This is a re-purposed presentation, the information provided was taken from the works of the people who are acknowledged in the last slide of this presentation about the Newtons Law of Motions...Enjoy!!!
With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
Gravity The importance of Gravity What if gravity is too strongMervatMarji2
Directly proportional to the product of the masses of the objects being attracted
Inversely proportional to the distance between the objects squared
𝐹=𝐺 𝑚1𝑚2/𝑑^2
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the conver
hssb0704t_powerpresDNA as the transforming principle..pptMervatMarji2
Avery performed three tests on the transforming principle.
Qualitative tests showed DNA was present.
Chemical tests showed the chemical makeup matched that of DNA.
Enzyme tests showed only DNA-degrading enzymes stopped transformation.
Hershey and Chase confirm that DNA is the genetic material.
• Hershey and Chase studied viruses that infect bacteria, called bacteriophages.
• Tagged DNA was found inside the bacteria; tagged proteins were not.
They tagged viral DNA with radioactive phosphorus.
They tagged viral proteins with radioactive sulfur.
• Tagged DNA was found inside the bacteria; tagged proteins were not.
DNA structure is the same in all organisms.
• DNA is composed of four types of nucleotides.
• DNA is made up of a long chain of nucleotides.
Each nucleotide has three parts:
₋ a phosphate group.
₋ a deoxyribose sugar.
₋ a nitrogen-containing base
The nitrogen containing bases are the only difference in the four nucleotides.
Scientists Chargaff found:
The amount of adenine in an organism approximately equals the amount of thymine.
The amount of cytosine roughly equals the amount of guanine.
A=T C=G Chargaff’s rules
Watson and Crick determined the three-dimensional structure of DNA by building models.
They realized that DNA is a double helix that is made up of a sugar-phosphate backbone on the outside
with bases on the inside.
Watson and Crick’s discovery was built on the work of Rosalind Franklin and Erwin Chargaff.
₋ Franklin’s x-ray images suggested that DNA was a double helix of even width.
₋ Chargaff’s rules stated that A=T and C=G.
Nucleotides always pair in the same way.
The base-pairing rules show how nucleotides always pair up in DNA.
Because a pyrimidine (single ring) pairs with a purine (double ring), the helix has a uniform width.
A pairs with T
C pairs with G
The backbone is connected by covalent bonds.
The bases are connected by hydrogen bonds.
• Proteins carry out the process of replication.
• DNA serves only as a template.
• Enzymes and other proteins do the actual work of replication.
₋ Enzymes unzip the double helix.
₋ Free-floating nucleotides form hydrogen bonds with the template strand.
₋ DNA polymerase enzymes bond the nucleotides together to form the double helix.
₋ Polymerase enzymes form covalent bonds between nucleotides in the new strand.
₋ Two new molecules of DNA are formed, each with an original strand and a newly formed strand.
• Two new molecules of DNA are formed, each with an original strand and a newly formed strand.
• DNA replication is semiconservative.
Replication is fast and accurate.
DNA replication starts at many points in eukaryotic chromosomes.
There are many origins of replication in eukaryotic chromosomes.
DNA polymerases can find and correct err
This is a re-purposed presentation, the information provided was taken from the works of the people who are acknowledged in the last slide of this presentation about the Newtons Law of Motions...Enjoy!!!
With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
Gravity The importance of Gravity What if gravity is too strongMervatMarji2
Directly proportional to the product of the masses of the objects being attracted
Inversely proportional to the distance between the objects squared
𝐹=𝐺 𝑚1𝑚2/𝑑^2
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the converse of a theorem is found by exchanging the hypothesis and conclusion. The converse of a theorem is not automatically true. If it is true, it must be stated as a postulate or proved as a separate theorem.
Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
What if…? Suppose the corresponding angles on the opposite side of the boat measure (4y – 2)° and (3y + 6)°, where
y = 8. Show that the oars are parallel
A line through the center of the horizontal piece forms a transversal to pieces A and B.
Use the given information and the theorems you have learned to show that r || s.
Use the given information and the theorems you have learned to show that r || s.
A carpenter is creating a woodwork pattern and wants two long pieces to be parallel. m1= (8x + 20)° and m2 = (2x + 10)°. If x = 15, show that pieces A and B are parallel.
Recall that the conver
hssb0704t_powerpresDNA as the transforming principle..pptMervatMarji2
Avery performed three tests on the transforming principle.
Qualitative tests showed DNA was present.
Chemical tests showed the chemical makeup matched that of DNA.
Enzyme tests showed only DNA-degrading enzymes stopped transformation.
Hershey and Chase confirm that DNA is the genetic material.
• Hershey and Chase studied viruses that infect bacteria, called bacteriophages.
• Tagged DNA was found inside the bacteria; tagged proteins were not.
They tagged viral DNA with radioactive phosphorus.
They tagged viral proteins with radioactive sulfur.
• Tagged DNA was found inside the bacteria; tagged proteins were not.
DNA structure is the same in all organisms.
• DNA is composed of four types of nucleotides.
• DNA is made up of a long chain of nucleotides.
Each nucleotide has three parts:
₋ a phosphate group.
₋ a deoxyribose sugar.
₋ a nitrogen-containing base
The nitrogen containing bases are the only difference in the four nucleotides.
Scientists Chargaff found:
The amount of adenine in an organism approximately equals the amount of thymine.
The amount of cytosine roughly equals the amount of guanine.
A=T C=G Chargaff’s rules
Watson and Crick determined the three-dimensional structure of DNA by building models.
