Science 10th grade
LEARNING UNIT
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Curricular axis
Standard competencies
Background Knowledge
English Review topic
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LEARNING OBJECT
Why is it important to study the motion of objects in terms
of their velocity and acceleration?
SKILL 1: Explain the displacement of objects with uniform
rectilinear motion based on the interpretation of time Vs.
distance, and time Vs. Velocity graphs.
SKILL 2: Graph the displacement of objects with uniform
rectilinear motion.
SKILL 3: Explain the differences between acceleration and
velocity.
SKILL 4: Establish relations between object acceleration and
free falling.
SKILL 5: Determine the value of the acceleration of gravity
through experimentation.
SKILL 6: Establish relations between uniform rectilinear
motion and uniformly accelerated rectilinear motion in
projectile motion.
SKILL 7: Establish quantitative relations between angular
frequency, period, and velocity in uniform circular motion.
SKILL 8: Explain the relation between angular speed and
tangential speed in uniform circular motion.
SKILL 9: Establish similarities and differences between
speed, velocity and acceleration in uniform rectilinear
motion (URM), uniformly accelerated rectilinear motion
(UARM), and uniform circular motion (UCM).
English
Colombia
Physical Environment
Use biological, physical, and chemical models to explain
energy transformation and conservation.
Knowledge of velocity, acceleration, speed, and the
following types of motion: uniformly accelerated motion
(UAM), uniform rectilinear motion (URM), and uniform
circular motion (UCM).
Order of adjectives.
Displacement: vector that is the shortest distance from
the initial to the final position of a point P.
Motion: is a change in position of an object with respect to
time.
Vector: is a geometric object that
has magnitude (or length) and direction and can be added
to other vectors.
Definitions retrieved from Wikipedia, the free
Encyclopedia.
NAME: _________________________________________________
GRADE: ________________________________________________
INTRODUCTION
Objects present velocity and acceleration at all times, that may vary depending
on the type of object.
To exemplify the concept above, if a car travels at a speed of 40 km per hour,
how many kilometers will it travel in one hour?
By identifying the relation between distance and time, it is possible to answer
the previous question. However, if other variables are added, then the following
questions arise: how long to its destination? what is its acceleration?
There are different types of motion: uniform rectilinear motion, uniformly
accelerated rectilinear motion, uniform circular motion, etc. Depending on the
purpose, one or several of those types of motion can be widely studied.
OBJECTIVES
▪
▪
▪
To analyze URM, UAM, and UCM in terms of velocity and acceleration
To explain URM, UAM, and UCM differences.
To identify previous knowledge of URM, UAM, and UCM to contrast it with
new knowledge.
PRESENTATION
▪
Objects have motions that can be classified as follows, depending on their
characteristics: Uniform Rectilinear, Uniformly Accelerated Rectilinear, and
Uniform Circular Motion. In addition, objects have velocity and acceleration.
All those concepts will be developed in this unit.
ACTIVITY 1.1.
SKILL 1: Explain the displacement of objects with uniform rectilinear motion
based on the interpretation of time Vs. distance, and time Vs. Velocity graphs
Graph 1. Uniform Rectilinear Motion. Retrieved from:
http://www.quimicayalgomas.com/fisica/mru-movimiento-rectilineo-uniforme/
on 10/03/2016 at 5:49 pm
Velocity in URM is equal to travel time by travel distance (v=Δ/t), meaning that
velocity does not vary in relation to time, and the distance traveled can be found
by multiplying velocity by time.
When the travel time by travel distance function is graphed, the result is a
constant gradient since the velocity does not change, but the position of the
object does. For instance, if a car travels at 20 Km per hour, it means it travels
20 Km in an hour, 40 Km in two hours, and so on.
Activity 1.1. Exercise 1
Based on the previous example, come up with an exercise that involves time,
velocity, and traveled distance to exemplify Graph 1
ACTIVITY 1.2.
