PHYS 30 LESSONS Unit 3: Electromagnetism Quiz #1: Graphical Analysis Curve 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  Show that a c and r have a direct relationship.  If the relationship between a c and r was graphed, what would be the significance (and units) for the slope?

MV: r RV: a c Control: T Always get the RV (y) by itself.

MV: r RV: a c Control: T a c has a direct relationship with r

Thus, if you graph a c vs r, you would get a straight line through the origin. acac r

Units for the slope acac r y x Units:

Significance of the slope acac r y x The equation for the graphed line would be

Now, we can compare the derived equation with the known equation:

Problem #2 In a kinematics experiment, then acceleration of an object is varied and the responding displacement is measured. The known equation is  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: v f, t This 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: Units: 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

Now, we can compare the derived equation with the known equation: In order to compare them, they need to be put in the same form.

Now, they are in the same form.

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 electric field and the distance.  Determine the units for the slope.  How would you determine the charge Q using the significance of the slope?

MV: r RV: E Control: Q Always get the RV (y) by itself. Then, state the proportion.

Electric field has an inverse-square relationship with distance. However, electric field has a direct relationship with 1/r 2. Thus, if you graph E vs 1/r 2, you will get a straight line through the origin.

So, this would be the straight-line relationship.

y x Units for the slope Units:

y x Significance of the slope The equation for the graphed line would be

Now, we can compare the derived equation with the known equation:

To find the charge Q :

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 relationship b) the significance of the slope and determine the units for the slope c) explain how you could find the mass of the oil droplet, using the significance of the slope

V +++ FeFe FgFg Eq-q- Balanced forces (Newton’s 1 st law):

since and

MV: q RV: V Controls: m, g, d Always get the RV (y) by itself.

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.

This would be the straight-line graph.

Units for the slope Units:

Significance of the slope The equation for the graphed line would be

Now, we can compare the derived equation with the known equation:

Finally, to find the mass: