School Science Lessons
Physics - Motion in one dimension, kinematics
Updated: 2008-03-28 L
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- Physics teaching Table of contents
Motion in one dimension
14.1.0 Velocity, vector quantities and
scalar
quantities
14.2.0 Acceleration, uniform acceleration,
speed and
acceleration
of falling objects
14.3.0 Measuring g
14.1.0 Velocity
14.1.1 Toy car running on moving paper 14.1.2 Photograph uniform motion:
14.1.3 Terminal velocity:
14.1.4 Muzzle velocity, bullet timers 14.1.5 Time of flight 1.41 Falling parachutes (Primary) 4.16 Air resistance (Primary) 4.1.2
Qualitative analysis of graphs,
distance - time graph
14.2.0 Acceleration,
uniform
acceleration,
speed and acceleration of falling objects
14.2.1 Drop strings with attached weights
14.2.3
Timing a falling body with an electric
"ticker timer"
14.2.3.1 Make a ticker timer from an electric
bell mechanism
14.2.4 Simultaneous fall, ball bearings falling
together
14.2.5 Coins fall together
14.2.6 Guinea and feather, drop coin and feather:
14.2.7 Falling heavy and light balls
14.2.11 Coins on a slope
6.11 Forces on coins on a slope (Primary)
14.2.12 Acceleration of marbles rolling down
an incline
14.2.13 Path of a projectile, mid-air target,
monkey and hunter
14.2.14 Projectile paths 14.2.15 Parabolic trajectory of thrown chalk
4.147 Ball bearings fall together
4.148 Acceleration of marbles down
an incline
4.149 Simple pendulum 6.22 Pendulum tells the time (Primary)
4.150 Coupled pendulums
4.151 Time a falling body
4.152 Paths of projectiles, free fall
4.153 Three-holes can, 3-hole can, vase with three holes, spouting
cylinder,
Mariotte's
flask
4.154 Falling washers on a
string 14.2.13
Path of a projectile,
mid-air target, monkey and hunter
14.2.16 Gun
and tunnel
14.2.18 Range of a gun
14.2.19 Throw up and fall down
4.141 Measuring how much dust in the
air
14.3.0 Measuring g
14.3.1 Free fall timer
14.3.2 Dropping balls
14.3.3 Ink jet marker
14.3.4 Falling drops
14.3.5 Reaction time, falling meter stick, catch
a meter stick 14.3.6 Catch a coin
14.3.7 Rotating turntable
14.3.8 Pendulum-timed free fall
14.3.9 Many bounce method
14.1.0 Velocity
Velocity, motion in one dimension,
linear
uniform motion, kinematics, motion in a straight line, velocity,
acceleration,
vectors, kinematics, motion in two dimensions, displacement in one
direction,
motion in a straight line, kinematics
If an object changes position from A to B along any path, you measure
its displacement by a straight line from starting point A to finishing
point B. This is a vector quantity, which has magnitude (size) and
direction., linear uniform motion, description of motion (kinematics),
how
objects
move and an analysis of motion (dynamics), scalar / vector quantities.
distance / displacement.
speed / velocity, acceleration, construction and interpretation of
graphs
of speed / velocity and acceleration with time, quantitative analyses
of
these, problems involving equations for linear uniform motion, uniform
velocity: v = s / t, uniform acceleration: v = u + at, s = ½(u +
v)t,
s = ut + 1 / 2at2, s = (v2 - u2) / 2a,
free
fall involving terminal velocity
Average velocity, uniform motion = displacement / time taken.
Instantaneous
velocity is the rate of change of displacement with respect to time as
measured by a speedometer
Average acceleration = change in velocity / time taken. Instantaneous
acceleration is the rate of change of velocity with respect to time as
measured by an accelerometer in an aircraft. You can read velocity and
acceleration from displacement-time graphs and velocity-time graphs.
Equations of motion, motion in one dimension, motion in a straight
line
u = initial velocity, v = final velocity, a = acceleration, t = time,
s = distance (displacement), V = u + at
s = (u + v) / 2 X t
s = ut + ½ at2
v2 = u2 + 2as
Vector quantities and scalar quantities
Vector quantities have both size and direction and you can represent
vectors by lines, with length proportional to the size and direction
indicated
relative to some reference direction, e.g. displacement, velocity,
acceleration,
force and momentum. You can add vectors to find the resultant
vector,
by placing drawn vectors head to tail. You can resolve vectors into two
perpendicular component vectors, rectangular components, so that the
two
components are equivalent to the single vector. Scalar quantities have
size but no direction, e.g. density.
Velocity and speed, velocity (vector) (steady speed), speed (scalar),
speedometer, velocity-time graph (V-t graph)
Other experiments: Toy bulldozer on Moving Sheet, Constant velocity
(air track), linear air track and glider, Examine a table of
velocities
ranging from continental drift to the speed of light, Ballistics,
maximum
height and range, Stroboscope, hand stroboscope, Dynamics trolley,
skate
board
14.1.1 Toy car running on moving paper:
Run a toy car at constant speed in both directions on moving paper
to show how velocities add and subtract. Time a toy bulldozer with a
stop
clock as you pull it across the table at constant velocity in front of
a meter stick.
14.1.2 Photograph uniform motion
Take an open shutter photograph of a toy clockwork motor car
14.1.3 Terminal velocity
Let a marble roll down a tube of water at a slight incline to reach
terminal velocity and allow you to measure slow constant velocity.
14.1.4 Muzzle velocity, bullet timer
Fire a bullet to pass through two aluminium foil strips and show the
signal on an oscilloscope Fire an air gun through two rotating
cardboard
discs separated by a known distance.
14.1.5 Time of flight:
Release a projectile fired from a pendulum apparatus by timing signals
from two microphones.
14.1.6 Examine a table of velocities ranging from
continental
drift to the speed of light.
14.2.0 Speed and acceleration of falling
objects,
average acceleration, uniform acceleration, deceleration (retardation)
See also 16.2.0.1: Falling object
| See: also 36.0.10:
Newton's
universal law of gravitation | See also
30.0.7:
Gravitational potential energy
Other experiments: String and weights drop, Rolling ball on incline
14.2.1 Drop strings with attached weights
Drop two strings with attached weights, one with equal distance
intervals
and the other with equal time intervals (1, 4, 9, 16). Let strings
hit a hard floor and listen to the sounds of weights hitting the floor.
Drop a string with wood blocks or lead balls tied at unit intervals and
equal time intervals.
14.2.3 Timing a falling body with an electric
"ticker timer", ticker timer tape chart
See diagram 14.2.3
1. Attach a weight to a strip of paper tape. Pass the tape between
the armature of an electric bell and a pad of carbon paper. Release the
paper tape so that the weight falls and drags the paper after it. The
end
of the arm of the timer hits the carbon paper against the tape and
makes
marks on it at equal time intervals. Measure the distance between the
marks.
A ticker timer uses low volt AC power source to make a vibrating spring
print a series of points on paper tape using circular carbon paper.
When
the paper tape moves with the object, the greater the space between
points
the further the object has moved. The time between any two points is
equal
to the reciprocal of the AC frequency, 50 HZ, so the time interval is
0.02
s.
2. To study the motion of a long window blind, tape the paper tape
to the bottom of the blind and let the paper tape moves up through the
ticker timer. Find a convenient starting point A on the paper tape and
record it as 0, even if it is not the first point. Then mark each point
every 5 dots, i.e. 5 x 0.02 = 0.1 second. Measure the distance between
points AB, BC, CD, DE etc. and calculate the average speed in every
space,
e.g. from A to B, v = distance / time = 5.0 cm / 0.1s. 3. To draw
the V
- t graph calculate the instantaneous speed equal to the average speed.
Note that the window blind had begun to move before the selecting point
A of t = 0, so there is a part of the graph before t = 0. The graph
shows
that the curtain moves in constant acceleration before 0.35 seconds, it
moves in constant speed of 2 m / s between 0.35 s and 0.65 s, and then
it
moves in constant deceleration. Calculate the acceleration in AD stage
from changes in the instantaneous speed in the centre of the time
intervals
AB and CD: (1.5 - 0.5) / (0.25 - 0.05) = 5.0 (m / s2). You
can
calculate the acceleration in each stage by this method and draw an
Acceleration-time
graph of motion of the window blind.
Points
Distance cm
travelled in 0.1 sec
Average v, m / s
AB
05.0
0.5
BC
10.0
1.0
CD
15.0
1.5
DE
20.0
2.0
EF
20.0
2.0
FG
20.0
2.0
GH
20.0
2.0
HI
17.0
1.7
IJ
08.0
0.8
JK
04.0
0.4
14.2.3.1 Make a ticker timer from an
electric
bell mechanism
See diagram 9.10: Electric bell | See
diagram 32.5.4.4: Electric bell circuit
Remove the clapper and extend the armature by soldering a strip of
metal to it. At the end of this extension drill a hole to fit a small
round
headed screw. Fix the screw head downwards to act as a marking hammer.