SKILL 2: Graph the displacement of objects with uniform rectilinear motion.
Graph 2. Uniformly Accelerated Rectilinear Motion.
As shown in Graph 2, the position of the object changes quickly in relation to
time, shaping an upwards parabola, and since its acceleration is constant it
represents a UAM, in which the final position is reached faster and the velocity
varies. For more details on this topic, watch the following video:
https://www.youtube.com/watch?v=0kQrz4dfxDw
Did you know that?
when you throw an object, two types of motion intervene: UAM and URM, which
combined result in projectile motion.
Activity 1.2. Exercise 1 A car travels with constant acceleration covering the
distances in Table 1 during the first 10 seconds of the trip. Graph the Distance
Vs. Time relation according to the information given, and provide an explanation.
Time (s)
Distance
(m)
2
5
4
20
6
45
8
80
10
125
Table 1. UAM. Time - Distance
ACTIVITY 1.3.
SKILL 3: Explain the differences between acceleration and velocity.
Velocity
Acceleration
m/s is how the change ratio of
displacement can be known, if the
magnitude and the direction are known.
Therefore, one meter per second is the
velocity in which an object travels one
meter, in one second, with a uniform
motion.
m/s2 is the velocity change ratio in
relation to time. Therefore, one meter
per second square is the acceleration
of an object, with varied uniform
motion, which velocity varies every
second.
Activity 1.3. Exercise 1
Watch the following video. In a paragraph, explain the differences between
velocity and acceleration units.
Retrieved from: https://www.youtube.com/watch?v=BMkSAsjJ9ZU
ACTIVITY 2.1.
SKILL 4: Establish relations between object acceleration and free falling.
When an object falls due to the gravitational force, they are in freefall. Freefall
acceleration is around 10 meters per second, or 10 m/s2. This acceleration is
the result of the gravitational force, which is in average 9.8 m/s2 on the Earth
rounded up to 10 m/s2.
Table 2 shows how the velocity of an object, from its resting state, on the Earth,
increases 10 m per second when in freefall. (Wikipedia, the free encyclopedia,
2016)
Fall Time
Acquired Velocity
(s)
(m/s)
0
0
1
10
2
20
3
30
4
40
5
50
SKILL 5: Determine the value of the acceleration of gravity through
experimentation.
The acceleration of gravity is the manifestation of the universal attraction that
impels objects towards the center of the Earth. Gravity determines the weight
of objects. The acceleration of gravity is notated with a ‘g’, and it is defined as
the constant increase of the velocity per time unit of a free falling object (La guia
metas, 2002).
Activity 2.1. Exercise 1
Find the acceleration of a free falling object with the following characteristics:
Fall Time
Acquired Velocity
(s)
(m/s)
0
0
1
2
2
4
3
6
4
8
5
10
Activity 2.1. Exercise 2.
Watch the following video and verify the acceleration of gravity through an
experiment. Prepare a comparative chart with the results you obtain and support
your results. https://www.youtube.com/watch?v=wIzvfki5ozU
ACTIVITY 2.2.
SKILL 6: Establish relations between uniform rectilinear motion and uniformly
accelerated rectilinear motion in projectile motion.
When an object is thrown with certain elevation angle, said object shows two
simultaneous motions: a vertical one (Y), and a horizontal one (X). The motion
along the X axis is a URM, and the one along the Y axis is a UAM which
acceleration is -g.
The following video will give you a much better idea:
https://www.youtube.com/watch?v=q6_bc3BDV4E
Activity 2.2. Exercise 1
1. Answer the following questions to complete the diagram in point 2 of this
activity:
Which forces act on the object? For an object to travel a long distance, what
must be taken into account and why?
2. Prepare a diagram to show the behavior of an object with projectile motion,
showing the relation between Uniform Rectilinear Motion and Uniformly
Accelerated Rectilinear Motion.
ACTIVITY 3.1
SKILL 7: Establish quantitative relations between angular frequency, period,
and velocity in uniform circular motion.
