Download Informal Lab: Inertial Mass Balance Name ________________ Date

Informal Lab: Inertial Mass Balance
Name _________________ Date ______
Purpose: to build and calibrate an instrument that measures the inertia of an object
Materials: meter stick, clamp, known masses (100 g, 200 gram, stopwatch, unknown mass (ball)
Description of Apparatus:
An aluminum meter stick is clamped to a wooden block which is clamped to a table. When the meter stick is
pulled to the side it vibrates horizontally back and forth. We call this back and forth motion an “oscillation”.
A small cup is attached to the end of the meter stick to hold additional mass.
Diagram of Apparatus:
Collecting Data: Use a stopwatch (0.01 second precision) to time 20 bounces of the balance with various
amounts of known mass: 100 – 500 grams.Take three trials of each mass and calculate your average time to
0.01 second precision.
Background Information:
What is Mass? Mass has two basic properties: inertia and weight. Weight
is the gravitational pull an object experiences because it is on the Earth. Weight is a type of force, a vector,
and is always directed downwards, towards the center of the Earth. Weight is measured in metric units called
newtons (N).
The other basic property of mass is called “inertia”. Inertia is a scalar quantity; that is, it has no directional
property. Inertia is measured in mass units: grams or kilograms.
Inertia represents the tendency of an object to persist in its current state of motion. (to resist changes in
motion)
Newton’s First Law of Motion states that
“Objects at rest tend to remain at rest, and objects moving with a
constant velocity (in a straight line at constant speed) tend to remain moving at constant velocity unless acted
upon by an unbalanced net force.” Summarized in three words: “objects resist acceleration due to their
mass”.
Note that the first law does not say that objects resist motion, but rather that objects resist changes in motion,
or acceleration. We don’t know exactly why all objects have this property, but we call this property of matter
inertia.
Sometimes inertia is confused with friction, but these are two completely different concepts. Friction is a type
of force which opposes motion. Inertia is not a force, it is a basic property of matter which opposes changes in
motion, or acceleration.
The inertia of an object is the same value no matter where it is, and is independent of the strength of gravity.
Data:
Timings
Trial 1
Trial 2
Trial 3
average
< =================== MASS (grams)
==================>
0
100
200
300
400
500
UNKNOWN
Trial 1
Trial 2
Trial 3
average
% Error:
Actual mass of UNKNOWN = ________ grams ( +/- 0.1 gram)
Your estimated mass of Unknown = _______ grams
% error = ____________ %
% error = 100 x (your estimated value – true value) / (true value)
Show your calculations here:
Questions:
1. If you did the experiment on the Moon, where gravity is only 1/6th that on Earth, would the period of
oscillation for each known mass change? Yes / No
Explain your answer:
2.
Would your graph of MASS vs. TIME be any different on the Moon?________
Defend your answer:
3.
Would the derived mass for the pool ball be the same or be different on the Moon? Explain your answer in
detail.
4. How do you suppose NASA measures the mass of astronauts while they are in orbit in the Shuttle or
International Space Station? Astronauts can’t “weigh” themselves in the sense of standing on a scale because
weight has no meaning while in orbit (free fall around the Earth). Describe what equipment NASA would
need to measure an astronaut’s mass while in orbit. Research this on the web.
Lab Procedure: Use the check off list to do each step.
____With an empty can at the end of the meter stick, pull the meter stick to the side so that it oscillates a few
centimeters. Do not produce large wild oscillations.
____Time 20 bounces with a stopwatch to the nearest 0.01 second. Repeat 2 times. Record all data in a
table. Calculate the average of all three trials to 0.01 second precision. Repeat a measure if it looks “bad”
____Place 100 grams in the can and repeat the timings. Repeat for 200, 300, 400, and 500 grams (all known
masses).
____Place the “unknown” mass (ball) in the can, and repeat the timings two times, Record all the data into
your table.
____ Each person create a graph of the averages in Graphical Analysis on a computer.
____In the DATA Window, double-click on Y and fill in the dialog box.
Y axis will be the known MASS and the units are GRAMS.
____Double-click on the X in the DATA Window and fill in the dialog box.
X axis will be the TIME for 20 of oscillations, in SECONDS.
____Enter your data for known masses: 0, 100, 200, 300, 400, 500 grams.
Do not plot the unknown mass data (it’s mass is unknown at this time).
____Go to GRAPH options on the menu bar. Turn off “connect line” and turn on Point Protectors.
This will plot small circles for data points. Title your graph and put your names on it.
___Go to ANALYZE on the menu bar and select CURVE FIT. Use the automatic curve fit routine to
determine the best mathematical function to represent (model) your data. If the data look linear, then start
with a LINEAR FIT. If the data looks like a definite type of gentle curve, select QUADRATIC fit
A quadratic equation has the form: Y = aX2 + bX + c and the graph is a parabola.
