Vers. 1.2 2011/11/08
Experimental Science
P6: Indirect measurement of physical quantities
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1. Purpose
•
Indirect measurement of physical quantities: volume, specific mass and density.
•
Specific mass measurement of various substances by 3 different methods.
•
Measurement of a student’s hand mass.
2. Introduction
The specific mass,
ρ, is a physical quantity that is characteristic for each substance
and is defined as the mass, m, that that substance contains in a unit volume, V:
ρ=
m
V
The derivation of a specific mass requires therefore the measurement of mass and
volume.
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Specific density should not be confused with density. In fact, density (d) is an
dimensionless physical quantity. It compares the substance’s specific mass to that of
water:
d=
ρsubstância
ρH 2O
3. Experimental activity
3.1 Material
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Graduated cylinder (50 or 100 ml), calliper, 3 scales, water, cylinder, sphere and a 4
cylinders set made of the same material and different volumes.
3.2 Experiment plan
Our aim is to determine experimentally the specific mass of 3 different substances by 3
distinct methods.
The first 2 methods will be applied to a sphere and a cylinder. The third method will be
applied to the 4 cylinders set.
In all methods it is necessary to measure the mass and volume of the object.
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The object’s mass is measured indirectly from its weight. The measurements are made
using scales. A scale has a sensor that deforms proportionally with the object’s weight, P.
This weight is directly proportional to the object’s mass, m. That is, P = mg, where g is the
earth’s gravitational acceleration.
Sometimes it is difficult to immobilize an object at the scale’s plate centre. On such
cases a second stabilizing object should be used (e.g., a recipient, a washer). Before
starting the measurement you must tare the scale. This means to adjust the device’s zero
so that it has a zero reading when subject only to the stabilizer’s weight. In order to do so,
just push the tare/zero button. The device’s zero should be checked always before and
after a measurement.
The volume measurements will depend on the method. In one method the volume is
estimated from the fluid displacement when the object is submerged. In the other two
methods the volumes are derived from object’s dimensions.
3.3 Procedure
Organize your data into tables. These tables should contain each measurement’s error
as well as the corresponding units.
Method 1:
a) Mass measurement
Measure the sphere’s mass with the 10 g-1 resolution scale.
b) Volume measurement
Fill the graduated cylinder half way with tap water. Record the water’s initial volume
while the cylinder is placed on a horizontal surface. Avoid the parallax error. Due to the
water meniscus’s curvature use the maximum device error written on the cylinder (instead
of half of the smallest division).
Place the object into the cylinder so that it becomes totally submerged. Record the
observed volume in the graduated cylinder. The increase in volume is solely due to the
object’s volume.
At the end of the measurements you should have a table with the following header:
m (g)
V1 (cm3)
V2 (cm3)
where m is the object’s mass, V1 is the initial liquid volume inside the graduated cylinder
and V2 is the final volume measured with a totally submerged object.
Repeat method 1 for the cylinder with just one modification: instead of the 10 g-1
resolution scale use the smallest resolution scale (1 g-1).
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Method 2:
a) Mass measurement
Measure the sphere’s mass with the 103 g-1 resolution scale.
b) Volume measurement
Use a calliper (and/or a micrometer) to measure the sphere length(s) needed to
calculate its volume.
At the end of the measurements you should have a table with the following header:
m (g)
D (cm)
where the sphere’s mass is m and diameter is D.
Repeat method 2 for the cylinder.
At the end of the measurements you should have a table with the following header:
m (g)
D (cm)
h (cm)
where the cylinder’s mass is m, diameter is D and height is h.
Method 3:
a) Mass measurement
Measure the mass of each of the cylinders from the 4 cylinder set using a scale with a
resolution higher than 1 g-1.
b) Volume measurement
Use a calliper (and/or a micrometer) to measure the cylinder length(s) needed to
calculate its volume.
At the end of the measurements you should have a table with the following header:
m (g)
D (cm)
h (cm)
where the cylinder’s mass is m, diameter is D and height is h.
Extra activities:
a) Propose a method to measure the specific mass of water. Perform the necessary
measurements.
What is the water’s specific mass standard value at room temperature?
b) Propose a method to measure your hand’s mass (volume from the radio-carpal joint
to the distal extremity).
The joint line will be defined placing a rubber band around your wrist just touching the
radius distal extremity and the ulna’s styloid process.
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Before the actual measurement perform the mental exercise of estimating the volume
of your hand. (e.g. is it bigger than ¼ of a litre? ½ litre?).
Let’s say your estimate was 300 cm3. Your indirect mass measurement could be, for
instance:
m = ρV = 1
g
× 300 cm3 = 300 g
3
cm
General recommendations:
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a) A review about the measurement devices used in the first class will be useful.
b) ALL measurements should be repeated; Repetition will tell you if the physical
quantity variation is resolvable.
c) Always ask yourself if the measured value MAKES SENSE. Using the natural units
will therefore be very useful (e.g. cm3 instead of m3).
d) Whenever possible choose the HIGHEST RESOLUTION available device.
e) Avoid as much as possible object handling (your hands temperature may alter the
results).
f)
Always check the scales’ zero and measure at the centre of the plate (use a ring to
hold a sphere).
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