School Science Lessons
Physics - Mechanics, simple machines, work and energy
Updated: 2008-07-16
Please send comments to: J.Elfick@uq.edu.au
See also: Interesting
websites
Table of contents
21.0.0
Mechanics, simple machines, work and
energy
21.1.0 Levers
21.1.01 Balances
21.2.0 Wheel and axle
21.3.0 Inclined plane,
ramp, screw, thread, wedge
21.4.0 Gears
21.5.0 Pulleys
21.1.0 Levers
4.170 Three orders of lever, machines
4.171
Class 1 levers, first order levers, type 1 levers
4.172 Class 2 levers, second order levers, type 2 levers
4.173 Class 3 levers, third order levers, type 3 levers
21.1.1 Type 1 levers
21.1.2 Type 2 levers
21.1.3 Type 3 levers
21.1.3.1 Use chopsticks
21.1.4 Application of levers in
everyday life
21.1.5 Move our arms
21.1.01 Balances
4.145 Balance with a see-saw
(teeter-totter)
4.146 Balance with a metre stick,
stationary
meeting point, centre of mass, centre of gravity
1.3 Weighing devices (primary)
21.2.0 Wheel and axle, screwdriver, windlass,
crank
handle, steering wheel
4.174 Wheel and axle
21.2.1 Windlass, raising weight with rotary
pencil
sharpener
21.3.0 Inclined plane,
ramp, screw, thread, wedge
4.178 Inclined plane, screw, thread, wedge
21.3.01 Screw jack
21.3.02 Surfing, motion of a surfer on a
surfboard
21.3.1 Measure force on inclined plane
21.3.2 Wedge
21.3.3 Paper inclined plane, paper thread
21.3.4 Mechanical car jack
4.187 Propeller
21.4.0 Gears
4.179 Belt drive
4.180 Gear wheel
21.4.1 Bicycle gears
21.4.2 Bottle top gears
21.4.3 Rolling coins
21.2.2 Belt drives, transmission belts
21.5.0 Pulleys, block
and tackle, broomstick
pulley
4.175 Simple pulley
4.176 Single fixed pulley
4.177 Single movable pulley
6.10 Pull with pulleys (Primary)
21.5.4 Block
and tackle
21.0.0 Mechanics, simple machines, work and
energy
See diagram 16.06: Work and wheels
Work
1 Joule of work done = 1 newton force moves object through 1 metre,
Work done = force distance in direction of force, W = Fs, Work and
Energy
Work = force X distance (displacement), joule (newton.metre). Work
done on an object changes its energy that may be stored as potential
energy
or cause change in speed, kinetic energy. When a wheel is moved by a
force,
the work done = displacement X component of the force in the direction
of the displacement
Kinetic energy
Kinetic energy of any mass, m, moving at speed, v = ½ mv2.
Change in kinetic energy, joule = work done, joule.
Potential energy
Potential energy is the stored energy that an object has due to the
state it is in, e.g. steam compared with water, compressed spring
compared
with relaxed spring, or its position, e.g. height compared to ground
level
above the earth. Work can be done when potential energy is released
from
storage. If an object falls, the gravitational potential energy lost,
Ep
= mgh = the kinetic energy gained, Ek, = ½ mv2
Angular momentum and its conservation
Work, simple machines, non-conservative forces, conservation of energy,
mechanical power, mechanical energy and power
Kinetic, elastic and
gravitational
potential energy (constant field only)
W = Fs cos theta, P = W/t, KE = 1/2mv2, EPE = 1/2kx2,
Calculation of work from force vs extension graphs for a spring
The 3 functions of machines:
1. Amplify force
A man with a strong hand shake can exert 20 kg force
but using pliers he can exert a force of more than 60 kg force. In the
ear there 3 tiny connecting bones pass on x 30 or more the force from
sound
waves.
2. Amplify movement and speed
Increasing displacement and speed:
Sometimes a machine passes on only a fraction of the force which is
applied
to it, but it will then increase or amplify movement and speed. A lever
of this type is common in jib cranes.
3. Change direction of force
The single fixed pulley just changes
the direction of an applied force from up to down. Sometimes it is more
convenient to pull down than to pull up
See diagram 21.1.2
Machines allow a force called the effort to overcome another force
called the load. If an effort of 10 N applied to a machine can move a
load
of 25 N, the mechanical advantage, MA, of that machine = 25/10 = 2.5.
