Class4 physics

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KINEMATICS
ONE DIMENTIONAL MOTION
A car moving at 10 m/s speeds up uniformily to a velocity of 30 m/s in a time of 5 seconds.
What was the car’s acceleration?
4m/s2
A bus is moving at a velocity of 20 m/s, when it begings to slow at a constan trate of 5m/s2 in
order to stop at a bus stop. If it comes to rest at the bus stop, how far away was the bus from
the stop?
40m
A block starting from rest slides down the length of an 18m plank with a uniform acceleration
of 4.0 m/s2. How long does the block take to reach the bottom?
3sec
An airplane initially flying at a speed of 60.0m/s2 accelerates at 5.0m/s2 for 600 meters. What
is its velocity after this acceleration?
98 m/s

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1. A biker passes a lamppost at the creat of a hill at +4.5 m/s. She acelerates down the hill at a constant rate of +0.40
m/s2 for 12 s. How far does she move down the hill during this time?
83m
2. A pilot stops a plane in 484 m using a constant acceleration of -8.0 m/s2. How fast was the plane moving before
braking began?
88m/s
3. Wile E. Coyote has strapped himself to an ACME rocket and is moving along at 25.0 m/s in pursuit of the roadrunner.
As he is cruising along he realices that he is heading directly for the edge of a cliff. He drags his feet in order to slow
down at a constant rate of 5.86m/s2 until he comes to rest. If the cliff is 35.0 meters away, by how much does he
overshoot the edge?
17.3m
4. A rocket traveling at 88m/s is accelerated to 132 m/s over a 15 second interval. What is its displacement in this time?
1650m
5. A car sits in an entrance ramp to a freewat, waiting for a break in traffic. The driver sees a small gap between two
vehicles and accelerates with constant acceleration along the ramp onto the freeway. The car starts from rest, moves in a
straight line, and has a speed of 20 m/s when it reaches the end of the 120-m ramp. What is the acceleration of the car?
1.7m/s2
6. How much time does it take the car to reach the end of the ramp?
12s
7. The traffic on the freeway is moving at a constant speed of 20m/s. What distance does traffic travel while the car is
moving the length of the ramp?
240m
KINEMATIC PROBLEMS

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An airplane drops a payload while traveling due north, parallel to the
ground, at a constant speed of 100m/s. If air resistance is neglected, what
it the velocity of the payload relative to the plane 4.0s after it is released?
A)0
B)40m/s down
C)80m/s down
D)100m/s north and 40m/s down
E)100m/s south and 40 m/s down
Source: GRE Physics Test Practice Book 2013

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Source: GMAT 2016
Car A is 20 miles behind Car B, which is traveling in the same direction
along the same route as Car A. Car A is traveling at a constant speed
of 58 miles per hour and Car B is traveling at a constant speed of 50
miles per hour. How many hours will it take for Car A to overtake and
drive 8 miles ahead of Car B?
A)1.5 B)2.0 C)2.5 D)3.0 E)3.5

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DESCRIBE FREE FALL WITH EQUATIONS

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FREE FALL PROBLEMS
1. Find the velocity of an egg that is dropped off the Media Center as it impacts the ground, if the media
center roo fis 15 m tall. Find the velocity of the egg if it is thrown downwards at 10m/s.
2. How long will it take for a ball kicked straight upwards at 17m/s to reach its highest point?
What will be the displacement of the ball at this point?
What will be the approximate velocity of the ball when it returns the ground?
3. Find the velocity and displacement of a ball that is tossed upward at 20m/s from the edge of a tall
building, 6 seconds after the ball is released.
4. A ball is thrown upwards by a small boy. If you measure the time it takes the ball to reach its highest
point to be 0.5 seconds, how long will the ball be in the air altogether provided the boy catches the ball
5. If you toss a ball upwards at 6m/s, how long will it take to return to your hand?
How fast will the ball be moving when you catch it?

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PROJECTILE MOTION

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Maximizing the Firing Angle of a Projectile
Suppose a projectile is fired from ground level with an initial velocity v0 .
1. At what angle should the projectile be fired to maximize the down range distance?
2. If the projectile is fired up a ramp which makes an angle of …. with respect to the
horizontal
what angle should the projectile be fired to maximize the distance traveled down the
ramp.

