School Science Lessons
Physics - Mass and weight, matter, centre of gravity
Updated: 2008-07-21
Please send comments to: J.Elfick@uq.edu.au
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Table of contents
4.145.0
Balances
8.2.0 Centre of gravity
8.3.0 Gravity
8.4.0 Inertia
10.1.0 Diffusion, particles of
matter, Brownian movement
8.2.0 Centre of
gravity
8.2.1 Centre of gravity of an irregular shaped
object
8.2.2 Balancing pins, centre of gravity and
stability
of an object
8.2.3 Centre of gravity and stability of an object
8.2.4 Centre of gravity of a double cone, uphill
roller, circular cone with two heads on a ramp
8.2.5 Centre of gravity of a shape, wobbling
circles
8.2.6 Centre of gravity of man and woman
8.2.7
Statics of rigid bodies, finding centre
of gravity
8.2.9 Centre of gravity of maps
8.2.10 Centre of mass of biased bowls
8.2.11 Centre of gravity of pine trees
2.2.1 Centre of gravity outside an
object, U-shape cardboard
8.2.12 Hidden centre of gravity, weight under
false bottom
4.146
Balance with a metre stick, metre ruler, metre stick on fingers
8.2.8.0 Statics of rigid bodies, exceeding
centre
of gravity
8.2.15 Tipping bottle
8.2.9.0 Stable, unstable and neutral equilibrium
8.2.13 Hanging belt
8.2.14 Shared centre of gravity, brace
8.2.16 Balancing H-shape
8.2.17 Centre of gravity of playing dice
8.2.18 Shape of a hanging cable or flexible
chain, catenary curve
9.2.3 Roll-back jar, come back can
1.21 Balanced mobile (primary)
3.17 Make a plumb bob (primary)
8.3.0 Gravity
4.147
Ball bearings fall together
4.148 Acceleration of marbles down
an incline
4.149 Simple pendulum
4.150 Coupled pendulums
4.151 Time a falling body
4.152 Paths of projectiles, free
fall
4.153 Three-holes can
4.154 Falling washers on a
string
2.239.3
Foucault pendulum
14.2.13
Path of a projectile,
mid-air target, monkey and hunter
4.105
Weightlessness
4.106 Satellite launcher
4.107 Weight of a falling chain
4.108 Ball projected upwards from a cart
4.109 Velocity of an arrow
1.41 Falling parachutes (Primary)
3.22 Throw up and fall down (Primary)
8.4.0 Inertia
4.155 Inertia with a stone
4.156 Inertia with two drink-can
pendulums
4.157 Inertia tricks
4.13 Inertia tricks (Primary)
8.1.0 Mass, balances
Weighing devices,
inertial
balance to measure mass, linked spring balances, force meter, top
loading
balance, compression balance, kitchen scale, bathroom scale
Mass is the quantity of matter in an object as measured by its inertia.
Mass determines the acceleration produced in an object by a given force
acting on it, the acceleration being inversely proportional to the mass
of the object. The mass also determines the force exerted on an object
by gravity on Earth, although this attraction varies slightly from
place
to place. In the SI system, the base unit of mass is the kilogram. You
call
the force of gravity acting on an object weight. A spring balance
supporting
an object measures this invisible force. At a given place, equal masses
experience equal gravitational forces. You can compare the mass of
objects
by comparing the weight of objects at the same place. A platinum
iridium
cylinder of one kilogram is the standard unit of mass to which you can
compare
all other masses.
8.1.1 Letter scale
Use adhesive tape to attach a heavy coin to the top right hand corner
of a picture post card. Punch a hole in the bottom left hand corner of
the post card and insert a wire paper clip through the hole. Attach a
second
paper clip to the first paper clip. Push a thick pin or nail through
the
top left hand corner of the post card. Push the pin into a vertical
board
and let the post card hand down from the pin as pivot. Hang a letter
with
exact weight, e.g. 50 g, from the second paper clip and then mark the
position
of the top right hand corner of the post card on the wall. Use a second
letter of exact weight to make a second mark on the wall. Now you can
weigh
letters and decide what stamps to stick on them. This letter scale is a
first order lever. The left hand edge of the post card is the load arm.
The pin is the fulcrum. The upper edge of the post card is the force
arm,
effort arm. The letter scale measures small differences in weight
because
the force arm is longer than the effort arm.