If
MA > 1, i.e. heavier loads are moved by smaller efforts, then the
effort
must move further than the load. Velocity ratio, VR, = distance
travelled
by the effort / distance travelled by the load. Machines lets us
overcome
a resistance at one place with an effort by applying a force at another
place to move a load. Most people cannot crush an empty match box
between
their thumb and fingers however crushing the matchbox with pliers needs
little effort. The effort force is multiplied because the distance to
where
you grip the handles of the pliers is much greater than the distance to
the end of the jaws of the pliers. A big stone may be too heavy to
carry
but you can move it on a wheelbarrow. Our fingers may be too big to
pick
up very small objects or pick up objects inside small spaces but you
can
use tweezers to help us. Lever, pulley and axle are simple machines
developed
according to the lever principle. Inclined plane, wedge and screw are
simple
machines developed according to the principle of inclined plane. The
machines
may save labour but do not save work because force (effort) X distance
(effort) = force (load) X distance (load), neglecting the force of
friction.
Mechanical advantage (MA) is the number of times the load moved by a
machine
is greater than the effort applied to that machine, i.e. MA = load /
effort.
MA has no unit, as it is a ratio. If MA > 1, load > effort, i.e.
you an
use a smaller effort to move a bigger load. However the effort must
move
further than the load. Distance moved by the effort / distance moved by
the load = velocity ratio, VR. Efficiency of a machine = energy output
/ energy input, as percentage. No machine is 100% efficient because
always some
energy is lost due to friction. Work = force X distance. Efficiency =
work
done on the load / work done by the effort = load X distance moved by
the
load / effort X distance moved by the effort = MA X 1/VR = MA/VR X
100%.
21.1.0 Levers, moments, levers.
parallel
forces, couples, beams, structures
See diagram 21.1: Types of lever
3 types of levers: The distance of the effort from the fulcrum is
called
the effort: arm and the distance of the load from the fulcrum, the load
arm. To arrange the lever so that a small effort would lift a big load
the effort arm must be as long as possible and the load arm as short as
possible. A fishing rod gives a loss in force, but gives a gain in
distance
and speed instead. Examples of levers: scissors, wheelbarrow, forearm,
claw hammer to draw a nail, sugar tongs, boat oars, nut-crackers,
pliers,
can opener, bottle opener, crow bar.
Lever is a simple machine consisting of a rigid rod pivoted at a fixed
point called the fulcrum, used for shifting or raising a heavy load or
applying force. The lever principle states that motive force ×
the
arm of the motive force = resistance × the arm of resistance.
Classify levers into 3 orders or types according to where the effort is
applied, and the load moving force developed, in relation to the
position
of the fulcrum. A first order or type 1 lever has the load and effort
on
opposite sides of the fulcrum, e.g. seesaw, beam balance, pair of
scissors
(two first order levers!), tin snips, bolt cutters. A second order or
type
2 lever has the load and effort on the same sides with the load nearer
the fulcrum, e.g. nutcrackers, wheelbarrow, fishing rod, broomstick,
biceps
muscle on upper arm. A third order or type 3 lever has the effort
nearer
the fulcrum than the load with both on the same side of it, e.g.
tweezers,
tongs, chopsticks. Machines are used to change the direction of a
forces.
Usually they allows a smaller applied force, the effort, to overcome a
larger resistance force, the load. Levers have a rigid beam supported a
one point, the fulcrum (F) with a load force (L) applied at one point
and
an effort force (F) applied at another point. The Lever Principle can
be
stated as: Load x Length of load arm = Force x Length of force arm.
Each
side of this equation is a moment, i.e. Force x Perpendicular distance
to pivot. Hence moments clockwise = moments anti-clockwise. The three
types
of lever depend upon the relative positions of F, L, and E: Type 1
Fulcrum
between load and effort (E F L); Type 2 Load between effort and
fulcrum (F L E); Type 3 Effort between fulcrum and load (L E F). The
mechanical
advantage of a machine, M. A., is the ratio of the load to the effort,
L/E. The velocity ratio of a machine, V. R., is the ratio of the
distance
moved by the effort to the distance moved by the load. The efficiency
of
the machine is the ratio M. A. /V. R. Efficiency is always less than
100%
because when a machine is used there is always some energy loss.
21.1.1 Type 1 lever
See diagram 21.1.1: Lever 1
1. Use a metre stick with a hole drilled in the centre. Hammer a nail
horizontally into the side of a table. Suspend the metre stick at the
centre
by the nail through the hole. Use a loop of string and a small mass to
balance the metre stick. Tie a loop of string around the metre stick
each
side of the nail. Attach a spring balance to one loop, hanging down.
Attach
a weight to the other loop. Tie a loop of string to a weight. Move the
loops to any position along the bar. Pull down on the ring end of the
spring
balance to raise the weight. Note the weight, the reading on the spring
balance, the distance from weight loop to nail, the distance from
spring
balance loop to nail. Also, note how far the spring balance loop moves
down and how far the weight loop moves up.
2. Use a board the same height as a desk. Place a stick across the
board and use it as a lever to raise the table. Note that the longer
end
of the stick moves further than the shorter end. The force exerted by
the
shorter end, load, is greater than the force used to move the longer
end,
effort.
3. Close a wooden match box and try to crush it between the
thumb
and fingers. You cannot do it. Hold the match box in the jaws of a pair
of pliers. You can easily crush it by squeezing the handles together.
Pliers,
tin snips, and bolt cutters have two Type 1 levers with each fulcrum as
a pivot. When cutting paper or cloth with scissors the effort < load
because you want a long length of scissors blade and cloth does nor
require
much force to cut it. Try using a pair of scissors as tin snips to feel
the difference.
4. Hammer a nail into a big piece of wood. Try to pull
the nail out with your fingers. You cannot do it. Use a claw hammer to
pull out the nail. The load is the force of the nail on the claw. The
fulcrum
is the round part of the hammer head. The effort is your pull on the
handle.
The hammer is being used as a bent lever to pull out the nail.
21.1.2 Type 2 levers
See diagram 21.1: Lever 2
Use a metre stick with a hole drilled in the centre near one end.
Hammer
a nail horizontally into the side of a table. Suspend the metre stick
at
one end by the nail through the hole and attach a spring balance to the
other end. Tie a loop of string to a weight. Pass the bar through the
loop
so that the bar can support the weight. Move the loop to any position
along
the bar. Examples include wheelbarrow, nutcracker.
21.1.3 Type 3 levers
See diagram 21.1: Lever 3 | See
diagram 9.232: Arm joint
1. Use the same apparatus as for Type 2 lever but put the weight,
load, at the end of the bar and suspend the bar by a loop of string
attached
to a spring balance, effort. Since a Type 3 lever has the effort
between
the fulcrum and the load, the effort is always greater than the load,
M.
A. < 1. Pick up something heavy with tweezers, forceps, or
chopsticks.
They consist of two Type 3 levers joined at the fulcrum. For chopsticks
the fulcrum is the angle between your thumb and forefinger. The force
you
apply with your fingers, effort, is greater than the force exerted by
the
ends of the tweezers or chopsticks, load. Type 3 levers are convenient
for picking up small things. a. Catch a fish with a rod and line. The
load
is the pull of the fish. The effort is your pull on the rod. The
fulcrum
is where you hold it lower down or where the rod touched the ground. b.
Keep your upper arm vertical and your forearm horizontal in front of
the
body. Pat a heavy stone in the palm of your hand and move it up towards
your mouth without moving the upper arm. The load is the weight of the
stone. The effort comes from the shortening of the biceps muscle in
your
upper arm. The fulcrum is the elbow joint.
2. Use a wooden ruler; a spring balance; a weight of mass 50g; a
large wood board; a piece of string. Saw the wood board into several
small
boards according to the sizes. Drill a hole of F5 differently at two
vertical
boards and the place with 50 cm mark on the ruler. To be more accurate,
drill a small pit with a nail then drill a hole. Place the two vertical
boards hole to hole on a level board. Make sure the distance between
the
two vertical boards just fit to insert the ruler. Fixed the two
vertical
boards on the level board with nails. Insert the ruler into the crack
between
the two vertical boards and make the hole on the ruler just opposite to
the holes on the boards. Fix them with a set of screws through the
holes.