Learning Activity
Analyze the following exercise. Find the relation between angular frequency,
period, and velocity in a uniform circular motion (UCM)by preparing a concept
map in which the elements above are shown in a quantitative form.
Exercise
A car travels a 50 cm radius circumference with a frequency (F) of 10 Hz.
Find:
a) its period.
b) its angular speed.
c) its acceleration.
A 50 Hz frequency means a frequency of 50 1/s. To solve the problem, you
just need to apply some formulas.
We know that
, then
, angular speed (039)
The period (T) is
s (Period)
We know its angular speed and the radius, so we can calculate its tangential
speed:
, tangential speed.
Its acceleration is the centripetal acceleration, which is always heading towards
the center of the circumference. The value of said acceleration can be
calculated through any of the following two formulas:
And by using the second formula:
”
ACTIVITY 3.2
SKILL 8: Explain the relation between angular speed and tangential speed in
uniform circular motion.
“Tangential speed is the velocity of the object (Distance traveled in time).
Therefore, for different radiuses and at the same angular speed, the object
travels at several tangential velocities. The larger the radius, and with the same
quantity of rotations per second, the wider the distance traveled by the object,
since the perimeter of said circumference is larger and therefore the tangential
speed is also wider.” Retrieved from: http://www.fisicapractica.com/velocidadtangencial-UCM.php on 13/03/2016 at 12:26 am
Retrieved
http://www.humbertomosquera.com.co/Movimientocircular.html
13/03/2016 at 12:37 am
from:
on
Activity 3.2. Exercise 1
Based on the following video, do the exercise at the end of the Learning Activity:
Video: https://www.youtube.com/watch?v=9QDKnQm_poI
Exercise: An object rotates with UCM at 1240º in 10 s, with a radius of 0.5m.
Find its angular speed and tangential speed. Explain the relation between those
two.
ACTIVITY 3.3.
SKILL 9: Establish similarities and differences between speed, velocity, and
acceleration in uniform rectilinear motion (URM), uniformly accelerated
rectilinear motion (UARM), and uniform circular motion (UCM).
A motion is defined as rectilinear when it describes a straight trajectory. In this
type of motion, acceleration and velocity are always parallel. In general, two
specific cases of rectilinear motion are studied:
Uniform Rectilinear Motion, which trajectory, besides being a straight line, is
covered at a constant velocity; it is to say, with null acceleration. This implies
that the average velocity between two given moments will always have the same
value. In addition, instantaneous and average velocity of said motion will match.
Uniformly Accelerated Rectilinear Motion is the one in which an object moves
along a straight line with constant acceleration. This means that, at any time
interval, the acceleration of the object will always have the same value. For
instance, a free falling object, with constant gravity acceleration.
Circular motion is based on a constant rotation axis and radius: the trajectory
will describe a circumference. If, in addition, turning velocity is constant, then
uniform circular motion is produced, which is a particular circular motion with a
fixed radius and constant angular speed.
Velocity cannot be treated as a constant since, by being a vector quantity, it
involves speed and direction. Speed of velocity keeps constantly changing during
the whole motion, but the direction is constantly changing, being always tangent
to the circular trajectory. It implies the presence of certain acceleration that,
even if in this case does not make the speed of the velocity to vary, makes its
direction to change.
Average speed or celerity is the relation between the distance traveled and the
time taken to cover it. Its magnitude is noted as ‘v’. Celerity is dimension scalar
magnitude. Speed and velocity share the same dimension, but velocity is a
vector quantity. Instantaneous celerity precisely represents the speed of the
instantaneous velocity. The difference between velocity and speed is that the
former is a vector quantity and the latter is a scalar quantity” Retrieved from:
(Wikipedia, the free encyclopedia, 2016)
Activity 3.3. Exercise 1
Prepare a comparative chart, based on the text above, to establish the
similarities and differences between speed, velocity, and acceleration in URM,
UAM, and UCM.