8.2.0 Centre of gravity
Centre of gravity of
geometric
shapes
Gravity and centre of gravity, statics of rigid bodies, finding centre
of gravity and exceeding centre of gravity
Centre of gravity, centre of mass, is the point in or near an object
from which its total weight, or mass, appears to originate and act. The
gravitational force acted on an object by earth goes through a point,
called
the centre of gravity of the object. If the pulling force or supporting
force acted on an object goes through the centre of gravity and are
equal
to gravitational force in size, the object will be in equilibrium. The
centre of gravity of an object is the point around which all its mass
is
balanced. For a regularly shaped object made of homogeneous material,
the
centre of gravity is at its geometrical centre. A symmetrical
homogeneous
object such as a sphere or cube has its centre of mass at its physical
centre. A hollow shape, such as a cup, may have its centre of mass in
space
inside the hollow. In a uniform gravitational field, centre of gravity
and centre of mass are in the same place.
8.2.1 Centre of gravity of an irregular shaped
object
See diagram 8.2.1
Draw an irregular picture on cardboard, e.g. a potato. Cut out the
picture with scissors. Punch 3 small holes at the edge of the cardboard
shape such that the distances between holes are about the same. Pass a
thread through one hole and tie it. Suspend the cardboard shape by
lifting
the thread. The centre of gravity must be directly below the point of
suspension.
When the cardboard shape stops moving put the edge of a ruler on the
thread
and slide the ruler over the cardboard shape vertically down along the
direction of the thread. Hold the ruler and cardboard shape together
tightly
with your fingers, lay them on the table and draw a straight line on
the
cardboard shape with the ruler. Untie the thread, tie it in other holes
and repeat as above until you have drawn 3 lines on the card. The 3
lines
intersect at the centre of gravity of the cardboard shape. Test that
the
point is the centre of gravity, by supporting the cardboard shape with
the end of sharpened pencil below the point. The cardboard shape will
remain
in equilibrium.
8.2.2 Balancing pins, centre of gravity and
stability
of an object
See diagram 8.2.2
Put a large cork stopper on the table with the larger area down. Hold
a long plastic knitting needle vertically over the centre of the
smaller
area of the cork then push the pointed end down through the centre of
the
cork. Cut off the head of the knitting needle and insert the cut end
into
a Styrofoam ball. Push two other plastic knitting needles through the
holes
of 1-hole rubber stoppers so that the stoppers reach the heads of the
knitting
needles. Insert the pointed ends of these knitting needles into each
side
of the cork Place the end of the knitting needle pushed through
the
cork on any convex point and the system remains balanced about the
convex
point pivot. If you move the rubber stoppers up the knitting needles,
the
system becomes less stable because the centre of gravity of the system
approaches the level of the pivot. By slanting the knitting
needles
with the rubber stoppers pushed down, the centre of gravity of the
system
is lowered below the pivot, and the stability of the system is
increased.
The bottom of a racing car is as low as possible to obtain the lowest
possible
centre of gravity and prevent the racing car rolling over during a
turn.
8.2.3 Centre of gravity and stability of an
object
Every object has a centre of gravity. The centre of gravity does not
change if the distribution of mass in an object does not change. An
object
in
water is acted on by water buoyancy due to the displacement of the
weight
of water. Buoyancy also has its own centre of action, called the centre
of buoyancy, determined by the mass of water displaced by the object.
The
shape of the displaced water determines the position of the centre of
buoyancy,
if the density of water is constant. The centre of gravity may not be
in
the same position as the centre of buoyancy. Only when the two
positions
are under a certain condition can the object maintains a stable
equilibrium
state. If the state of the object changes, the stability of equilibrium
of the object is lost.
8.2.4 Centre of gravity of a double cone,
uphill
roller, circular cone with two heads, ramp
See diagram 8.2.4
1. As a double cone moves up an set of inclined rails its centre of
gravity lowers. The double cone appears to roll uphill. A double cone
rolls
up an inclined track. Make a circular cone with two heads: (a) Tape
together
two plastic funnels at their mouths with a smooth connection. (b) Cut
out
two identical equilateral triangles from cardboard with one side in the
shape of an arc. Roll the triangles, beginning at a straight side, then
tape together the straight sides to form two circular cones. Rub smooth
the bottom of each cone and tape them together.