Do not screw too tightly. Use string to make two sheaths. Tie a sheath
on the weight and tie the other sheath on the hook of the spring
balance.
Fix the weight at some point of the ruler and record the scale. Slowly
remove the spring balance. When the system balances, record the reading
of the ruler scale, the spring location and the reading on the spring
balance.
21.1.3.1
Use chopsticks
To
use chopsticks in a Chinese restaurant, hold one the thicker end of
one chopstick in the crook of the hand, i.e. where the first
finger
and the thumb join on the hand. Let it rest on the end of the middle
finger. This lower chopstick never moves during the eating motion.
Hold the upper chopstick
between the end of the thumb and the end of the forefinger (index
finger, second finger) with the thumb touching a thicker part than the
forefinger. The thinner ends of the the two chopsticks should meet so
that you
can pick up piece of food with a pincer motion. Tap the ends of the
chopsticks on the table to even them. Grasp a piece of food by closing
the end of the upper chopstick down onto the end of the lower
chopstick. The action of the upper chopsticks is that of a type
three
lever. The end of the thumb is the fulcrum. The end of the index
finger supplies the effort. The resultant force of the food on the ends
of the chopsticks is the load.
The action is similar to the action of tweezers or forceps. Note the
mechanical disadvantage but the advantage of being able to select and
pick up the small pieces of food and dip them into sauces, a practice
characteristic of Chinese cuisine.
21.1.4 Application of levers in everyday life
See diagram 21.1.1
Look for levers used at everyday life and classify them according to
the type of lever, e.g. Chopsticks belongs to the third order lever.
Using
it needs greater effort but can prevent food from slipping away.
Balances
See diagram 1.11: Beam balance boys
2.232 Balance with a see-saw
See diagram 21.1.1d: Type 1 levers
a. Use a strong board about three metres long and a sawhorse to make
a see-saw. Use two students of equal weight. Sit at either end of the
board
so that they balance. Measure the distance from the balance point to
each
student. Multiply the distance by the student's weight. b. Select a
heavier
student and a lighter student. Tell them to sit on the board so that
they
balance. Measure the distance from the balance point to each student.
Multiply
the distance by the student's weight. c. Select a heavier student,
weight
m1, and a lighter student, weight m2. Sit on the
board so that they balance. Measure the distance from the balance point
to each student, d1 and d2. Multiply the distance
by the student's weight. You will discover that m1d1 =
m2d2. d. Select a heavier student, weight m1,
and two lighter students, weight m2 and m2. Sit
on
the board so that they balance. Measure the distance from the balance
point
to each student. Multiply the distance by the student's weight. Add the
products for the two lighter students. In each experiment the ratio of
the masses is the reciprocal of the ratio of the distances from the
balance
point or centre of mass for the system,
m1d1 = m2d2
m1d1 = m2d2 + m3d3
2.233 Balance with a metre stick
See diagram 2.233
Rest a metre stick lightly on your two forefingers. Place your fingers
under the ends of the metre stick. Move your fingers towards the centre
of the metre stick. Where do your fingers meet?
Place the finger of your right hand under one end of the metre stick
and the finger of your left hand half way between the centre of the
stick
and the other end. Where do your fingers meet?
Place the finger of your left hand under one end of the metre stick
and the finger of your right hand is placed about halfway between the
centre
and the other end. Note where your fingers meet now. Your fingers
should
meet at the balance point, or centre of mass, for the system.
21.2.0 Wheel and axle, screwdriver, windlass,
crank
handle, steering wheel
See diagram 4.174: Wheel and axle | See diagram 21.2.0
A set of wheel and axle consists of two wheels having different radii.
The large wheel has radius R and the small
wheel
an axle, has radius r, such that R > r. Wind one rope around the
wheel
and
another rope in the opposite direction around the axle. Pulling on the
wheel rope supplies the effort. The wheel around the axle bears the
load.
When you pull on the wheel so that it make one complete turn, a point
on
the circumference of the wheel has moves through 2 pi R and a point on
the circumference of the axle has moved through 2 pi r. So velocity
ratio
= 2 pi R/ 2 pi r = R/r. Taking moments about the centre of the axle
effort
X R = load X r so R / r = load / effort = mechanical advantage.
21.2.1 Windlass
See diagram 21.2.1
Remove the cover from a pencil sharpener and tie a string tightly
around
the end of the shaft. When you turn the handle you find the force
needed
to turn the handle is much less than the force of gravity on the books.
Feel the magnitude of the force lifting the heavy weight. Lift the
heavy
weight directly. Compare the magnitudes of the forces at two
conditions.
21.2.2 Simple belt drives, transmission belts
See diagram 2.258
1. Drive two long nails into a block of wood. Place spools, one larger
than the other, over the nails so that these can be used as axles. Slip
a rubber band over both spools. Rotate the larger spool through one
turn
and note whether the smaller spool makes more or less than one full
turn.
In which direction does the small spool turn? Try crossing the rubber
band
and observe the result.
2. Use several spools with different diameters; a wooden block; two
long nails; a piece of elastic. Nail the two nails on the block. Cover
the two spoons on the two nails to make the nails as axles. Cover the
elastic
on the two spools. Tighten the elastic at fit degree, not too loose and
not too tight. Rotate the spool with a larger axle a circle and
meanwhile
observe the small spool's rotating amount and direction. Again cover
the
elastic across on the two spools. Repeat the experiment and observe the
small spool's rotating amount and direction again. Compare the above
two
conditions and find the difference. Redo the experiment but differently
using two spools with the same diameters and using two spools with very
different diameters. Compare and analyse the experiment data to find
the
relationship of the spool's diameter and the way of covering the spool
with elastic to the rotating amount and direction.
21.3.0 Inclined plane, ramp, screw, thread,
wedge
See diagram 21.3.1
Use a smooth board at an angle of 300 to the table. Weigh
the trolley by suspending it from a spring balance. This is the effort
needed to lift the trolley from the table to the top of the board. Put
the trolley on the smooth board. Pull it slowly up the board noting
the
reading on the spring balance. The effort will be about its weight. The
smooth plank is twice as long as it is high at the top. By taking a
longer
path, the slope will be less and the effort less. Inclined plane is a
slope
that allows a load to be raised gradually using a smaller effort than
would
be needed if it lifted vertically upwards. So it is a force multiplier.
The ratio of the height of the top point of the inclined plane to the
length
of the plane is called the gradient. The smaller the gradient the more
force is saved.
21.3.01 Screw
See diagram 21.3.0.1
A screw is a simple type of machine, acting like an inclined
plane rolled up in a helix. The pitch of the screw is the distance
between the threads. So
for one revolution of the screw, it moves laterally through a screwed
nut a distance equal to the pitch. The screw is usually turned by a
force applied tangentially at one end of an arm. The other end of the
arm is fixed to the screw.
Work done by the effort = effort X distance travelled by the effort =
effort X 2pi X r, where r = radius of the screw
Work done on the load = load X pitch
So load X pitch = effort X 2pi X r
Mechanical advantage = load / effort = 2pi X r / pitch
A screw may transfer between translation and rotation. The screw
thread
is a ridge in the form of a helix on a cylindrical core. The ridge may
be triangular (v-shape) or square or round. If the screw thread is
triangular,
greater friction may be used. If the screw thread is square, larger
loads
may be lifted. The distance between the adjacent threads of a
screw
or bolt is called pitch. When you turn a screw through one full turn,
it moves up
or down a distance equal to the pitch of its thread. Different standard
screw threads include pre metric British Standard Whitworth (BSW) with
an angle of 55o, Sellers or USS screw thread (pre metric USA
standard) with an angle of 60o, and various metric screw
threads.
An Archimedes screw is a hollow inclined screw so that rotation of the
screw raises water. It was invented by Archimedes but apparently was
not
invented in China.
21.3.02 Surfing The motion of a surfer on a
surfboard
Water waves are a combination of transverse and longitudinal waves
resulting in the water molecules describing a roughly circular path
about
a fixed point. At the crest of the wave the molecules are moving
forwards
in the direction of the wave but at the base of the wave they are
moving
backwards (undertow). All forms of circular motion require a
centripetal
force. This comes from the forces of adhesion between the water
molecules.
A surfer sitting on a surfboard will just bob up and down as the crest
of the waves pass. However, there may be some movement in the direction
of the wave due to frictional forces between the water molecules near
the
surface and the surfboard. If the surfer puts the legs down into the
water,
this movement will increase due to more friction with the legs. The
friction
component might come from the linear velocity that is tangential to the
circular motion of the water molecules. A centripetal force is in the
direction
towards the centre of the circular motion. However this force is
negligible
when describing surfing the wave. The surfer "catches the wave" by
matching
the wave's velocity by paddling then moving the weight of the body
forward
of the centre of gravity of the surfboard that then tends to slide down
the wave. This is like an object moving down an inclined plane. However
to "stay on the wave" the surfboard must move at the same speed as or
faster
than the wave in transverse direction. The surfer must have some
component
of his motion in the direction of the wave's propagation and at the
same
speed of the wave's propagation. If the surfer's motion in the
direction
of wave propagation is greater than the wave's the surfer will be in
front
of the wave and no longer sliding (surfing) down the incline. This is
why
surfers surf across waves and not straight down the face. If they surf
straight down the face two things can and often do happen. If the nose
of the surfboard does not plough straight into the water at the base of
the wave tossing the surfer forward over the front of the board, the
surfer's
velocity, in the direction of propagation, exceeds that of the wave and
the surfer simply surfs off the front of the wave. This is done by
applying
force through paddling or moving the weight of the body more forward of
the centre of gravity. The steeper the transverse progressive wave the
less extra force is needed. The surfer can "get off " the wave by
transferring
weight to a point behind the centre of gravity. A surfer standing on a
surfboard does this by applying a torque. One foot is kept above the
centre of gravity and the other foot is place behind the centre of
gravity.
The torque is applied by shifting more weight in to the back foot. The
effect of this is to reduce the velocity of the surfer to less than
that
of the wave allowing the wave to simply pass on by. A surfer riding a
breaking
wave is helped by the mass of broken water also sliding down the
inclined
plane of the forward wave surface. So the wave is like a moving
inclined plane made of water with water flowing up the plane. The
surfer can use this upward flow to stop falling down the plane by
pushing rails and fins on the bottom of the surfboard into the water at
the exact angle needed. On a perfect wave the surfer can stand still
and maintain speed.
21.3.1 Measuring force on an inclined plane
See diagram 21.3.1 |
See diagram 21.3.1 A and B
1. Attach a heavy toy car or a roller skate to a spring balance and
pull it up an inclined plane. Note the force required to move the car
and
compare it with the force needed to lift it vertically. Note also that
in moving up the inclined plane, the force is exerted over a greater
distance
than when the car is lifted vertically to the same height above the
table.
Neglecting friction, the work required is the same in both cases. Point
out that this is also true for other simple machines.
2. Using an inclined plane to lift weights can save force, and the
relations between saving force and inclined angle, saving force and the
distance. Use a piece of elastic band, a piece of black thread and a
small
plastic bottle. Tie an elastic band to the neck of the bottle
containing
water. Use a smooth long wooden board supported at one end several
books.
Adjust the height of the inclined plane by pushing the books towards
the
lower end of the plane, not by changing the number of books. Tie a
black
thread marker to the elastic about 20 cm from the neck of the bottle.
Place
the bottle at the bottom of the inclined plane at minimum inclined
angle.
Pull the bottle to the top of the inclined plane and note the distance
from the black thread marker to the neck of the bottle. Repeat the
experiment
by increasing the slope of the inclined plane five times. In each
experiment
try to maintain the same speed of pulling. Observe which situation the
deformation of the elastic band is the smallest and longest.
21.3.2 Wedge
See diagram 21.3.2
A wedge is two inclined planes, base to base. Their wedges give a large
gain in force. Wedges are to split logs and to split off blocks of
stone
in quarries. A wedge has two inclined planes and a third surface that
may
be hit to apply force to lift an object (under one leg of an unsteady
table)
or lock (door jamb) or split (woodcutter's wedge) or cut (axe). Many
tools
are in the shape of a wedge, e.g. knife, chisel, the spade, drill, awl.
The mechanical advantage of an incrined plne increases as the angle
decreases. Also the sharper edge of a wedge allows a small force to
produce a large pressure. Use a pile of heavy books. Try to put your
small finger inside that
lowest
book. Fold cardboard then open it to make an angle. Hold the folded
cardboard
in your hand and push the thin edge between the pages of the bottom
book.
