Question

lab test: falling bodies and inclined plane
100 points
directions: choose the best answer to each question.
you may use a cheat - sheet to answer the questions.
circle your answers.
1: how would aristotle support his claim that big, heavy things fall faster than small, lighter things?
a) big things have less air resistance than small things
b) big things are more attracted to the earth than small things
c) big things have more air resistance than small things
d) big things are less attracted to the earth than small things
2: you are rolling balls down a ramp. you are using a metronome to time them. at one click of the
metronome, a ball rolled 1 meter. how far would galileo predict the ball would roll by 4 clicks of the
metronome?
a) 4 meters; b) 8 meters; c) 12 meters; d) 16 meters; e) 25 meters
3: you are rolling balls down a ramp. you are using a metronome to time them. at one click of the
metronome, a ball rolled 5 cm. which set of data looks most like what you would get in real life for 2, 3, and 4
clicks of the metronome? (circle correct data set: a, b, or c.)
data set a (distances in cm)
time (clicks of metronome)
0 5 20 45 80
data set b (distances in cm)
0 5 30 75 135
data set c (distances in cm)
0 5 15 30 50
4: you are rolling balls down a ramp. you are using a metronome to time them. at one click of the
metronome, a ball rolled 10 cm. in distance set a, which distance would aristotle have predicted for the 3rd
click?
time (clicks of metronome)
0 1 2 3 4
data set a (distances in cm)
0 10 x x x
a) 30cm; b) 60cm; c) 90cm; d) more than 90cm
5: you are rolling balls down an inclined plane. lets pretend that your data read as follows:
time (clicks on metronome)
0 1 2 3
distance rolled (cm)
0 8 32 72
if you collected these data, they would:
i: falsify the greek notion that things travel at steady rates of speed
ii: confirm galileos predictions on how things accelerate
iii: falsify galileos predictions on how things accelerate
iv: confirm galileos predictions on how things accelerate
a) i is true
b) ii is true
c) ii and iii are both true
d) i and iv are both true

Explanation:

Step1: Recall Aristotle's view

Aristotle believed heavier objects fall faster and have a linear - like motion relationship. For rolling balls, he might assume a simple proportional increase in distance with time.

Step2: Analyze question 1

Aristotle thought big, heavy things are more attracted to the earth than small things. So the answer to question 1 is c.

Step3: Recall Galileo's law for question 2

Galileo's law for a ball rolling down a ramp gives \(d=\frac{1}{2}at^{2}\) (where \(d\) is distance, \(a\) is acceleration and \(t\) is time). For a metronome - timed experiment, if at \(t = 1\) click the ball moves a certain distance, at \(t = 4\) clicks, \(d\propto t^{2}\). If at \(t = 1\) click \(d = 1\) unit, at \(t=4\) clicks \(d = 16\) units. So the answer to question 2 is d.

Step4: Analyze data sets for question 3

Galileo's law implies \(d\propto t^{2}\). Looking at the data sets, Data Set C shows a quadratic - like relationship (\(d = 5t^{2}\) approximately). So the answer to question 3 is Data Set C.

Step5: Apply Aristotle's view for question 4

Aristotle would assume a linear increase in distance. If at 1 click the ball rolled 10 cm, at 3 clicks he would predict \(10\times3=30\) cm. So the answer to question 4 is a.

Step6: Analyze the data for question 5

The data shows that the distance is not increasing linearly (e.g., from \(t = 0\) to \(t = 1\) distance changes from 8 to 32, from \(t = 1\) to \(t = 2\) from 32 to 72). This falsifies the Greek notion of steady - speed motion (I is true) and confirms Galileo's prediction of acceleration (IV is true). So the answer to question 5 is d.

Answer:

1. c
2. d
3. Data Set C
4. a
5. d