Thickness of a paper - thickness of an Aluminum foil - volume of your hand
distance to the moon - height of a tree
INTRODUCTION: Very
often, in Science you can not directly measure a distance because
it is too small (thickness of a paper, size of an atomic nucleus, size
of a molecule)
or too large ( distance across our galaxy, size of the universe or just the radius of the Earth). No way you can use a meter tape or a ruler.
Some mass are also too small to measure (mass of a sand grain, mass of an electron, mass of a boulder) and you can't use a scale.
It is easy to find the volume of a cube but what about the volume of your hand ?
Physicists have found indirect ways to measure physical quantities like distance, volume, mass, speed, wavelength, energy ..
In these labs you will investigate some of simple methods to perform indirect measurements.
PART1: THICKNESS OF A PAPER - indirect measurement of distance
procedure . get a ram of 500 paper.
1) Get a ram of copy machine papers. A ram has 500 sheets. Each of you should measure the thickness of the pack.
Each partner should try so you have at least 4 measurements of the thickness. Find the average. call it Haverage.
you need 2 decimals.
H1 = ___________cm H2 = ____________cm H3 = ___________cm H4 = ______________cm Haverage = __________cm
2) You have the thickness of 500 sheets. Can you find the thickness of 1 sheet ? h = _________ cm = ________ mm
(hint: 1cm = 10mm)
PART 2: THICKNESS OF AN ALUMINUM FOIL - indirect measurement of distance
An aluminum foil is really thin. Here is a way to find the thickness of a foil.
The density of aluminum is about d = 2.7 g/cm3. (2.7g per cubic meters). That means, a cube of volume 1 cm3 has a mass of ____ g.
1) Cut a piece of piece of an aluminum foil 10cm by 10 cm. !!!! It has to be exactly 10cm. Use a ruler in cm and scissors.
So make sure the edge matches the zero and that you are not using the inches side of your ruler.
Be neat. Start over if you mess up. You can trace your square with a pen before cutting it.
so width = W = _______ cm and length = L = ________ cm. So Area = ______ cm2.
2) Use a sensitive scale and scale your piece to the nearest 0.01g. You can fold the foil. m = ________ g
(keep as much decimals as possible)
3) Le'ts find the thickness or height H of the foil. Think of the piece of aluminum as a box of height H, width 10cm and length 10cm.
First find the volume of the piece using its mass and its density. V = ________ cm3
hint: you know that 2.7g has a volume of 1 cm3. To find the volume of your piece of mass m, solve the proportion. (divide the mass m by 2.7)
4) You have the volume of your piece. (how much space it takes). You know that volume = width x lengthx height with width = length = 10cm.
Find its height in cm (thickness). H = _____ cm = ________ mm = ______ micrometer
(1000 micrometers = 1 mm)
hint: Volume = H x W x L = H x 10 x 10. so V = H x 100. You have V and you are solving for H)
5) How would you find the thickness of a penny ?
6) How would you find the mass of a grain of sand. (say you can get a handful of grains)
PART3: Volume of your hand - indirect measurement of volume - displacement of water.
1) Each one of you ,should measure the volume of her/his hand.
Find a large beaker (500ml) and a larger container that will collect the water that spills out from the beaker.
Fill the beaker with water until the water pours from the sprout. Once the water has stopped dripping, Carefully,
without spilling any water, place the beaker in the larger container. Carefully, submerge your hand to the wrist and wait until the displaced
water flows into the container. The amount of water in the collection container represent the volume of your hand.
Find this volume V1 = _________ ml = _____ cm3 (1ml = cm3). You can use a graduated cylinder to find the volume
Repeat 3 times, making certain your hand is submerged to the same depth each time.
V2= ________cm3 V3 = _________ cm3 . What is the average value of the volume of your hand ? V = ______ cm3
Who has the larger volume in your group ______________ the smallest in your group __________
the largest in the class _______________ the smallest in the class ____________-
2) How can you find the volume of a wrench ?
PART4: Find the distance between the Moon and the Earth, knowing the diameter of the Moon.