Put your small finger in this angle and take the book out of the
pile.
21.3.3 Paper inclined plane, paper thread,
screw
See diagram 4.178
A screw thread is an inclined plane wound around a cylinder. Make an
imitation of a screw thread by wrapping a right angled triangle around
a pencil, starting with the shorter of the two sides about the right
angle
parallel to the axis of the pencil. The hypotenuse represents the path
of the screw thread. The pitch of a screw is small compared to its
circumference;
so the slope is very gentle and the gain in force is high. A further
gain
in force is added when a lever, the spanner, is used to turn the nut.
For
one complete turn of the nut, it advances by the distance of one pitch.
1. Make a simple screw thread. Cut a piece of white paper to make
a right angle triangle 50 cm hypotenuse and 30 cm along its shortest
side.
Use a round rod about 40 cm long and roll the triangular piece of paper
on the rod beginning at the short side and rolling towards the point of
the triangle. Keep the base line of the triangle even as it rolls.
Observe
that the inclined plane, the hypotenuse, spirals up the rod as a screw
thread. A screw thread is an inclined plane.
2. Make a simple screw thread. Cut out several vertical triangles
from a sheet of paper, each triangle has a different size. Draw an
obvious
line in texts along the edge of the hypotenuse in each triangle. Roll
each
triangle cardboard around the biro to make it like a screw nail.
Compare
the distance of the screw of each nail, analyse the difference between
them. The principle of the screw nail is similar to the inclined plane
in which a weight is pushed upward. Although a screw is a spiral
inclined
plane, it acts like a second class lever. The screw's point is the
fulcrum,
where the thread meets a substance such as wood is the load, and the
effort
is applied to the head of the screw.
21.3.4 Mechanical car jack
See diagram 21.3.4
1. Make a simple lifting jack. Bore a hole through a block of wood
to fit a carriage bolt. Select a bolt that is threaded nearly its
entire
length. Sink the head of the bolt in the wood, so that it is flush with
the surface and nail a piece of board over it. Over the projecting
threads
put a nut, then a washer and short piece of metal pipe. The inside
diameter
of the pipe must be slightly larger than the diameter of the bolt. By
turning
the nut with a wrench the device acts as a lifting jack.
2. To make a model jack use two wooden blocks of about 10 cm length.
Drill a hole at the centre of the smaller block. Use a screw of more
than
twice of the block thickness. Make a groove with a knife at the centre
of the other block so that the screw can be placed in the groove. Use a
screw with a six angle head or flat-head head. Forcibly twist the screw
through the hole on the smaller block. Put the groove on the larger
block
on the screw cap. Put the two blocks together then tightly nail them
together
with small nails. Make sure that the screw does not rotate and it is
not
loose. The contact surface between the two blocks is flat and level. If
the screw is loose because the hole is too large, twist a nut to fix
it.
If it is very difficult to make the groove that can contains the screw
cap, place cardboard or iron gaskets between the two blocks instead of
the groove. The iron gaskets should be able to be just passed by the
nails
nailing the two blocks. Place the device upside down. Twist a nut on
the
screw and put an iron gasket on the nut and cover a piece of sawed iron
tube on the gasket. The inner diameter of the iron tube should be
slightly
larger than the screw and its outer diameter should be smaller than the
gasket so that it can stay on the gasket, not to slip away. The iron
tube
may is slightly shorter than the pole of the screw appearing. Rotate
the
nut and the tube will go up or down. When use the device to lift a
heavy object,
use a spanner to screw the nut and underlay the
tube with a rigid board to reduce the pressure of the tube. A
real screw jack is upright like the model and when the screw is turned
through one full turn the heavy is lifted up or down a distance equal
to
the pitch of its thread.
21.4.0 Gears
Gear wheel, gear train, motor
vehicle
gears, servo- mechanism, transmission systems, clutch,
differential
gear, automatic gear change
See diagram 21.4.0
Gears mesh directly into each other without any chain. A car has a
box of gears which can be changed. Imagine a large gear wheel and a
small
one. When the larger gear wheel is attached to the engine, and the
small
gear wheel is attached to the back axle you say the car is in top gear
because
you get maximum revolutions of the car wheels per revolution of the
engine.