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FREE BODY DIAGRAMS

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NEWTON’S LAWS
The ideal models of a particle or point mass constrained to move along
the x-axis, or the motion of a projectile or satellite, have been studied
from Newton’s second law
𝑭 = 𝒎𝒂
In the mks systems of units, F is the forcé in Newtons, m is the mass in
kilograms and a is the acceleration in meter per second per second.
The closely-related Newton universal gravitation law
𝑭 = 𝑮
𝒎𝟏𝒎𝟐
𝑹 𝟐
Is used in conjuncition with (1) to determine the system’s constant value
g of gravitational acceleration. The masses m1 and m2 have centroids
at a distance R. For the earth g=9.8m/s2 is commonly used

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79. A block with mass m1 that slides on a frictionless table is
attached by a massless string over a massless, frictionless pulley to
a hanging ball with mass m2, as shown in the figure above. The
tensión in the string must be
A)Equal to m2g
B)Greater than m2g
C)Less than m2g
D)Equal to m1g
E)Greater than m1g
Source: GRE Physics Test Practice Book 2013

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The temperatures at the Golden Gate bridge can vary from -20 °C to +40°C. If
the bridge is made out of steel (α = 1.1x10-5 °C-1), how much will the length of
the bridge change for this temperatura change? The length of the Golden Gate
Bridge is around 1250 meters.
Using the de_nition for α in linear expansion, we have:
∆𝐿 = 𝐿0 𝛼∆𝑇
∆𝐿 = 1250 1.1𝑥10−5
60
∆𝐿 ≈ 0.825𝑚𝑒𝑡𝑒𝑟𝑠
since ∆𝑇 is 60°C. Expansion joints are needed to handle the temperature change.

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CALORIMETRY
Calorimetry is the accurate and precise measurement of heat flow
for chemical and physical processes.
It operates under the law of conservation of energy:
Heat loss = Heat gained
A device used to measure the absorption or reléase of this heat is
called Calorimeter
The relationship between the temperatura change of an object
and the resulting heat flow is:
∆𝑄 = 𝑚 𝑘𝑔 𝑥𝐶𝑒(
𝐶𝑎𝑙𝑜𝑟𝑖𝑒𝑠
𝑔𝑟𝑎𝑚. °𝐶
)∆𝑇

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CALORIMETRY-SPECIFIC HEAT AND LATENT HEAT
In Thermodynamics we saw that energy is needed to break inter-atomic
attractions when a substance melts or boils.
This energy is called latent heat.
The temperatura is constant during this change of state.
The following equation is used to calculate energy needed for a change
of state.
Heat transferred = mass x specific latent heat capacity
∆𝑄 = 𝑚 𝑘𝑔 𝑥𝐿(𝐽 𝐾𝑔−1
)
Specific latent heat, L is the energy needed to change the state of 1kg
of the substance (without change in temperatura)

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CALORIMETRY-SPECIFIC HEAT AND LATENT HEAT

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Your task is to design an immersion heater that will bring a cup of 400
grams of water from a temperature of 20°C up to a temperature of
100°C. You want the heating time to be 2 minutes. What should the
wattage be for your immersion heater.
𝑄 = 𝑚𝐶𝑒∆𝑇
= 400𝑔𝑟𝑎𝑚𝑠
1𝑐𝑎𝑙
𝑔𝑟𝑎𝑚°𝐶
80°𝐶
= 32000𝑐𝑎𝑙 = 133952𝐽𝑜𝑢𝑙𝑒𝑠
If this much energy needs to be transfered in 2 minutes (120 seconds), the
power of the heater must be
𝑃𝑜𝑤𝑒𝑟 =
133952𝐽𝑜𝑢𝑙𝑒𝑠
120𝑠𝑒𝑐
≈ 1116𝑊𝑎𝑡𝑡𝑠

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Exercise: Raman is served 500 grams of very hot tea, which is at a
temperature 100°C. He wants to add some ice at -10°C to cool it to
60°C. How much ice should he add?
500.1.40 = 𝑥 0.5 10 + 80𝑥 + 𝑥(1)(60)
The first term on the right is the energy gained by the ice as its temperatura
increases from -10° to 0°. The middle term, 80x, is the energy gained when the
x grams of ice melts without changing temperatura. The last term on the right
is the energy gained when x grams of wáter has a temperatura increase of
60°C. Solving for x gives
𝑥 =
20000
145
≈ 138𝑔𝑟𝑎𝑚𝑠

