
Control: T
2
24
T
rac
rac ac has a direct relationship with r
Thus, if you graph ac vs r, you would get a straight line through the origin.
ac
r
Units for the slope
x
y
Slope
ac
r
y
x
r
ac
Units:22
2
s
1
m
1
s
m
ms
m
Significance of the slope
ac
r
y
x
The equation for the graphed line would be
xmy
rac slope
Now, we can compare the derived equation with the known equation:
rac slope 2
24
T
rac
2
24slope
T
rr
rac slope 2
24
T
rac
2
24slope
T
rr
2
24slope
T
Problem #2
In a kinematics experiment, then acceleration of an object is varied and the responding displacement is measured.
The known equation is
2
2
1tatvd f
determine the units for the slope and the y-intercept.
determine the significance of the slope and y-intercept.
For the displacement - acceleration graph:
d
a
MV: a
RV: d
Controls: vf , tThis is NOT a direct relationship. Thus, it will NOT go through the origin.
As we will soon discover, the slope will be negative.
Units for slope:
x
y
Slope
a
d
Units: 22
2
sm
s
1
m
smm
d
a
y
x
Units for y-intercept:
d
a
y-int
The y-intercept crosses the d axis.
Thus, it will have the same units as the displacement.
i.e.
Units: m
d
a
y
x
Significance of the slope and y-int:
The equation for the graphed line would be
bxmy
intyslope ad
intyslope ad
Now, we can compare the derived equation with the known equation:
2
2
1tatvd f
In order to compare them, they need to be put in the same form.
intyslope ad2
2
1tatvd f
tvtad f 2
2
1
Now, they are in the same form.
intyslope ad tvtad f 2
2
1
2
2
1slope taa
2
2
1slope taa
2
2
1slope t
intyslope ad tvtad f 2
2
1
tv f inty
Problem #3
In an electrostatic experiment, the distance r from a central charge Q is varied and the electric field E is measured.
Sketch the straight-line relationship between the electricfield and the distance.
Determine the units for the slope.
How would you determine the charge Q using thesignificance of the slope?
2r
QkE
MV: r
RV: E
Control: Q
Always get the RV (y) by itself.
Then, state the proportion.
2
1
rE
2
1
rE
Electric field has an inverse-square relationship with distance.
However, electric field has a direct relationship with 1/r2.
Thus, if you graph E vs 1/r2, you will get a straight line through the origin.
2
1
r
E
So, this would be the straight-line relationship.
2
1
r
E
y
x
Units for the slope
x
y
Slope
21
r
E
Units:
C
mN
1
m
C
N
m1
CN 22
2
2
1
r
E
y
x
Significance of the slope
The equation for the graphed line would be
xmy
2
1slope
rE
2
slope
rE
2
slope
rE
Now, we can compare the derived equation with the known equation:
2r
QkE
22
slope
r
Qk
r
2
slope
rE
2r
QkE
22
slope
r
Qk
r
Qkslope
Qkslope
To find the charge Q :
kQ
slope
Problem #4
In a Millikan experiment, the charge of the oil droplets is varied and the potential difference required to suspend the oil droplet is measured.
Determine:a) the graph that would lead to a straight-line
relationshipb) the significance of the slope and determine the
units for the slopec) explain how you could find the mass of the oil
droplet, using the significance of the slope
V
+ + +
Fe
Fg
E q-
Balanced forces (Newton’s 1st law):
ge FF
ge FF
gmEq
gmd
Vq
since
d
VE
q
FE e
and
gmd
Vq
MV: q
RV: V
Controls: m, g, d
dgmVq
q
dgmV
Always get the RV (y) by itself.
q
dgmV
qV
1
Voltage has an inverse relationship with q.
However, voltage has a direct relationship with 1/q.
Thus, if you graph V vs 1/q, you would get a straight line through the origin.
q
1
V
This would be the straight-line graph.
q
1
V
Units for the slope
x
y
Slope
q
V
1
Units:
CV1
C
1
V
C1V
q
1
V
Significance of the slope
The equation for the graphed line would be
xmy
q
V1
slope
qV
slope
Now, we can compare the derived equation with the known equation:
qV
slope
q
dgmV
q
dgm
q
slope
qV
slope
q
dgmV
dgmslope
q
dgm
q
slope
dgmslope
Finally, to find the mass:
dgm
slope