1) READ:
The idea is to use a technique that will allow you to find the distance between you and a fake moon (L2) knowing:
the diameter of a black board marker (D1) , the diameter of the moon (D2), the distance between your eye and the pen (L1):
You will use the formula for similar triangles. (see Annex).D2/D1 = L2/L1 you are solving for L2.
2) Get a large marker (like the white board marker) and find its diameter (distance across) D1 = _______ mm
3) With a compass cut out a large paper moon. (a circle). You can make a 20cm radius moon. (diameter = 40cm)
Find its diameter D2 = ______cm = ______mm. Write Moon on it and tape it on a wall. At about the same height as your eyes.
Move away, across the room. you are going to find the distance between you and your moon indirectly. (like for the real moon).
With a tape, mark your position. Stand in front of the moon, but far away. (around 4 meters)
4) Hold one end of a meter stick carefully alongside your eye with the end in approximately the same plane as your retina.
of your eye. Place a cylindrical pen next to the side of the stick. See image.
Now push the pen away from your eye until the diameter of the pen just blocks your view of the moon.
Measure the distance from your eye in millimeters. L1 = _________mm
Now using your knowledge of similar triangles (see annex at the end of this lab and hint), find the distance between you and the moon.
L2 = ______ mm = ________ m (1m = 1000mm)
(hint: use formula above solve for L2)
5) Check how good you are, by measuring directly the distance between you and the wall in meters. Using a meter stick.
true L2 = _________m . Were you close ?
6) Let's find the % error = _______ %
hint: %error = ( true value L2 - calculated value L2) / true value x 100
7) You can find the height of a tree , the same way. That time the height is unknown but the distance to the tree is known.
PART5: Height of a tree using the shadows. You need chalks, meter tape and a SUNNY DAY.
1) With your team, get some tapes, meter stick, string, chalk, the lab. Go outside on a Sunny day.
2) Find a pole or a tree on a flat ground with a nice , visible shadow. You have to be quick because the Sun moves.
Decide who will measure distances, who will collect the data in the tABLE and who will have her/his shadow recorded.
3)Measure the length of the tree's shadow. You can use the string. (Someone hold the string at the base of the tree to the tip of the shadow). Then use your meter stick to find the length.
Units are in meters. Record in the TABLE
4) Quick. Measure the the length of the person shadow.
5) Back in the lab find the height of the person. She or he should stay against a wall. Record in the TABLE.
6)Find the height of the tree using similar triangles 's rule. Use the image below to help you.
shadow2/shadow1 = X/H
(same ratios between the sides of the similar triangles )
Plug the numbers into the equation and solve for X. X = ______________
Does this number makes sense ?
ANNEX:
their sides are proportional. This means that every side of one triangle will be in a fixed ratio with the corresponding side of the other triangle.
a/b = d/e or a/d = b/ e
learn more about similar triangles
GOING FURTHER
1) The tips of the tree's shadow and of Susie shadow match. Find the height of the tree.
2) Let's say you know the radius of the moon. (1738 km).
A) Convert the radius to cm R = _________ cm. (hint: 1 km = 1000m and 1 m = 100cm)
B) Suppose the moon is a sphere. Find its volume in cm3. Vbig = ____________cm3
hint: volume sphere = 4/3 (3.14) R3. 3.14 is an approximation of the number PI
C) Let's say you want to indirectly measure the mass of the Moon.
You have a moon rock brought back by the Astronauts from the Apollo mission.
Using a spring scale you find the mass of the rock to be m = 33.3 g
Then you find the volume of the rock by finding the volume of water displaced when the rock is placed in a beaker.
you find Vsmall= 10cm3
Suppose you have the equality: small mass/ small volume = large mass / large volume/ or m / Vsmall = M / V big.
This is true if you suppose the moon to be rocky and homogeneous. (the same material every where, same density)
m is the mass of the rock in grams
Vsmall is the volume of the moon rock in cm3
M is the mass of the moon, the unknown in grams.
Vbig is the volume of the moon in cm3
Solve for M in grams M = _______________________ grams (standard notation) = __________g (scientific notation)
= ____________________ kg (scientific notation divide by 1000 )
Check with wikipedia or other source if this number makes sense.
or too large ( distance across our galaxy, size of the universe or just the radius of the Earth). No way you can use a meter tape or a ruler.
