Graphing Experiment

Name:_________________________________________________________________

Purpose of graphing in science:

The purpose of graphing in science is to examine the relationship between variables. Often there is a theory that predicts how the two variables are related, and a graph of the experimental data can help confirm or disprove a theory. The relationship between variables can be complicated. In this lab, we will consider the simple case of a linear relationship between variables.

Some things to consider when constructing a graph:

- Identify the variables that you are going to plot, and decide which axis you want to plot each variable.
- Determine the variable range and the scale of the graph. The scale and range should be chosen to that the graph fills up most of the available space on the page.
- Label and number each axis. Remember to include the correct units on the axis.
- Plot the data points.
- Draw the graph. Do not connect the data points like a “connect-the-dots” picture. Draw a curve or line that “best fits” the data points.
- Calculate any quantities from the graph that are appropriate. For example if the data lie in a straight line, the slope of the line might be an important quantity.
- Title the graph.

a) Choose one of the circular objects in the lab. Using a ruler, measure the diameter of the circle to the nearest millimeter. Measure the circumference of the circle to the nearest millimeter by wrapping a string around the outside and measuring the length of the string.

b) Repeat part a) for many circular objects and construct a data table as shown below:

__Diameter (cm)__ __Circumference (cm)__

______________ _________________

______________ _________________

……. ………..

c) After taking data on at least 5 circles, make a graph of diameter vs. circumference. Plot diameter on the horizontal (“x”) axis, and circumference on the vertical (“y”) axis.

d) We expect that the data points lie in a straight line. Do they? If so, draw the “best-fit” straight line that goes through the data points. (Do not connect the dots!)

e) Find the slope of the “best-fit” line. Write your answer on the board for comparison with the rest of the class. Is the slope close to what you expect?

The scientific method refers to the process of verifying or disproving theories by doing experiments. Stated differently, it means doing experiments and drawing conclusions based on the outcomes. In Physics we often try to find mathematical connections between different quantities. In the next 3 exercises, you will interpret the results of your experiments.

The period of oscillation for a pendulum is the time it takes for the pendulum to swing back and forth. Your goal is to determine if the period of a pendulum depends on how much mass is swinging back and forth. Your pendulum will be washers tied to the end of a string.

a) Tie a washer to the end of a string, and make a pendulum with a single washer.

Make the length of the pendulum around 50 cm.

b) Using the stopwatch, time how long it takes for the pendulum to swing back and

forth 10 times. Divide this time by 10 to find the period of the pendulum.

c) Repeat part b) using 2 washers, 3 washers, 4 washers and 5 washers. You can probably slip the extra washers over the string. Be sure that the pendulum is the same length for every measurement (around 50 cm).

d) Construct a table of your data:

__Number of washers__
__time for 10 oscillations__ __Period=time for __

__one oscillation __

1

2

3

4

5

e) Comment on what conclusions you can make about how the period depends on the hanging mass of the pendulum.

**III. Period of a Pendulum vs. length of pendulum**.

** Hypothesis**:

Your goal: Is the hypothesis true or false?

a) Measure the period of a pendulum for different lengths. To do this, tie 3 washers to the end of the string and measure the period for the following lengths: 20, 40, 60, 80, 100, 120, 140, and 160 cm. As done in the previous experiment, measure the period by timing 10 cycles and dividing by 10. Construct a data table: (see next page)

__Length
of Pendulum (cm)__ __time
for 10 oscillations__ __Period=time
for __

__one oscillation __

20

40

60

80

100

120

140

160

b) Comment on what conclusions you can make about how the period depends on the length of the pendulum.

Goal: Determine which shapes roll down an incline the fastest and slowest.

Prop up the board to make a slight incline. You should use all the shapes in the classroom: solid cylinder, ring, solid sphere, hollow sphere, ….

a) Which rolling object rolls the fastest?

b) Which rolling object rolls the slowest?

After you have determined the fastest and slowest, we will test your results with the rest of the class.

a) The instructor will show you how to make a simple helicopter from a piece of paper. You should design your helicopter so it falls as slow as possible.

b) Measure the times that it takes the helicopter to fall the following 4 distances: 200 cm, 150 cm, 100 cm, and 50 cm.

c) Construct a data table:

__distance (cm)__ __time__ __speed
(cm/s)__

50 ……

100 ……

150 …..

200 …..

d) Does the helicopter fall with constant speed or constant acceleration?

e) Find the average speed of your helicopter.

f) Write your answer on the board to see whose helicopter is the slowest.

a) Set up the teeter-totter so that it balances when no weights are on it.

b) Place 6 pennies at a distance of 30 cm from the fulcrum (center point).

c) Where should you place 9 pennies to balance out the 6 pennies?

Distance = ___________________________

d) Do the clockwise torques balance the clockwise torques? Show your calculation below:

clockwise torque =

counter-clockwise torque =

e) How much more does a quarter weigh than a penny? Show your work below:

Write your answer on the board

f) How much more volume does a quarter have than a penny?

g) Which coin has the greater density, the quarter or the penny?

**VII. Determining if a penny is pure copper by measuring
its density**.

a) Using a ruler, measure the diameter of a penny to the nearest mm, in units of cm. You can do this most accurately by placing 10 pennies side by side, measuring the total distance and dividing by 10.

b) Stack a large number of pennies (at least 15), and measure their height. Divide the height by the number of pennies to find the average thickness of one penny in cm.

c) Calculate the volume of one penny.

d) Determine the mass of a penny in grams by balancing a stack of 10 (or more) pennies with a known mass on the “teeter-totter”.

e) Divide the mass
of a penny by its volume to determine its density. The density of pure copper is 8.96 grams/cm^{3}. Is the penny pure copper?

Show your data and work here: