A resolver problemas
Problema 1
1. ¿Cuál es la trayectoria más corta?
2. ¿Con qué finalidad se utilizaría?
3. ¿Con cuál se desplazó más?
Problema 2
• ¿Por qué las hormigas
siempre terminan llegando
a su alimento utilizando la
trayectoria más corta?
• Piensen en tres ejemplos
más en los que fuera
sensato usar dicha línea…
como
camino
para
trasladarse.
Colonia de hormigas
• La idea original proviene de la observación de la
explotación de los recursos alimentarios entre hormigas,
en el que las habilidades cognitivas de las hormigas son
individualmente limitadas y en conjunto son capaces de
buscar el menor camino existente entre la fuente de
comida y su nido o colonia.
• La primera hormiga encuentra la fuente de alimentos
(F), a través de cualquier camino (a), entonces retorna a
la colonia (N), dejando tras sí un rastro de feromonas;
• Las hormigas indiscriminadamente siguen cuatro
caminos posibles, pero el fortalecimiento de la pista
hace más atractivo la ruta más corta;
Colonia de hormigas
• Las hormigas toman la ruta más corta y largas porciones de
otras rutas empiezan a perder su rastro de feromonas.
• En una serie de experimentos en una colonia de hormigas
donde existe la elección de dos rutas diferentes que llevan
hasta la fuente de comida, los biólogos observaron que las
hormigas tienden a usar la ruta más corta.
• El siguiente modelo explica este comportamiento:
1. Una hormiga (llamada “blitz”) vaguea de manera aleatoria
alrededor de la colonia;
2. Si esta encuentra una fuente de comida, ella retorna a la
colonia de manera más o menos directa, dejando tras sí un
rastro de feromonas;
Colonia de hormigas
3. Estas feromonas son atractivas, las hormigas más cercanas
se verán atraídas por estas y seguirán su pista de manera
más o menos directa;
4. Regresando a la colonia estas hormigas habrán fortalecido
dicha ruta;
5. Si existen dos rutas para que llegan a la misma fuente de
alimentos entonces, en una misma cantidad de tiempo dado,
la ruta más corta será recorrida por más hormigas que la
ruta más larga;
6. La ruta más corta habrá aumentado en cantidad de
feromonas y por tanto empezará a ser más atractiva;
7. La ruta más largar irá desapareciendo debido a que las
feromonas son volátiles;
8. Finalmente, todas las hormigas habrán determinado y
escogido el camino más corto.
Problema 3
• Imagina que planeas hacer un viaje en automóvil
desde Mazatlán hasta Veracruz. Según el mapa,
la distancia que separa ambos puntos es de
aproximadamente 1160 km en línea recta. Pero
al consultar una guía de carreteras, te
encuentras que la trayectoria más corta por la
carretera federal 15 tiene una distancia de 1404
kilómetros.
Problema 3
http://mx.lasdistancias.com/
Problema 3
http://mx.lasdistancias.com/
Preguntas de discusión
• ¿Puedes explicar esta diferencia de kilómetros
utilizando los conceptos de distancia,
desplazamiento y trayectoria?
• ¿Cuánto tardaría el viaje si la rapidez promedio
fuera siempre de 100 km/h?
• ¿Será lo mismo en tiempo y distancia viajar de
Mazatlán a Veracruz que de Veracruz a
Mazatlán?
• ¿El desplazamiento será el mismo en estos
viajes?
Problema 4
• Escuchas por radio
que una tormenta
eléctrica está
viajando con una
rapidez de 25 km/h.
• ¿Te deberías
preparar para la
tormenta?
• ¿Cuál es la diferencia
entre rapidez y
velocidad?
DESCRIBING MOTION WITH WORDS
Distance vs displacement
Speed vs Velocity
http://www.physicsclassroom.com/
1-D Kinematics Lessons a) to d)
http://www.tutorvista.com/physics/
Old word, new concepts
• You have used words and phrases such
as going fast, stopped, slowing down,
speeding up, and turning provide a
sufficient vocabulary for describing the
motion of objects.
• We will be expanding upon this vocabulary
list with words such as distance,
displacement, speed, velocity, and
acceleration.
Scalars and vectors
Scalars vs vectors
• The mathematical
quantities that are used to
describe the motion of
objects can be divided
into two categories.
• The quantity is either a
vector or a scalar.
• These two categories can
be distinguished from one
another by their distinct
definitions:
Scalars
• Scalars are quantities
that are fully
described by a
magnitude (or
numerical value)
alone.
Vectors
• Vectors are
quantities that are
fully described by
both a magnitude and
a direction.
Common directions:
•
•
•
•
•
•
Forward
Backward
Northward
Southward
Eastward
Westward
Examples
Exercise 01
•
Consider the following quantities listed
below. Categorize each quantity as being
either a vector or a scalar.
a)
b)
c)
d)
e)
f)
5 meters
30 m/sec, East
5 miles, North
20 degrees Celsius
256 bytes
4000 Calories
Distance vs displacement
Distance and Displacement
• Distance and
displacement are
two quantities that
may seem to mean
the same thing yet
have distinctly
different definitions
and meanings.
Distance
• Distance is a scalar quantity that refers to
"how much ground an object has covered"
during its motion.
• Distance can be defined as how far two
objects are. Distance in physics may refer
to physical length.
• Distance is the scalar path between two
locations measured along path connecting
them.
Example 01
• In the right figure you can
see a rat and cheese. If
the rat want the cheese it
must follow the blue path.
And the length of blue
path is the distance. Or it
can be said in another
way. How far the rat is
from cheese. If you ask
this question your self the
result you get is nothing
but the distance.
Displacement
• Displacement is a vector
quantity that refers to "how
far out of place an object
is"; it is the object's overall
change in position.
• Displacement can be
defined as shortest distance
between the starting point
and end point.
• Displacement can be
defined as imaginary
straight path which is
different from the actual
path.
Example 01
• In the left figure the green
path present between the
rat and cheese is the
displacement because it
is the shortest path.
• So by this we can
conclude displacement
is a vector measure of
the interval between
two locations measured
along the shortest path
connecting them
Example 02
Example 03
• A physics teacher walks 4 meters East, 2 meters
South, 4 meters West, and finally 2 meters
North.
• Even though the physics teacher has walked a
total distance of 12 meters, her displacement is
0 meters.
• During the course of her motion, she has
"covered 12 meters of ground" (distance =12 m).
• Yet when she is finished walking, she is not "out
of place" - i.e., there is no displacement for her
motion (displacement = 0 m).
Example 04
•
You ride your bicycle from
Manhattan to New Jersey.
• Getting there is a three step
process.
1. Follow the Hudson River 8.2 km
upriver.
2. Cross using the George
Washington Bridge (1.8 km
between anchorages).
3. Reverse direction and head down
river for 4.5 km.
• The distance traveled is a
reasonable 14 km, but the
resultant displacement is a mere
2.7 km north. The end of this
journey is actually visible from the
start. Maybe I should buy a canoe.
Example 05
• Use the diagram to determine the resulting displacement
and the distance traveled by the skier during these three
minutes.
• The skier covers a distance of (180 m+140 m+100 m) =
420 m and has a displacement of 140 m, rightward.
Exercise 01
• The distance traveled by
an object is the total
length that is traveled by
that object.
• Displacement of an
object from a point of
reference, O is the
shortest distance of the
object from point O in a
specific direction.
• What is the distance
travelled and the
displacement?
Answer 01
• Distance travelled = 200m
Displacement = 120 m, in the direction of
Northeast
• Distance is a scalar quantity,
• Displacement is a vector quantity
Exercise 02
• What is the displacement of the crosscountry team if they begin at the school,
run 10 miles and finish back at the school?
Answer 02
• The displacement of the runners is 0 miles.
• While they have covered a distance of 10 miles,
they are not "out of place" or displaced.
• They finish where they started. Round-trip
motions always have a displacement of 0.
Exercise 03
• What is the distance
and the displacement
of the race car drivers
in the Indy 500?
Answer 03
• The displacement of the cars is
somewhere near 0 miles since they
virtually finish where they started.
• Yet the successful cars have covered a
distance of 500 miles.
Exercise 04
• What’s the distance?
• What is the displacement?