2. Make a ramp: (a) Cut out a long narrow strip of cardboard and
fold in half to make a V-shape. Cut cardboard in rectangle shape and
tape
it to the V-shape to make a ramp. (b) Use two rulers leaning on a book
or use two drinking straws.
3. Put the cones on a lower end of the cardboard ramp. If the
surfaces
of the cone and ramp are smooth the cone rolls up along the ramp.
4. Adjust the upper distance between two rulers or straws to make
the cone roll up or down the ramp. Hold the upper ends of the rulers or
straws to first make the distance between them small then move them
apart
until the cone begins to roll upward. Before the cone arrives at the
top
of the ramp decrease the distance between the two ends of the rulers or
straws to make the cone roll down. Measure the height of the top of the
cone before and after the rolling. The top of the cone after rolling is
lower than the height before the rolling. The cone is symmetrical so
its
centre of gravity is on the line the connecting of the two tops, so the
height of the tops is the height of the centre of gravity of the cone.
When the bottom of the ramp is narrower, the cone at the lower place of
the ramp has a higher centre of gravity. While the cone rolls up to the
top of the ramp due to the wider width of the top, the centre of
gravity
of the cone is lower. Thus the centre of gravity of the cone is higher
at bottom, the centre of gravity of the cone is lower at the top, so
the
cone does not roll upward but downward.
5. An object in the shape of a cylinder cannot roll up itself on such
a ramp, because its centre of gravity will rise.
6. Repeat the experiment with a ball. Put a ball with a suitable
size on the ramp. It can roll up itself and the speed of rolling is
faster
than the speed of a cone.
8.2.5 Centre of gravity
of a shape, wobbling
circles
See diagram 8.2.5
All flying objects spin around their centre of gravity. Cut cardboard
into a kidney shape. Support it on your finger to let it balance and
find
its centre of gravity then mark the centre of gravity of it by a
pencil.
Draw concentric circles around the centre of gravity on one surface of
the cardboard, called A surface, by a compass and thicken the circles
with
the marker. Draw the same concentric circles on other side of the
surface,
B surfaces, but around a spot about 3 cm away from the centre of
gravity.
All you have done above is in the condition without having the students
observation. Let the A surface of the card face to the students, hold
the
edge of it by your fingers, throw it by using wrist action to make it
spin
vertically in the air. Catch it when it comes down. Then reverse it to
make the B surface face to the students, throw it again. What are the
circles
on the card like as the card flies in the air? The situations of the
spinning
on two sides of the card are different. The circles are steady in the
first
spin and wobbling in the second. All objects spin around their centre
of
gravity. On the A side of the cardboard the concentric circles are
around
the centre of gravity, so they stay steady as they spin. When you see
the
other side B, the circles wobble, because it is off the centre of
gravity
and the circles spin around a point outside the centre of gravity
making
a wobbling motion.
8.2.6 Centre of gravity of man and woman
See diagram 8.2.6
1. Stand with right shoulder and foot against the wall and raise your
left foot. Stand with your heels against the floor and try to touch
your
toes.
2. Understand the difference between the centres of gravity of a
woman and a man due to the different shapes of their bodies. Draw a
line
parallel to the base line of a wall, the distance between lines equal
to
twice the length of the schoolboy's shoe. The schoolboy stands upright
behind the line, bends forming 90o with his legs so that
his
head touches on the wall. Other one carries a chair with a vertical
back
and push the chair's back against the wall, under the schoolboy's top
half.
The schoolboy holds the chair with his hands and tries to make his
waist
straight. You will find he cannot do it. A schoolgirl does the above
experiment.
You will find she can make her waist straight then stand upright again.
Is a schoolgirl stranger than a schoolboy? At fact the result of this
experiment
has nothing to do with a person's strength but has something to do with
the position of the centre of gravity and the length of the shoe. The
rump
of a schoolgirl is wider and her shoulder is narrower usually so her
centre
of gravity is at her rump. The centre of gravity of a schoolboy,
however,
with narrower rump and wider shoulder is above his rump. Leonardo Da
Vinci
finished the first research on the position of the centre of gravity of
human body. He thought the above reasons caused the difference between
the positions of the centre of gravity of a woman and a man. In
addition
the shoe of a schoolboy is longer than that of a schoolgirl usually. So
he stands farther from the wall. When he bends his waist into 90o,
his centre of gravity is moved at the middle of his feet and the wall
thus
it is very difficult for him to try to stand upright again. Yet doing
it
is easy for a woman because her centre of gravity is above her feet.