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Ronald McDonald wants to help with the energy problem by not
wasting the ice in his drink. He wants to know how much ice at 0°C
he should add to 500 grams of wáter at 20°C so that the wáter
cools down to 0°C just as the last bit of ice melts. How many grams
of ice should he add to his 500 gram drink?
HOMEWORK EXERCISE

LAW OF CONSERVATION OF ENERGY
In a closed system, i.e., a system that isolated from its surroundings, the total energy
of the system is conserved.
In SI units, energy has units of Joules. 1 Joule = 1 kg.m2.s-2.
SOME FORMS OF ENERGY:
1. Kinetic energy-energy of motion.
2. Potential energy-energy of location with respect ot some reference point.
3. Chemical energy-energy stored in chemical bonds, which can be released in
reactions.
4. Electrical energy-energy created by separating charges; energy stored in a battery,
for example.
5. Thermal energy-energy given off as heat, such as friction.
Since everything has a microscopic origin, the last three are really cases of potential and
kinetic energies, however, the classification is useful.
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CONSERVATION OF ENERGY

The kinetic energy of an object of mass m, moving with a velocity v is given by:
𝑲𝑬 =
𝟏
𝟐
𝒎 𝒗 𝟐
Recall that 𝑣 is the speed v of the particle
The gravitational potential energy is a little less straightforward.
𝑷𝑬 = 𝒎𝒈𝒉
Where g is the acceleration due to the Earth’s gravity.
The elastic potential energy is potential energy stored as a result of deformation of
an elastic object, such as the stretching of a spring.
𝑬𝑷𝑬 =
𝟎
𝒙
𝒌𝒙𝒅𝒙 = 𝒌
𝒙 𝟐
𝟐
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The Total Mechanical Energy
The total amount of mechanical energy is the sum of the potential
energy and the kinetic energy.
𝑻𝑴𝑬 = 𝑷𝑬𝒈𝒓𝒂𝒗 + 𝑷𝑬𝒔𝒑𝒓𝒊𝒏𝒈 + 𝑲𝑬

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THERMODYNAMICS
Thermodynamics is the study of the effects of work heat and energy on
a system. Thermodynamics is only concerned with large scale
observations.

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THERMODYNAMIC LAWS

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28. A sample of nitrogen gas undergoes the cyclic
thermodynamic process shown above. Which of the following
gives the net heat transferred to the system in one complete
cycle 1 -> 2 -> 3 ->1?
A)-80J
B)-40J
C)40J
D)80J
E)180J

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PRESSURE IN A LIQUID
Atomospheric pressure p0 pushes down with a forcé of p0A
The weight of the column pushes down
With force mg.
For a liquid with density ρ
m= ρV =ρAd
Because the liquid is in static equilibrium, the upward force from
pressure, pA, must equal the downward forces.
pA = p0A + ρAdg so p = p0 + ρgd (hydrostatic pressure)
When you descend in a liquid, the weight of the liquid above you causes
the pressure to increase

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Three vessels are full of the same liquid and open to the same
atmosphere. The pressure is measured in each at a distance of 3m
below the surface. What can we say about the pressures?
A. Only two are the same
B. All three are different
C. All three are the same
The hydrostatic pressure is

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ARCHIMEDES PRINCIPLE
A body partially or fully immersed in a fluid feels an upward force equal
to the weight of the displaced fluid.
This force is called the buoyant force: 𝑭 𝑩 = 𝝆 𝒇 𝑽 𝒇 𝒈
If the object is fully immersed then the volumen of the displaced fluid is
equal to the volumen of the object: 𝑽 𝒇 = 𝑽 𝟎
Note that volumen is related to mass and density: 𝒎 𝟎 = 𝝆 𝟎 𝑽 𝟎
If an object is only partially submerged, the volumen of the displaced
fluid is less than the volumen of the object: 𝑉𝑓 < 𝑉0

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BUOYANCY

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BOUYANCY

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Exercise: A 2 cm by 2 cm cube of iron (ρ = 8 g/cm3) is weighed
with the iron outside, half in and fully in the wáter, as shown in
the diagram. Waht is the measure weight in each case?

