Physics
GROUP # _______
PHYS 110 Workshop #1: Scientific Method
|
The big idea: |
Exploring the scientific method |
The scientific method is the way we take observations of the world around us and develop models to help us explain what we’ve seen and measured.
The main steps are:
Observations and measurements of what’s happening in the world
Developing a model (an equation or set of rules) based on the observations
Developing a hypothesis to explain the observations and model
Testing the hypothesis with more observations
In this workshop, you’ll practice creating a model for the pendulum. A pendulum is created when you hang an object with mass (called “the pendulum bob”) from a string. The bob can swing back and forth. We measure the amount of time it takes for the bob to make this swing—if it starts on the left, swings to right, then swings back to the left, that amount of time is called “the period” and gets the variable T. We’ll measure the period in seconds.
|
Pendulum Clock |
Our Set-up |
Pictorial Representation |
|
|
Can you think of at least 5 different things that could affect the period of a pendulum? |
|
|
|
There are some factors you may have come up with that might be important, but which would be difficult for us to modify to see their effect on the bob: the temperature of the air (it’s hard to adjust the thermostat in a precise way), the composition of the string (we only have one string), or how hard the bob is pushed at the beginning of the swing (we couldn’t measure how hard we push, so then we couldn’t be consistent).
However, three factors that we can easily control and measure are
the mass of the bob
the length of the string
the angle at which the bob is released
We’ll look at these one at a time.
|
|
PREDICTION 1: If you increase the mass of the bob, will the period of the pendulum increase, decrease or stay the same? ________________ |
|
|
Why? |
Three lab groups measured the swing of the pendulum with different masses of bobs. For each group, they used the same length of string (25 cm) and same initial angle of release (10 degrees). The bob was always released from rest. Here is their data:
|
Mass (g) |
Group A Period (s) |
Group B Period (s) |
Group C Period (s) |
|
10 |
0.98 |
1.00 |
1.01 |
|
20 |
0.96 |
1.02 |
0.97 |
|
30 |
1.05 |
1.04 |
0.98 |
|
40 |
1.03 |
1.01 |
0.99 |
|
50 |
0.99 |
0.99 |
1.02 |
|
|
QUESTION 1: Does the mass of the bob affect the period of the bob? Hint: Look at trends. Do the numbers generally get smaller as mass increases? Do they generally get bigger as mass increases? Or do they alternate between bigger and smaller? |
Next, let’s make observations on the length of the string.
|
|
PREDICTION 2: If you increase the length of the string, will the period of the pendulum increase, decrease or stay the same? ________________ |
|
|
Why? |
The three lab groups measured the swing of the pendulum with different length strings. The mass was always 30 g and the initial release angle was 10 degrees, and it was alway released from rest. Here is their data:
|
Length of string (cm) |
Group A Period (s) |
Group B Period (s) |
Group C Period (s) |
|
10 |
0.65 |
0.61 |
0.60 |
|
20 |
0.87 |
0.91 |
0.88 |
|
30 |
1.10 |
1.09 |
1.12 |
|
40 |
1.28 |
1.25 |
1.23 |
|
50 |
1.44 |
1.40 |
1.45 |
|
|
QUESTION 2: Does the length of string affect the period of the bob? Hint: Look at trends. Do the numbers generally get smaller as length increases? Do they generally get bigger as length increases? Or do they alternate between bigger and smaller? |
Before you look at the angle of release, let’s compare what you’ve seen to the accepted physics model of the pendulum.
|
Which variable should be included in the pendulum’s period model? [Mass/Length] |
|
One model physicists have developed to predict the period of a pendulum is given by:
Where
So, this model does include the length, because the period T changes when the length changes, but does not include the mass, because the period T does not change when the mass changes.
Choose data from a group where length was the variable that changed. Let’s test the model to see if the data is consistent with the model.
Record the measured periods for a given group from their data above, in the measured T column
Use the equation to calculate the period for each length. Record these times in the Tmodel column.
Find the percent difference to compare the period measured in the experiment to the period calculated using the model.
|
Length of string (m) |
Period T (Measured) (s) |
Model period Tmodel (s) |
PD (%) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Percent Difference (PD) is a useful way to compare two numbers or measurements where the difference between the two numbers is expressed as a percentage of the average of the numbers.
If PD is small (less than 10%), then you can say the two numbers are close enough to be considered “the same.”
The general formula to calculate the percent difference is given by:
|
|
QUESTION 3: Is this model a good one? That is, do the measured values match the model numbers, within 10%? |
So far you’ve observed what happens with mass and length, but you haven’t yet explored what happens with different angles.
|
|
PREDICTION 3: If you increase the angle of release, will the period of the pendulum increase, decrease or stay the same? ________________ |
|
|
Why? |
The three lab groups measured the swing of the pendulum with different release angles. The mass was always 30 g and the length of string was 25 cm, and it was alway released from rest. Here is their data:
|
Angle of release () |
Group A Period (s) |
Group B Period (s) |
Group C Period (s) |
|
10 |
0.98 |
1.00 |
1.01 |
|
25 |
1.02 |
1.01 |
1.03 |
|
50 |
1.05 |
1.04 |
1.07 |
|
75 |
1.11 |
1.12 |
1.10 |
|
90 |
1.18 |
1.20 |
1.19 |
|
|
QUESTION 4: Does the angle of release affect the period of the bob? Hint: Look at trends. Do the numbers generally get smaller as angle increases? Do they generally get bigger as angle increases? Or do they alternate between bigger and smaller? |
Let’s check and see how well the model handles different release angles. For one group, fill in the table below, calculating the percent difference between the measurements and the model.
|
Angle of release () |
Period T (Measured) (s) |
Model period Tmodel (s) |
PD (%) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
QUESTION 5: Should the angle of release always be included in the model? Hint: does the angle always make the measurement agree or disagree with the model? Or are there some angles where the measurements and model agree, and some measurements where they don’t? Include your evidence! |
The model we’ve been using for the pendulum period is called the “small angle” model. It was created using an assumption: that the angle of release would be small (less than 25 or so degrees). In order to incorporate the effect of the release angle, you’d have to remove that assumption. However, that makes the model much more complicated! While it’s an important part of the scientific method to refine your models with more observations, we can also use models that don’t work in every circumstance…as long as we know when they work.
Workshop #1 Group Worksheet | Page of
Workshop #1 Group Worksheet | Page of
Workshop #1 Group Worksheet | Page of