8.2.7
Statics of rigid bodies, finding centre
of gravity
1. Find centre of gravity with a plumb bob. Use a chalk line on the
plumb bob and snap it to make a quick vertical line. Suspend various
regular
shapes and an irregular board from several points and use a plumb bob
to
find the centre of gravity.
2. Hang a potato from several positions and stick a pin in at the
bottom in each case so that all pins point to the centre of gravity.
3. Place a block on an incline and raise the incline until the block
tips.
8.2.8 Centre
of gravity outside an object, U-shape cardboard
See diagram 4.2.1 | See
also 8.2.1
To verify the existence of a centre
of
gravity not on the object, lay a U-shape magnet on a piece of
cardboard, then draw along
the
boundary between magnet and cardboard to make an U-shape picture. Cut
off
this U-shape cardboard. Draw two vertical lines used to hang the
cardboard. Define two points in two
ends of each thread, up and down AA' and BB', punch four holes at these
four points. Thread through A and make a knot. The other end of the
thread
goes through A', around back under the cardboard, and meets again with
thread in A'. Tie them together. Fix another thread at BB' with the
same
operation. Make each thread as tight as possible. Pick up the cross
point
of two threads with tweezers, the U-shape cardboard will maintain
horizontally
in the air. This shows that the point is its
centre
of gravity. Punch another hole at the C point besides the A' (or B').
Untie
A' (or B') and move to C, tie it. Pick up the new cross point of two
threads
with tweezers. You cannot balance the U-shape cardboard.
8.2.8.0 Statics of rigid bodies,
exceeding centre of gravity
1. Stack blocks until the top block sticks out beyond any part of
the bottom block
8.2.9 Centre of gravity of
maps
1. Suspend a map of the state from holes drilled at large cities to
find the centre of gravity of the state.
2. Draw a map of China or your country on another piece of cardboard.
Cut it out. Find the centre of gravity by the same method above.
Thus,
you will find "centre of gravity" of China.
8.2.9.0 Stable, unstable and neutral
equilibrium
1. A thin block on a cylinder is stable, a thick block is not.
2. Stick two forks and a match together and balance on a glass while
pouring out the water.
3. Balance ten landscape spikes on the head of a single upright
spike.
4. Hang a giant food service spoon with
curved handle end on your
nose.
5. Toy horse has an attached weight to lower the centre of mass as
an example of a stable equilibrium of a centre of gravity object.
6. A tightrope walking toy unicycle rider carrying a balancing pole
travels along a string. A model of a tightrope walker shows the centre
of mass moves up with tipping.
7. Wires form a support at the centre of gravity of a laboratory
stool. Construct a stool so that wires crossed diagonally will
intersect
at the centre of gravity. The stool can be oriented in any direction.
8. Hide heavy weights in the ends of a stool's legs so it will
balance
on a vertical rod placed under the seat.
9. Spread the bristles and a straw broom will stand upright.
10. Stick the neck of a wine bottle through a hole in a slanted board
and it stands up.
8.2.10 Centre of mass of biased bowls
See diagram 8.2.10
After Steve Ritchie, The Australian Science Teachers Journal, Vol.
33 No. 1
The bowl used in lawn bowls has a biased shape so when bowled in a
straight line it follows a curved path. To find the bias of a bowl
and how this affects its path of the bowl you need a lawn bowl, metre
stick,
chalk, and a carpet or evenly grassed surface. Observe different size
discs
on the sides of the bowl. Stand the bowl on its rolling surface and
push
it gently. When it stops it leans to one side or falls onto its side
with
the small disc closer to the ground. Stand the bowl with its rolling
surface
resting on a bench. Place a metre rule horizontally across the top of
the
bowl. Mark this spot with a piece of chalk. Hold the piece of chalk at
this spot while rotating the bowl, keeping it in its upright position
during
rotation. After one complete rotation you have drawn a complete chalk
circle
on the bowl, called the running line. The running line is not in the
centre
of the running surface. Draw a cross-section of the bowl and include
the
running line. Identify the sides of the bowl in your diagram with a
large
and small disc. The running line of the bowl is closer to the end
marked
by the large disc. Bowls are made of a plastic composition and there is
more plastic mass on the small disc side of the running line. The bowl
is unbalanced when bowled because there is more mass on one side of the
running line. The bowl is weighted or biased to one side of the bowl.