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Buyancy question: An ice cube is floating in a glass of wáter. As
the ice cube melts, the level of the wáter…
A. Rises
B. Falls
C. Stays the same
Response:
The buoyant forcé is always equal to the weight of the liquid displaced by
the object.
Since the ice cube is in equilibrium, the weight of wáter displaced is
equal to the weight of the ice cube.
When the ice cube melt it becomes wáter with the same weight as the
ice cube so real wáter takes the place of the displaced water

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ELECTRIC CURRENT
What is Electric Current?
An electric current is formed by moving charges
Definition:
An electric current is a measure of the rate of flow of electric
charge through a given cross-section of a conductor
𝑰 =
𝑸
𝒕
Where: I=current;
Q=charge;
t=time taken.
The SI unit of electric current is the ……………(A)

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STATIC VS CURRENT ELECTRICITY

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Resistors in Series and Parallel

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Example: In the following circuit calculate the total current
( IT ) taken from the 12v supply.
Source: https://www.electronics-tutorials.ws/resistor/res_5.html

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For the circuit shown in the figure above, what is the current i through the 2Ω
resistor?
A)2 A B)4 A C)5 A D)10 A E)20 A

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LAW OF MAGNETISM
Magnets and magnetic materials créate pulling and pushing forces on
each other when they are close. They attract or repel each other
Like poles repel
Unlike poles attract
Different poles attract Same poles repel
Source: Learning Comes First
https://app.oncoursesystems.com/school/webpage/19815/624172

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NATURE OF MAGNETISM
It is now believed that magnetism is due to the spin of electrons within
the atoms.
Since the electron is a charged particle, the concept implies that
magnetism is a property of a charged particle in motion

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MAGNETIC FIELD OF FORCE
Magnetic force on a moving charge is directed perpendicular to the
magnetic field.
It is found experimentally that the strength of the magnetic force on the
particle is proportional to the magnitude of the charge q, the magnitude of
the velocity v, the strength of the external magnetic field B, and the sine of
the angle between the direction of v and the direction of B.
𝑭 = 𝒒𝒗𝑩𝑺𝒊𝒏𝜽
This expression is used to define the magnitude of the magnetic field as:
𝑩 =
𝑭
𝒒𝒗𝑺𝒊𝒏𝜽

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Source: www.shutterstock.com
FLEMING’S RIGHT HAND RULE

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MAGNETIC FIELD OF CURRENT
The magnetic field lines around a
long wire which carries an electric
current form concentric circles
around the wire. The direction of
the magnetic field is perpendicular
to the wire and is in the direction
the fingers of your right hand
would curl if you wrapped them
around the wire with your thumb
in the direction of the current.
Source: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

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Earth’s Magnetic
Field Earth has a
moving liquid iron
core. A moving
conductor creates
electric currents.
Electric currents
make magnetic fields.
Earth’s magnetic field
Source: https://www.nasa.gov/topics/earth/features/2012-poleReversal.html

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http://whsastronomy.blogspot.com/2018/02/what-causes-northern-lights.html
Source: What Causes the Northern Lights?
NORTHEN LIGHTS EXPLANATION
Earth's magnetic field prevents charged
particles in the solar wind from reaching the
surface

47
[1] Cómo un baño dio lugar al principio de Arquímedes - Mark Salata
[Online] Available:
https://www.youtube.com/watch?v=ijj58xD5fDI
[2] Bouyancy, what’s bouyancy?
[Online] Available:
https://slideplayer.com/slide/8427435/
[3] Definición de FPGA dada por Xilinx
[Online] Available:
http://www.xilinx.com/products/silicon-devices/fpga/index.htm
[4] Magnetic Field of Current
[Online] Available:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html
[5] Circuit Design with VHDL
Volnei A. Pedroni
[6] What Causes the Northern Lights?
[Online] Available:
http://whsastronomy.blogspot.com/2018/02/what-causes-northern-lights.html
[7] GRE Physics Test
Practice Book 2013
[8] The official Guide for GMAT review 2016
Graduate management admission council mba.com
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4823/10/2018 Taller 2018
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