Answer 04
• In the last figure we can see earth moving
around the sun. Let the earth begin its
journey around the sun from point A. After
one year the again it will reach the point A.
• Now the path which the earth followed is
elliptical path. So the distance travelled is
nothing but the circumference of that
elliptical path.
How far does the Earth
travel in one year?
• In terms of distance, quite far (the circumference
of the earth's orbit is nearly one trillion meters),
but in terms of displacement, not far at all (zero,
actually).
• At the end of a year's time the earth is right back
where it started from. It hasn't gone anywhere.
• Since both the starting point and the end point
are same it is zero. Hard to believe but it is true.
By this you can understand the difference
between distance and displacement.
Exercise 05
Describe distance travelled and displacement.
Answer 05
• IN THE FIGURE LET THE STARTING POINT
OF THE EARTH BE A AND POINT BE D. NOW
• DISTANCE=
• CIRCULAR LENGTH BETWEEN A AND B +
CIRCULAR LENGTH BETWEEN B AND C +
CIRCULAR LENGTH BETWEEN C AND D.
• DISPLACEMENT = LENGTH OF BLACK LINE
WHICH YOU CAN SEE FROM THE FIGURE.
• THIS IS ALL ABOUT DIFFERENCE BETWEEN
DISTANCE AND DISPLACEMENT.
• HOPE YOU ENJOYED IT !
Speed vs Velocity
Reactivate
• What do you think
when you hear the
word “Speed”?
• Describe a sport or
activity in which
speed is important?
• What examples are
there of velocity?
• Do these concepts
mean the same?
Speed
• The motion of an airplane
is fast. (260 m / second)
• The motion of a snail is
slow. (1 mm / second)
• By using these words,
your are describing the
object’s speed.
• The speed or the airplane
is much greater that the
speed of the snail
because the airplane
travels mucho farther
than the snail in the same
amount of time.
Gary the snail
Speed (Scalar quantity)
• Refers to "how fast an
object is moving“
• Speed is the rate of
change in distance with
respect to time.
• A fast-moving object has
a high speed while a
slow-moving object has a
low speed.
• An object with no
movement at all has a
zero speed.
So, What is speed?
• The speed of an object is the distance
the object moves per unit of time.
• To calculate the speed of an object, divide
the distance the object travels by the
amount of time it takes to travel that
distance. (m/s = meters per second)
What is the relationship between
speed, traveled distance and time?
Calculating Speed
• The motorcyclist has
traveled a total
distance of 24
Kilometers in 3 hours.
What has his average
Speed?
Exercise 01
• While on vacation, Lisa Carr traveled a total
distance of 440 miles. Her trip took 8 hours.
• What was her average speed?
Exercise 02
• You are driving to Mexico
to visit your Grandmas to
eat her scrumpcious
snickerdoodle cookies. In
5 hours you drove 1000
meters to stop for milk.
You still had 940 more
meters to go.
• If you got to grandmas
house in a total of 8 hours
what is your average
velocity between your
milk rest and grandmas.
Velocity (vector quantity)
• Refers to "the rate at
which an object
changes its position“.
• Velocity is the rate of
change in
displacement with
respect to time.
Example
• You hear that a thunderstorm is travelling at a
speed of 25 km/h. Should you prepare for the
storm?
– Can you know the velocity of the storm?
– What do you need?
Exercise 01
• The physics teacher
problem
• ¿What was the
distance travelled?
• If he entire motion
lasted 24 seconds
¿What was the
average speed?
• ¿What is the velocity
of the teacher?
Air traffic controllers & stunt pilots
Exercise 02
• A car travels 90. meters due north in 15 sec.
• Then the car turns around and travels 40.
meters due south in 5.0 seconds.
• What is the magnitude of the average velocity of
the car during this 20 - second interval?
• A)2.5 m/s
• B)5.0 m/s
• C)6.5 m/s
• D)7.5 m/s
Exercise 03
• The position of an object is +35 meters at
2.0 seconds and is +87 meters at 15
seconds.
• Calculate the average velocity of the
object.
Remember
• If you know the distance an object travels
in a certain amount of time, you can
calculate the speed of the object.
• When you know both the speed and the
direction of an object´s motion, you know
the velocity of the object.