The
bowl is biased on the small disc side of the running line. When a bowl
is delivered, i.e. bowled, it curves in the direction of the bias.
Refer
to the diagram to predict the direction of aim, A or B, taken for the
bowl
to approach the target, T. Change the bias, i.e. turn the bowl around.
Try to deliver the bowl in such a way that the bowl stops on the
target.
The bowl curves towards the bias because throughout the path of the
bowl,
the bowl gradually leans over towards its bias. This leaning of the
bowl
shifts its centre of its mass, and running line, sideways thus causing
a curved path.
8.2.11 Centre of gravity of pine
trees
See diagram 8.2.11
A pine tree growing by itself with no other trees near it receives
sunlight from all sides. Its largest branches are near the bases of the
tree and the branches get smaller towards the top. Consequently its
centre
of gravity is in the trunk near the base. However, when pine trees grow
close together in a forest their sides are shaded by other trees so the
lower branches do not develop much and later dies. They receive light
only
from above. Consequently forest trees have the centre of gravity in the
trunk near the top of the tree. They are "top heavy" and compared to
free
standing trees of the same age, their trunks are longer and thinner and
their roots do spread out so far. During a very strong wind the free
standing
tree will just bend with little damage except to the tip of the tree.
However
around a clearing in a many trees may be knocked down due to
their
high centre of gravity.
8.2.12 Hidden centre of gravity
See diagram 8.2.12
Make a double bottom, "false bottom", in a small cardboard box with
a lead weight in the space below. Shake the lead weight to one end of
the
box. You can place the box on the table so that only the lead weight is
over the table and the box does not fall. A smuggler make carry gold in
the false bottom of a suitcase. However when the smuggler carries the
suit
case through the customs office it tilts to one side so that the centre
of gravity, now at the side, is vertically below the suspension point
of
the suitcase handle.
8.2.13 Hanging belt, "sky hook"
See diagram 8.2.13
Dissemble a plastic two arm clothes-peg and remove the clip. Hang a
heavy leather belt evenly over one arm of the clothes-peg and use the
clip
to secure the belt to the arm. You can raise the system by raising only
your finger tip under one end of the clothes-peg arm. The system is
stable
when the clothes-peg arm is inclined slightly downwards away from you.
At this angle, the belt hanging down is slightly inclined towards you
so
the centre of gravity of the system lies vertically below your finger
tip.
8.2.14 Shared centre of gravity,
stability brace
See diagram 8.2.14
Ride your bicycle parallel to another cyclist and at the same speed.
Take hold of the handle bar nearest to you of the other cyclist. The
other
cyclist takes hold of your nearest handle bar. Straighten both your
arms
while still holding the other's handle bar. You can both slow to a stop
and not fall over because the arm brace of the two cyclists has given
the
system a common centre of gravity. Within construction towers and
scaffolding,
braces between vertical elements form stable triangles with two brace
sides
and one vertical element side.
8.2.15 Tipping bottle
See diagram 8.2.15
Put a plastic bottle with an oval base, e.g. a shampoo bottle on a
sloping window sill as follows: (a) full bottle with longer axis of the
oval base parallel to the edge of the window sill (b) half full bottle
with longer axis of the oval base parallel to the edge of the window
sill (c) full bottle with longer axis of the oval base at right angles
to
the
edge of the window sill (d) half full bottle with longer axis of the
oval
base at right angles to the edge of the window sill. The bottle remains
stable on the sloping window sill only if the centre of gravity is
supported
by the surface of the window sill. (a) and (c) have a higher centre of
gravity than (b) and (d). (a) and (b) are more likely to topple over
than
(c) and (d). So the most stable system is probably (d) then (c) then
(b)
then (a), depending on whether the centre of gravity is supported.