Some mass are also too small to measure (mass of a sand grain, mass of an electron, mass of a boulder) and you can't use a scale.
It is easy to find the volume of a cube but what about the volume of your hand ?
Physicists have found indirect ways to measure physical quantities like distance, volume, mass, speed, wavelength, energy ..
In these labs you will investigate some of simple methods to perform indirect measurements.
PART1: THICKNESS OF A PAPER - indirect measurement of distance
procedure . get a ram of 500 paper.
1) Get a ram of copy machine papers. A ram has 500 sheets. Each of you should measure the thickness of the pack.
Each partner should try so you have at least 4 measurements of the thickness. Find the average. call it Haverage.
you need 2 decimals.
H1 = ___________cm H2 = ____________cm H3 = ___________cm H4 = ______________cm Haverage = __________cm
2) You have the thickness of 500 sheets. Can you find the thickness of 1 sheet ? h = _________ cm = ________ mm
(hint: 1cm = 10mm)
PART 2: THICKNESS OF AN ALUMINUM FOIL - indirect measurement of distance
An aluminum foil is really thin. Here is a way to find the thickness of a foil.
The density of aluminum is about d = 2.7 g/cm3. (2.7g per cubic meters). That means, a cube of volume 1 cm3 has a mass of ____ g.
1) Cut a piece of piece of an aluminum foil 10cm by 10 cm. !!!! It has to be exactly 10cm. Use a ruler in cm and scissors.
So make sure the edge matches the zero and that you are not using the inches side of your ruler.
Be neat. Start over if you mess up. You can trace your square with a pen before cutting it.
so width = W = _______ cm and length = L = ________ cm. So Area = ______ cm2.
2) Use a sensitive scale and scale your piece to the nearest 0.01g. You can fold the foil. m = ________ g
(keep as much decimals as possible)
3) Le'ts find the thickness or height H of the foil. Think of the piece of aluminum as a box of height H, width 10cm and length 10cm.
First find the volume of the piece using its mass and its density. V = ________ cm3
hint: you know that 2.7g has a volume of 1 cm3. To find the volume of your piece of mass m, solve the proportion. (divide the mass m by 2.7)
4) You have the volume of your piece. (how much space it takes). You know that volume = width x lengthx height with width = length = 10cm.
Find its height in cm (thickness). H = _____ cm = ________ mm = ______ micrometer
(1000 micrometers = 1 mm)
hint: Volume = H x W x L = H x 10 x 10. so V = H x 100. You have V and you are solving for H)
5) How would you find the thickness of a penny ?
6) How would you find the mass of a grain of sand. (say you can get a handful of grains)
PART3: Volume of your hand - indirect measurement of volume - displacement of water.
1) Each one of you ,should measure the volume of her/his hand.
Find a large beaker (500ml) and a larger container that will collect the water that spills out from the beaker.
Fill the beaker with water until the water pours from the sprout. Once the water has stopped dripping, Carefully,
without spilling any water, place the beaker in the larger container. Carefully, submerge your hand to the wrist and wait until the displaced
water flows into the container. The amount of water in the collection container represent the volume of your hand.
Find this volume V1 = _________ ml = _____ cm3 (1ml = cm3). You can use a graduated cylinder to find the volume
Repeat 3 times, making certain your hand is submerged to the same depth each time.
V2= ________cm3 V3 = _________ cm3 . What is the average value of the volume of your hand ? V = ______ cm3
Who has the larger volume in your group ______________ the smallest in your group __________
the largest in the class _______________ the smallest in the class ____________-
2) How can you find the volume of a wrench ?
PART4: Find the distance between the Moon and the Earth, knowing the diameter of the Moon.
1) READ:
The idea is to use a technique that will allow you to find the distance between you and a fake moon (L2) knowing:
the diameter of a black board marker (D1) , the diameter of the moon (D2), the distance between your eye and the pen (L1):
You will use the formula for similar triangles. (see Annex).D2/D1 = L2/L1 you are solving for L2.