Fasten the mechanism to a wooden base. Fix a 3 cm diameter disc of a
carbon
paper disc to the base with a drawing pin. The drawing pin holds the
disc
loosely at the centre so that the disc can rotate to expose a new
surface
as the tape passes under it. Attach staples to the base to guide the
path
of the ticker tape. If the extension to the armature strikes the paper
too hard, the timing may be uneven.
14.2.4 Simultaneous fall, ball bearings
falling
together
See diagram 14.2.4
1. Two balls simultaneously dropped and projected horizontally hit
the floor together. Drop one billiard ball and shoot another out
simultaneous.
One ball is projected horizontally as another is dropped
simultaneously.
Instructor rolls a ball off the hand while walking at a constant
velocity.
2. Use two clothes-pegs, a pair of ball bearings (a) and (b), a wide
rubber band about 8 cm long. Fix the rubber band lengthways around one
clothes-peg. Then open the clothes-peg and force ball-bearing (a)
against
the tension of the rubber band between the prongs of the clothes-peg.
Grip
ball-bearing (b) with the second peg. Hold the two pegs side-by-side,
pointing
away horizontally above a sheet of tin on the floor. Squeeze the ends
of
the arms of both clothes-pegs. At the same moment, ball-bearing (a)
begins
to fall vertically, and ball-bearing (b) is shot forwards. Observe what
happens by looking and listening when the ball-bearings hit the sheet
of
tin. Repeat the experiment from different heights and with a tighter
rubber
band. If the experiment is done correctly, ball bearings (a) and (b)
land
in different places on the sheet of tin but they strike the ground
simultaneously.
14.2.5 Coins falling at the same time
See diagram 14.2.5
Observe the falling object and horizontal projectile object start off
at the same time and fall down to the ground at the same time too. Fold
a paper card in half, then fold each side one third from the end
outwards
to form a convex. Place coins on each side of the centre ridge of the
card
and hold one end on the table edge. Flick the ridge oft he card to the
side with your middle finger of right hand. One of the coins will be
thrown
several metres away, the other will fall straight to the floor at the
exact
same moment. First observe if the two coins start motion at the same
time.
Then repeat the steps above, note which coin hits the floor first.
Flick
the card lightly, hear the click. If you hear only one click, that
means
the direction of the falling object at first has not any influence on
the
falling times. This is because the accelerations of the two falling
coins
are the same if the air resistance is disregarded.
14.2.6 Drop coin and feather
Drop a coin and feather in a glass tube full of air and evacuated.
Drop cork and lead ball. Know how to drop a heavy and light object
simultaneously
with one hand. Drop a ball of paper and then a sheet of paper.
14.2.7 Falling heavy and light balls
Estimate the height a light ball must be dropped so it hits the floor
at the same time as the heavy ball.
14.2.12 Acceleration down an incline
See diagram 14.2.12
1. Use a grooved three metre plank. Incline it so that marbles will
roll down the groove. Arrange small tin flags hung from wires so that
the
marbles hit them and make "clinks" sounds. Put the flags at regular
intervals,
e.g. 25, 50, 75, 100 cm, from the beginning of the plank. Roll a marble
down the groove and listen to the intervals between "clink" sounds. The
time between the "clinks" will reduce as the ball rolls down the
incline.
Arrange the flags so that the clinks occur at equal intervals of time.
Measure the distance between the flags. The distance between the flags
increases down the incline.
2. Use an inclined air track. For timing use a stop clock and meter
stick. Put lights that flash every second along an incline and
horizontal
track such that they are flashing at the moment the ball passes.
3. Observe a car on an inclined wire. Stretch a long wire diagonally
across the chalkboard with chalk marks at every metre. Time a car as it
accelerates past the marks.
4. Observe a ball on an incline. Roll a ball bearing down the groove
of a plastic meter stick Use a slow roller solid wheel turning on a
small
axis to roll down an incline.
5. Use a Duff's plane, chalk ball on incline. Use a ball that leaves
a trail while rolling down a chalk covered trough.
14.2.13 Path of a projectile, mid-air
target, monkey and hunter
See diagram 14.2.13
This experiment shows that the vertical and the horizontal velocities
of a projectile are independent of each other. The projectile is a ball
bearing and the target is a metal drink-can hanging from an
electromagnet.