8.2.16 Balancing H-shape
Select two identical coins and draw two H shapes on thin cardboard
with the widths of the vertical arms and cross arms of the H-shapes
slightly
longer than the diameter of the coins. Place the two coins at the
bottom
of the two vertical arms of one of the H shapes. Put the other H-shape
on top then join top and bottom H-shapes with adhesive tape. The usual
centre of gravity of an H-shape would be along the line bisecting the
cross
arm. However this H-shape can balance on a string held below the arms
containing
the coins.
8.2.17
Centre of gravity of playing dice
The cube dice have the opposite side labelled 1 and 6, 5 and 2 4 and 3.
Sides 4, 5 and 6 touch and side 1, 2 and 3 touch. If the spots on
the dice are made by drilling out a small holes, then the centre
of gravity is below the geometric centre of the cube and nearer the
smaller number. So when such dice are thrown, the faces with more
than three spots are more likely to be uppermost. However, if the
spots on the dice are made by painting on the spots, the faces with
less than four spots are more likely to be uppermost.
8.2.18 Shape
of a hanging cable or flexible chain, catenary curve, parabolic curve
See diagram 8.2.18: Catenary curve | See diagram 2.0.:5 Conic sections | See diagram 2.0.6: Parabola equation
The shape of a hanging chain, called the catenary, has the minimum
potential energy of any possible shape and the lowest possible centre
of mass. It is the shape of high voltage cables and overhead cables for
electric railways. Hanging cables or wires are never horizontal because
no horizontal force can have a vertical component to overcome the
weight of the hanging cable.
If symmetrical about the y axis, y = c cos h, where c = the point
where it intersects the y axis.
The cable of a suspension bridge hangs in a parabola if the droppers
allow the load to be suspended horizontally. A parabola is the
intersection of a cone with a plane parallel to the side of the cone. Y2
= 4 ax, where a = distance from the focus to the origin.
8.3.0 Gravity
Gravitation, weight, falling, S
= ½ gt2, measuring g, distance - time graphs,
Accelerated
Reference Frames, earth's gravitational field strength, g = 9.8 N / kg
Newton's Law of Universal Gravitation. qualitative understanding of
the inverse square law, quantitative treatment of the law F = Gm1m2
/ d2,
gravitational field strength (g) = force per unit mass
4.105 Discovering weightlessness
See diagram 36.54: Weightless toy soldier
To study the motion of an object you need a reference system, e.g.
something
relative to which it is possible to describe the location of the object
at any time. For many experiments you choose a reference system which
is
fixed to the earth, as for instance when you study a falling object. In
such a reference system the earth is at rest. If you want to study the
seasonal
changes, however, you prefer a reference system where the sun is at
rest
and where the earth will be moving in an orbit. You see from this that
the answer to the question whether an object is moving or not depends
on
what reference system you choose. Not only the position but the weight
of
an object depends on the reference system. The following experiment
will
show weightlessness.
1. Tie a string with a toy soldier or other object suspended from
it loosely across the top of the three pieces of wood joined as shown
in
the diagram. Lift the entire apparatus and when it is hanging
motionless
release the string. While the soldier is falling, he can be seen to
remain
in the same position inside the frame. Since he is not supported by
either
the string or the frame, he is in a weightless condition with regard to
his surroundings, e.g. the reference. system being used.
2. The weight of an object also depends on its location. Measured
in a reference system fixed to the earth, the weight of an object is
the
same as the earth's gravitational force acting on it. This force
decreases
as the object moves away from the earth and will eventually become
negligible.
The weight of the object is changing under the above circumstances.
Content
of matter of the object, measured in kg does not change, unless you are
dealing with relativistic physics, where objects experience speeds
approaching
that of light. An astronaut whose mass on the surface of the earth is
90
kg still has the same mass of 90 kg on the surface of the moon but his
weight, which is 90 kg weight on the earth's surface, would only be
about
15 kg weight on the moon's surface. Using SI units, the mass is m kg
but
the weight is mg Newton. Since g at the moon is about one sixth
of g at the earth, the weight of a man on the moon will be one sixth of
his weight on the earth.
3. A space-ship in orbit is still within the earth's gravitational
field. Its weight is exactly the force required to keep the ship in
orbit.
