Exercise 1: Proportionality

Physics 1A03 Team

Exercise 1: Proportionality

Let’s begin with the following relationship between the variables U, Q, and P (Note: 6 and 𝛑 are constants).

$U^2 = \frac{6P^2}{\pi Q}$

Fill in the table of values (you can do this manually, using the excel file provided, or any other spreadsheet and graphing software). Note that in each column, only one variable changes, while the other variable is held constant. For simplicity, we set the third variable equal to one. This is indicated in the brackets. We have completed two of the rows as an example.

$U$	$U^2$	$Q (P=1)$	$P (Q=1)$	$1/Q (P=1)$
1.0
2.0	4.0	0.48	1.4	2.1
4.0
8.0	64	0.03	5.8	34
12
20

Exercise 1.1 (3 marks)

Using your table of values above, create a plot of:

i) $P$ vs $U$

ii) $P$ vs $U^2$

iii) 1/ $Q$ vs $U^2$

When we say (something) vs. (something), this means y (vertical) vs x (horizontal).

Note that you can create these plots using whichever method you prefer. Graphing software or hand drawn graphs on graph paper are acceptable, make sure to look at the graphing appendix to remind yourself what we are looking for in submitted graphs. Do not connect your data points, and label your axis.

Exercise 1.2 (2 marks)

Which plot(s) from 1.1 is (are) linear? Choose all correct answers on Crowdmark.

a. $P$ vs $U$

b. $P$ vs $U^2$

c. $1/Q$ vs $U^2$

Exercise 1.3 (2 marks)

If $U$ is held constant (i.e. $U$ = 1), which graphing relationship(s) between $P$ and $Q$ would yield a straight line (i.e. the graph would be linear)? Choose all correct answers on Crowdmark.

a. $P$ vs $Q$

b. $P$ vs $Q^2$