ABSTRACT
An object is in motion when it changes its location in relation to a reference point
or object; said motion, depending on how the object behaves, may be different.
In Uniform Rectilinear Motion, the object moves in a straight line in which its
velocity does not change in relation to time. In Uniformly Accelerated Motion,
the object has equal changes in its velocity per each time unit, and therefore its
acceleration is constant.
Something similar happens with a free falling object in which said object starts
moving a velocity equal to zero and constantly increases it; for example, a free
falling object attracted by the Earth’s gravitational force, which is around 10
m/s2. On the other hand, if an object is thrown with an inclination angle, it will
have a combined motion: An AUM vertically and an URM horizontally.
Nevertheless, if the same object rotates around a fixed point, it will describe a
circular motion; and in such case, its angular speed is studied in relation to the
value of the angular displacement and the time it takes; its period, in terms of
the time it takes to give a full turn, and its frequency, which is related to the
number of turns per time unit.
HOMEWORK
Here, you will Find exercises to widen the acquired knowledge in terms of the
different types of motion:
1. Research and explain the concepts of trajectory and displacement.
2. Prepare a graph to compare acceleration Vs. time and Velocity Vs. time for
URM, UAM, and UCM. Then, compare them and explain the graph.
3. Based on daily-life situations, in one paragraph, explain and graph UAM, UCM,
and MRU.
4. Through an experiment, describe the difference between velocity and
acceleration.
5. Report your results in a paragraph.5. In groups of three students, design the
following objects, implement the steps suggested, explain your results and
socialize information with your classmates.
Materials:
●
A sliding rail
●
Three marbles (small, medium and big)
●
A wooden block (or a book may help)
●
A stop watch that counts tenths of seconds (digital watches have them).
Procedure:
1. Build the model shown above. The sliding rail must have the following
distances on it: 20, 40, and 60 cm.
2. Place one of the marbles on distance ‘0’ (try holding it with a pen, for
example). Release the marble (no throwing it, just releasing it) at the same
time you strip the stop watch (you can do both things yourself).
3. Stop the timer at the exact moment the marble is on the 20 cm mark.
4. Do the same when the marble is on the 40 cm mark.
5. Same thing when the marble is on the 60 cm mark (end).
6. Measure the time 4 times for each traveled distance, and then calculate the
measure of the obtained values.
NOTE: Repeat the same procedure for each marble and record their travel times
per each one of the traveled distances.
Results and Analysis:
Complete the following table for each marble and its average travel time:
Traveled
(cm)
distance
0
Time (s)
0
Squared time
0
Graph space - time
Graph distance - squared time.
Interpret the shape of each graph.
20
40
60
EVALUATION
1. Match the graph to its description
2. Match column A to column B with the corresponding characteristic.
Column A
1. __ URM
Column B
a) m/s.
2.
3.
4.
5.
__
__
__
__
UAM
UCM
Velocity
Acceleration
b)
c)
d)
e)
Constant Acceleration.
m/s2.
Circular Trajectory.
Constant Velocity.
3. Say if the following statements are True (T) or False (F):
a. Projectile motion involves only one dimension ( )
b. Acceleration is equal to gravity in free fall ( )
c.
The frequency in UCM is the number of turnings completed by an object (
)
4. Multiple choice question with single answer; mark with an ‘X’ the correct
answer: Which of the following motions is tangential speed and radial
speed?