___Go to FILE and then to PAGE SETUP. Print the graph and attach it to the lab.
Analysis Procedure: Use the check off list to do each step.
___ Estimate the mass of the unknown mass, based on your graph.
___Measure the actual mass of the UNKNOWN on a commercial balance (accurate to 0.1 gram) and then
calculate your percent error.
Actual mass of UNKNOWN = ________ grams ( +/- 0.1 gram)
___ Answer the questions.
Questions:
There are two major sources of error in using this instrument to measure mass:
1. measuring the period of oscillation accurately with your stopwatch
2. fitting a mathematical equation to best represent the timing data
Let’s look first at the timing errors.
Calculate the standard deviation (precision) of the time for 20 bounces with the unknown mass. You can do
this on your graphing calculator.
Time for 20 bounces for unknown mass = _____ seconds +/- ______ seconds (SD)
Recalculate the mass of the unknown based on your high estimate of timing
Average time plus standard deviation = _______ seconds
(show calculation for mass of unknown based on this higher estimate of time)
Recalculate the mass of the unknown based on your low estimate for time:
Average time minus standard deviation = ______ seconds
(show calculation for mass of unknown based on this time)
So the mass of the unknown is __________ grams +/- ___________ grams
based on the uncertainty of the timing data.
Uncertainty in the Model
How well does your mathematical model (equation) match the known data?
That is, how close is the line (or curve) to the known data points?
Does each data point touch the line or curve?
yes / no
Estimate how far the worst data point is from the curve = +/- _________ grams
Therefore, the ultimate precision of this instrument to measure mass is about
+/- _________ grams based on a margin of error in timings and the margin of error in the mathematical
“model” (curve fit).
Additional Question
If you did the experiment on the Moon, where gravity is only 1/6th that on Earth,
would the period of oscillation for each known mass change? Yes / No
Explain your answer:
Would your graph of MASS vs. TIME be any different on the Moon?
Defend your answer:
Would the derived mass for the pool ball be the same or be different on the Moon? Explain your answer in
detail.
How do you suppose NASA measures the mass of astronauts while they are in orbit in the Shuttle or
International Space Station? Astronauts can’t “weigh” themselves in the sense of standing on a scale because
weight has no meaning while in orbit (free fall around the Earth). Describe what equipment NASA would need
to measure an astronaut’s mass while in orbit. Research this on the web.
Calculate the mass of the unknown mass, in grams, and estimate its
uncertainty (margin of error).
Replace the variable X in your equation with the unknown mass’s timing.
Use the equation of best fit to calculate the mass of the unknown, in grams, to the nearest whole gram.
this calculation in detail here:
Show
Measure the mass of the UNKNOWN on a commercial balance (accurate to 0.1 gram) and then calculate
your percent error.
Actual mass of UNKNOWN = ________ grams
% error = ____________ %
% error = 100 x
Questions:
( +/- 0.1 gram)
show calculation below
(your value – true value) / (true value)
There are two major sources of error in using this instrument to measure mass:
1. measuring the period of oscillation accurately with your stopwatch
2. fitting a mathematical equation to best represent the timing data
Let’s look first at the timing errors.
Calculate the standard deviation (precision) of the time for 20 bounces with the unknown mass. You can do
this on your graphing calculator.
Time for 20 bounces for unknown mass = _____ seconds +/- ______ seconds (SD)
Recalculate the mass of the unknown based on your high estimate of timing
Average time plus standard deviation = _______ seconds
(show calculation for mass of unknown based on this higher estimate of time)
Recalculate the mass of the unknown based on your low estimate for time:
Average time minus standard deviation = ______ seconds
(show calculation for mass of unknown based on this time)
So the mass of the unknown is __________ grams +/- ___________ grams
based on the uncertainty of the timing data.
Uncertainty in the Model
How well does your mathematical model (equation) match the known data?
That is, how close is the line (or curve) to the known data points?
Does each data point touch the line or curve?
yes / no
Estimate how far the worst data point is from the curve = +/- _________ grams
Therefore, the ultimate precision of this instrument to measure mass is about
+/- _________ grams based on a margin of error in timings and the margin of error in the mathematical
“model” (curve fit).
Additional Question
If you did the experiment on the Moon, where gravity is only 1/6th that on Earth,
would the period of oscillation for each known mass change? Yes / No
Explain your answer:
Would your graph of MASS vs. TIME be any different on the Moon?
Defend your answer:
Would the derived mass for the pool ball be the same or be different on the Moon? Explain your answer in
detail.
How do you suppose NASA measures the mass of astronauts while they are in orbit in the Shuttle or
International Space Station? Astronauts can’t “weigh” themselves in the sense of standing on a scale because
weight has no meaning while in orbit (free fall around the Earth). Describe what equipment NASA would need
to measure an astronaut’s mass while in orbit. Research this on the web.