2) Get a large marker (like the white board marker) and find its diameter (distance across) D1 = _______ mm
3) With a compass cut out a large paper moon. (a circle). You can make a 20cm radius moon. (diameter = 40cm)
Find its diameter D2 = ______cm = ______mm. Write Moon on it and tape it on a wall. At about the same height as your eyes.
Move away, across the room. you are going to find the distance between you and your moon indirectly. (like for the real moon).
With a tape, mark your position. Stand in front of the moon, but far away. (around 4 meters)
4) Hold one end of a meter stick carefully alongside your eye with the end in approximately the same plane as your retina.
of your eye. Place a cylindrical pen next to the side of the stick. See image.
Now push the pen away from your eye until the diameter of the pen just blocks your view of the moon.
Measure the distance from your eye in millimeters. L1 = _________mm
Now using your knowledge of similar triangles (see annex at the end of this lab and hint), find the distance between you and the moon.
L2 = ______ mm = ________ m (1m = 1000mm)
(hint: use formula above solve for L2)
5) Check how good you are, by measuring directly the distance between you and the wall in meters. Using a meter stick.
true L2 = _________m . Were you close ?
6) Let's find the % error = _______ %
hint: %error = ( true value L2 - calculated value L2) / true value x 100
7) You can find the height of a tree , the same way. That time the height is unknown but the distance to the tree is known.
PART5: Height of a tree using the shadows. You need chalks, meter tape and a SUNNY DAY.
1) With your team, get some tapes, meter stick, string, chalk, the lab. Go outside on a Sunny day.
2) Find a pole or a tree on a flat ground with a nice , visible shadow. You have to be quick because the Sun moves.
Decide who will measure distances, who will collect the data in the tABLE and who will have her/his shadow recorded.
3)Measure the length of the tree's shadow. You can use the string. (Someone hold the string at the base of the tree to the tip of the shadow). Then use your meter stick to find the length.
Units are in meters. Record in the TABLE
4) Quick. Measure the the length of the person shadow.
| shadow2= shadow of the tree (meters) | shadow1 = shadow of the person (meters) | H = height of the person (meters) | X = height of the tree (meters) X= (shadow2/shadow1) x H |
5) Back in the lab find the height of the person. She or he should stay against a wall. Record in the TABLE.
6)Find the height of the tree using similar triangles 's rule. Use the image below to help you.
shadow2/shadow1 = X/H
(same ratios between the sides of the similar triangles )
Plug the numbers into the equation and solve for X. X = ______________
Does this number makes sense ?
ANNEX:
their sides are proportional. This means that every side of one triangle will be in a fixed ratio with the corresponding side of the other triangle.
a/b = d/e or a/d = b/ e
learn more about similar triangles
GOING FURTHER
1) The tips of the tree's shadow and of Susie shadow match. Find the height of the tree.
2) Let's say you know the radius of the moon. (1738 km).
A) Convert the radius to cm R = _________ cm. (hint: 1 km = 1000m and 1 m = 100cm)
B) Suppose the moon is a sphere. Find its volume in cm3. Vbig = ____________cm3
hint: volume sphere = 4/3 (3.14) R3. 3.14 is an approximation of the number PI
C) Let's say you want to indirectly measure the mass of the Moon.
You have a moon rock brought back by the Astronauts from the Apollo mission.
Using a spring scale you find the mass of the rock to be m = 33.3 g
Then you find the volume of the rock by finding the volume of water displaced when the rock is placed in a beaker.
you find Vsmall= 10cm3
Suppose you have the equality: small mass/ small volume = large mass / large volume/ or m / Vsmall = M / V big.
This is true if you suppose the moon to be rocky and homogeneous. (the same material every where, same density)
m is the mass of the rock in grams
Vsmall is the volume of the moon rock in cm3
M is the mass of the moon, the unknown in grams.
Vbig is the volume of the moon in cm3
Solve for M in grams M = _______________________ grams (standard notation) = __________g (scientific notation)
= ____________________ kg (scientific notation divide by 1000 )
Check with wikipedia or other source if this number makes sense.