The circuit of the electromagnet includes two bared wires fixed
parallel
to and each side of the axis of a cardboard tube. They project about
2.5
cm beyond the end of the tube. Complete the electrical circuit with a
short length of
copper wire resting on the projecting wires as a switch. Fix the tube
in a stand so
that it points towards the metal can. Note the angle of the cardboard
tube above the horizontal. Blow the ball bearing up the tube. When the
ball bearing passes the end of the cardboard tube, it displaces the
piece of copper wire, opens the switch and no electric current flows
through the electromagnet. So the
metal can is released to fall. The ball bearing can hit the metal drink
can in mid air if the angle of the cardboard tube above the horizontal
is correct. This experiment is called "The monkey and hunter" but
nowadays you use a tin can instead of a poor monkey!
14.2.14 Projectile paths
Water from a hose, hit a shuttlecock in front of the blackboard.
14.2.15 Parabolic trajectory of thrown chalk
See also 2.0.5: Conic sections, parabola | See also 2.0.6: Parabola equation
Throw a piece of chalk so it follows a parabolic path drawn on the
chalk board. Roll ink dipped balls down an incline onto a tilted stage
on an overhead projector. Roll a tennis ball covered with chalk dust
across
a tilted blackboard.
14.2.16 Gun and tunnel
A spring loaded gun on a cart shoots a ball vertically and after the
cart passes through a tunnel the ball lands in the barrel. A ball
fired
vertically from cart moving horizontally falls back into the barrel.
14.2.17 Mid-air target
A hunter shoots a compressed air at a target released when the gun
is fired The ball hits the target in mid air.
14.2.18 Range of a gun
Fire a spring loaded gun at various angles. Use a tennis ball serving
machine to find muzzle velocity and range of a gun
14.3.0 Measuring g
Acceleration due to
gravity,
falling objects, air resistance, electric stop clock, Distance - time
graph,
g = 2S / t2 14.3.1 Free fall timer
Time a ball as it drops 0.5 m, 1.0 m, 1.5 m, or 2.0 m. Drop a magnet
through
several
equally spaced coils of wire and examine the induced voltage on an
oscilloscope.
14.3.2 Dropping balls
Use a latching relay system for turning a standard timer on and off
so that an electromagnet releases the ball and starts the clock and a
catcher
stops the clock. Drop light and heavy balls through a multiple pass
light
beam and show the output on an oscilloscope.
14.3.3 Ink jet marker
Let slab of wood be dropped by a ink squirter which leaves lines at
equal time intervals. Use a rotating ink jet to spray a paper sleeve on
a falling meter stick.
14.3.4 Falling drops
Time 10 drips of water dripping through a tap at uniform rate.
14.3.5 Catch a meter stick, reaction time of a
person
See diagram 4.2.6
Drop a meter stick and use the distance it drops before catching it
to find the reaction time of the catcher. If a body falls from a
height
s, the distance it falls after t seconds = gt2 / 2. So if
you
measure s, you can obtain t, t = sqrt2S / g. Hold metre ruler
vertically
with the zero on the scale down and the 100 on the zero on the scale
up.
With your arm stretched horizontally, hold the ruler vertically between
the thumb and first finger with the lower edge of the first finger at
the
zero on the scale. Open your fingers then close them again as quickly
as
possible to catch the ruler again. Record the distance to the downward
edge of your first finger. Repeat the experiment and calculate the
average
distance down the metre stick. Use t = sqrt 2S / g to calculate the
time
of the falling ruler, i.e. your reaction time. Repeat the experiment
under
the following pairs of conditions:
1. Hold the ruler first with your
left
hand. Hold the ruler first with your right hand.
2. Talk to others
while
doing the experiment. Do not talk to others while doing the experiment.
3. Allow loud background music. Do not allow loud background music.
4. Try other contrasting conditions to see whether your reaction time
is affected.
14.3.6 Catch a coin
Catch a coin starting with the fingers at the midpoint of the coin.
14.3.7 Rotating turntable
Drop a ball on a turning phonograph turntable.
14.3.8 Pendulum-timed free fall
Let a pendulum released from the side hit a ball dropped from the
height
that gives a fall time equal to a quarter period of the pendulum.
14.3.9 Many bounce method
Time a bouncing ball for many bounces and find g using the
coefficient
of restitution.