a. Uniform rectilinear motion (URM)
c. Circular Motion
b. Uniformly accelerated motion
(UAM)
d. Uniform circular motion (UCM)
5. Answer: Which motion occurs when a spear is thrown?
1. Uniform rectilinear motion (URM) 2.
Uniform Circular Motion
3. Uniform Motion
4. Uniformly accelerated motion (UAM)
Being:
a) 1 and 2 are true
b) 1 and 4 are true
c) 2 and 3 are true
d) 2 and 4 are true
Bibliography
Fisica Práctica. (March 31, 2016). www.fisicapractica.com. Retrieved from:
www.fisicapractica.com: http://www.fisicapractica.com/velocidadtangencial-UCM.php
fisica y quimica en flash. (March 31, 2016). ESTUDIO DE UN MOVIMIENTO
RECTILINEO UNIFORMEMENTE ACELERADO. Retrieved from: ESTUDIO
DE UN MOVIMIENTO RECTILINEO UNIFORMEMENTE ACELERADO.:
http://fisicayquimicaenflash.es/cinematica/cinematica_lab03.htm
Frank P. Incropera, D. P. (1999). Fundamentos de transferencia de calor 4ta
edición. En D. P. Frank P. Incropera, Fundamentos de transferencia de
calor 4ta edición (pág. 2). Pearson Prentice Hall.
Hernan Puentes. (April 15, 2016). www.youtube.com. Retrieved from:
www.youtube.com: https://www.youtube.com/watch?v=hGjyJ2hpbVA
Hewit, P. G. (2004). Física conceptual novena ediciión. Atlacomulco: Pearson
Educación de México.
Jose Duran, e. a. (12 de 03 de 2016). www.youtube.com. Retrieved from:
www.youtube.com: https://www.youtube.com/watch?v=qod9RwpI0Do
La guia metas. (May 2002). Retrieved on MArch 27, 2016 from:
http://www.metas.com.mx/guiametas/La-Guia-MetAs-02-05-gl.pdf
LEXIS. (5 de 03 de 2016). LEXIS . Retrieved from: LEXIS:
https://sendafonaments.wordpress.com/2009/09/04/el-sistema-denumeracion-maya-numeros-mayores-de-100/
mas, q. y. (March 10, 2016). quimica y algo mas. Retrieved from: quimica y
algo mas: http://www.quimicayalgomas.com/fisica/mru-movimientorectilineo-uniforme/
MateMovil. (March 31, 2016). www.youtube.com. Retrieved from:
www.youtube.com: https://www.youtube.com/watch?v=CXju9jT_QDs
Mi Web de Física 2015. (March 31, 2016). Mi Web de Física 2015. Retrieved
from: Mi Web de Física 2015:
http://www.humbertomosquera.com.co/Movimientocircular.html
Profesor en linea. (s.f.). Retrieved on April 8, 2016 from:
http://www.profesorenlinea.cl/fisica/Fuerzas_paralelas.html
starterseries. (April 15, 2016). www.youtube.com. Retrieved from:
www.youtube.com: https://www.youtube.com/watch?v=FoVzlvbgr2Q
Wikipedia, the free encyclopedia. (18 de 04 de 2016).
https://es.wikipedia.org/. Retrieved from: https://es.wikipedia.org/: A
motion is defined as rectilinear when it describes a straight trajectory. In
this type of motion, acceleration and velocity are always parallel. In
general, two specific cases of rectilinear motion are studied:
GLOSSARY
Acceleration: rate at which the velocity of an object changes in time; changes
in velocity may occur bay changes in the magnitude (speed), the direction, or
both.
Acceleration = velocity/time interval change.
Distance: Traveled distance of an object from the starting point to its
destination.
Force: Any influence (expressed in newtons) that tends to accelerate, propel or
attract an object. Force is a vector quantity.
Frequency: for an object or vibration mean, the amount of vibrations per time
unit. When making a wave, the amount of crests that cross the same point in
the time unit.
Speed: the rate of promptness an object travels per time unit; velocity
magnitude. Term commonly related to velocity; change of a quantity divided by
the time said change takes. Speed =Distance/time
Velocity: speed of an object including its movement direction; equal to a vector
quantity
Tangential speed: component of velocity that is tangent to the trajectory of a
projectile.
Angular speed: rotary speed involving a direction: the direction of the
rotation axis or revolution. (Specified source is no valid).