In a reference system attached to the ship, however, everything inside
the ship is weightless and with a slight push against one wall of the
cabin
a man can propel himself towards the opposite wall. Further away from
the
earth, the gravitational force becomes negligible and the space-ship
will
move in a straight line unless acted upon by forces from its own engine
or from other objects like the moon, Newton's first law. Outside the
space-ship
a man could, if he were completely free to move, push himself of f in
any
direction never to return. To avoid such a possibility, safety lines
are
attached to the space suits of astronauts who work in space.
4.106 Satellite launcher
See diagram 4.106a
Materials required are a bucket, a football, a coat hanger, or other
suitable wire, sinker or weight, a piece of string and a test-tube or a
cap of some sort.
Place the ball securely in the bucket. Bend the wire so that about
30 cm of it is straight and the rest is curved into a circular base as
shown in the sketch. Using masking tape, secure the circular portion on
the ball, allowing the straight, 30 cm portion to stand upright in the
centre of the top of the ball. Attach the sinker or weight to the
string.
Fasten the other end of the string to the test-tube or cap with tape.
Invert
the cap on top of the upright wire, see diagram.
Explain that the ball represents the earth, and the sinker represents
the satellite. All that it takes to set the sinker into motion in any
direction
is the tap of a finger. Let the students find out what happens when the
satellite is launched in the following different ways:
1. With a slight tap, push the sinker up and away from the surface
of the ball, as shown in the figure. The sinker moves up and then falls
back to the starting point. This is how an object travels when it is
projected
at low speed straight up from the earth.
2. With a slight tap, push the sinker of f the surface of the ball
at an angle. Show by a diagram what happens. The sinker moves away from
the ball and then falls back at some distance from the starting point.
The distance spanned depends upon the angle of launching and upon the
forcefulness
of the tap.
3. With a stronger tap, push the sinker of f the surface of the
ball at an angle. Make a diagram of the orbit. The sinker moves away
from
the ball, circles it, and lands. Evidently, a complete orbit passes
through
the starting point of the orbit.
4.107 Weight of a falling
chain
Hold an end link of a linked chain vertically over a sensitive balance
with end of the bottom link touching the pan of the scale. Release the
upper link and observe how the chain forms a heap on the pan. Observe
the maximum reading on the scale while the chain forms a heap and
compare this value with the weight of the still heap. The force exerted
on the scale may be five times the weight force of the chain itself. So
the instantaneous force of a falling chain is much greater than the
simple weight force of the object itself due to its momentum. So
where a long flexible object is dropped attached to suspension, an
additional force is caused by the momentum.
4.108 Ball projected
upwards from a cart
Fix a vertical spring in a cart. The condensed spring is secured by a
pin attached to a long string. Attach the other end of the string to
the leg of the table. Put the cart on the floor and pull it away from
the table with constant velocity. At the length of the string from the
table leg, the pin is pulled out to release the spring that projects
the ball upwards to land again on the spring in the still moving cart.
4.109 Velocity of an arrow
Resolve the velocity of an arrow fired up
at angle alpha to the horizontal into a horizontal component, v
cos alpha, and a vertical component, v sin alpha. The range of the
arrow = horizontal velocity X time of flight.
Time of flight = time to reach greatest height, t X 2 (up and down). At
greatest height, v = 0. Use the equation: v = u + at. 0 = v sin
alpha - gt, so t = (v sin alpha / g) X 2 = 2v sin alpha / g
For greatest height, h, use the equation: v2 = u2
+ 2as. 0 = v2 sin2 alpha - 2gh, so h
= v2 sin2 alpha / 2g.
Range = v cos alpha X 2t = v cos alpha X 2v sin alpha / g = 2v2
cos alpha sin alpha / g [from trigonometry: sin alpha cos alpha
= 1/2 sin 2 alpha] so range = v2 / g X sin 2
alpha. R is maximum when sin 2 alpha = 1, i.e. when 2 alpha = 90o,
so alpha = 45o. Maximum range = v2 /g, when angle
to the horizontal = 45o.
8.4.0 Inertia
Inertia is the resistance of a body to change in its state of motion
either at rest or with uniform motion in a straight line, as stated in
Newton's first law of motion. The larger the mass of a body the greater
its inertia, so a measurement of mass is a measurement of inertia.
Mach's
principle states that the inertia of a body is caused by the
gravitational
interaction between that body and all the bodies in the rest of the
universe.
So if a body could be isolated from the gravitational forces from all
other
bodies it would have zero inertia.