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