If a smaller gear wheels is attached to the engine and a larger gear
wheel
is attached to the back axle you say the car is in low gear. If a
toothed
gear wheel with 10 teeth is meshed with a toothed gear wheel with 20
teeth.
For each complete revolution of the 20 teeth wheel the 10 teeth wheel
makes
2 revolutions. If the effort is supplied to the 10 teeth wheel to drive
the 20 teeth wheel, the velocity ration is 2 = number of teeth on the
driven
gear (load) / number of teeth on the driving gear (effort)
21.4.1 Bicycle gears
Examine the gearing of a bicycle by counting the teeth on the sprocket
wheel attached to the back wheel and the teeth on the large sprocket
wheel
to which the pedals are attached., e.g. 16 and 48. Each time you push
the
pedals round once, you pull around enough chain to cover 48 teeth.
However
there are only 16 teeth in the back sprocket, so it is turned more than
once, 48/16 = 3 times. So each time you turn the pedals once, the back
wheels rotates three times. When you reach a hill your bicycle will
be
easier to push if you used a back sprocket with more teeth or you used
a pedal sprocket with fewer teeth so that one revolution of the pedals
would give you fewer revolutions of the wheel.
1. Turn a bicycle upside down. Turn the pedal wheel exactly one turn
and note the number of turns made by the rear wheel.
2. Study the speed of rotation and transmission of roller chain.
Use a bicycle without chain box. Turn the bicycle upside down and let
it
stand on its saddle and handle. Count the amount of the teeth of the
large
gear at the middle shaft and that of the small gear at the back shaft.
Forcibly rotate a pedal of the bicycle a circle then differently count
the amount of the circles the large gear and the small gear rotating.
For
convenience, mark with colour on some tooth of each gear
beforehand. Calculate the ratio of the amounts of their circles and
teeth
and find the relationship of the two ratios. Observe how to transmit
the
large gear' rotation to the small one. Observe the direction of the
large
gear and that of the small one. Find the relationship of the direction
of transmission to the directions of rotations of the large gear and
small
one.
21.4.2 Bottle top gears
See diagram 2.260 | See
diagram 21.4.0
Punch holes exactly in the centres of bottle tops. Put two of the
bottle
tops on a block of wood so that the tooth like projections mesh. Fasten
them to the wood with small nails, but make sure that they still turn
easily.
Turn one of the bottle tops and note the direction that the other
turns.
Add a third bottle top and note the direction that each turns.
Gear is a toothed wheel that transmits the turning movement of one
shaft to another shaft. Gear wheels may be used in pairs, or in threes
if both shafts are to turn in the same direction. Gear with different
shaped
teeth or shaft may rotate at different angle. The gear ratio, the ratio
of the number of teeth on the two wheels, determines the torque ratio,
the turning force on the output shaft compared with the turning shaft
on
the input shaft. The ratio of the angular velocities of the shafts is
the
inverse of the gear ratio.
21.4.3 Rolling coins
Put two identical coins edge to edge and flat on the table. Hold the
first coin in a fixed position while you roll the second coin around
it. The second coin turne twice around its own axis when rollingce once
around the first coin. If the radius of the coins = r, and the
circumference = 2 X pi X r, the centre of the second coin
travels a distance of 2 X pi X 2r.
21.5.0 Pulleys, block and tackle, broomstick
pulley
See diagram 21.5.0: Types of pulleys
| See diagram 4.175: Simple pulley | See diagram 4.176:
Single fixed pulley | See diagram 4.177:
Single movable pulley
Observe the tension in a string or rope. Tie the upper end of a string
to a support, and tie a brick to the lower end. The string will be
tight,
i.e. have tension all along it.
21.5.4 Block and tackle
See diagram 21.5.0d | See
diagram 21.5.2: Pulleys
This pulley system is used in cranes and lifts. In a car garage,
the
mechanics can lift a car engine out of a car by hand using a block and
tackle. You will notice that they pull down a long way while the engine
block moves up a short way. In the diagram the pulleys have been
separated
here to show the path of the rope more clearly. Find the gain
in
force from the number of strings supporting the load. The tension in
the
string remains constant and is one fourth of the upward pull on the
load.