They realized that DNA is a double helix that is made up of a sugar-phosphate backbone on the outside
with bases on the inside.
Watson and Crick’s discovery was built on the work of Rosalind Franklin and Erwin Chargaff.
₋ Franklin’s x-ray images suggested that DNA was a double helix of even width.
₋ Chargaff’s rules stated that A=T and C=G.
Nucleotides always pair in the same way.
The base-pairing rules show how nucleotides always pair up in DNA.
Because a pyrimidine (single ring) pairs with a purine (double ring), the helix has a uniform width.
A pairs with T
C pairs with G
The backbone is connected by covalent bonds.
The bases are connected by hydrogen bonds.
• Proteins carry out the process of replication.
• DNA serves only as a template.
• Enzymes and other proteins do the actual work of replication.
₋ Enzymes unzip the double helix.
₋ Free-floating nucleotides form hydrogen bonds with the template strand.
₋ DNA polymerase enzymes bond the nucleotides together to form the double helix.
₋ Polymerase enzymes form covalent bonds between nucleotides in the new strand.
₋ Two new molecules of DNA are formed, each with an original strand and a newly formed strand.
• Two new molecules of DNA are formed, each with an original strand and a newly formed strand.
• DNA replication is semiconservative.
Replication is fast and accurate.
DNA replication starts at many points in eukaryotic chromosomes.
There are many origins of replication in eukaryotic chromosomes.
DNA polymerases can find and correct err
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
1. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 1
Chapter 4
Forces and Newton’s Laws of Motion
2. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 2
Forces and Newton’s Laws of
Motion
• Forces
• Newton’s Three Laws of Motion
• The Gravitational Force
• Contact Forces (normal, friction, tension)
• Application of Newton’s Second Law
• Apparent Weight
3. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 3
The net force is the vector sum of all the forces acting
on a body.
3
2
1
net F
F
F
F
F
Net Force
The net force is the resultant of this vector addition.
Bold letters represent vectors. The units of Force are Newtons, or
the abbreviation N, which represent the SI units: kg-m/s2
4. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 4
Free Body Diagrams
The free body diagram (FBD) is a simplified representation of an object, and the
forces acting on it. It is called free because the diagram will show the object without
its surroundings; i.e. the body is “free” of its environment.
We will consider only the forces acting on our object of interest. The object is
depicted as not connected to any other object – it is “free”. Label the forces
appropriately. Do not include the forces that this body exerts on any other body.
The best way to explain the free body diagram is to describe the steps required to
construct one. Follow the procedure given below.
(1) Isolate the body of interest. Draw a dotted circle around the object that
separates our object from its surroundings.
(2) Draw all external force vectors acting on that body.
(3) You may indicate the body’s assumed direction of motion. This does not
represent a separate force acting on the body.
(4) Choose a convenient coordinate system.
5. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 5
Free Body Diagram
T F
w1
N1
x
y
The force directions are as
indicated in the diagram.
The magnitudes should be
in proportion if possible.
6. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 6
Newton’s First Law of Motion:
Inertia and Equilibrium
Newton’s 1st Law (The Law of Inertia):
If no force acts on an object, then the speed and
direction of itsmotion do not change.
Inertia is a measure of an object’s resistance to
changes in its motion.
It is represented by the inertial mass.
7. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 7
If the object is at rest, it remains at rest (velocity = 0).
If the object is in motion, it continues to move in a
straight line with the same velocity.
No force is required to keep a body in straight line
motion when effects such as friction are negligible.
An object is in translational equilibrium if the net
force on it is zero and vice versa.
Newton’s First Law of Motion
Translational Equilibrium
8. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 8
Newton’s Second Law of Motion
Net Force, Mass, and Acceleration
Newton’s 2nd Law:
The acceleration of a body is directly proportional to
the net force acting on the body and inversely
proportional to the body’s mass.
Mathematically: a
F
F
a m
m
net
net
or
This is the workhorse of mechanics
9. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 9
An object’s mass is a measure of its inertia. The
more mass, the more force is required to obtain a
given acceleration.
The net force is just the vector sum of all of the
forces acting on the body, often written as F.
Newton’s Second Law of Motion
If a = 0, then F = 0. This body can have:
Velocity = 0 which is called static equilibrium, or
Velocity 0, but constant, which is called dynamic
equilibrium.
10. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 10
Newton’s Third Law of Motion
Interaction Pairs
Newton’s 3rd Law:
When 2 bodies interact, the forces on the bodies,
due to each other, are always equal in magnitude
and opposite in direction.
In other words, forces come in pairs.
Mathematically: .
12
21 F
F
designates the force on object 2 due to object 1.
11. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 11
Types of Forces
Contact forces: Normal Force & Friction
Tension
Gravitational Force
12. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 12
Contact Forces
Contact forces: these are forces that arise due
to of an interaction between the atoms in the
surfaces of the bodies in contact.
13. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 13
Normal force: this force acts in the direction perpendicular
to the contact surface.
Normal force
of the ramp
on the box
N
w
Normal force of the
ground on the box
N
w
Normal Forces
14. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 14
Example: Consider a
box on a table.
FBD for
box
mg
w
N
w
N
Fy
that
So
0
This just says the magnitude of the normal force
equals the magnitude of the weight; they are not
Newton’s third law interaction partners.
Apply
Newton’s
2nd law
N
w
x
y
Normal Forces
15. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 15
Friction: a contact force parallel to the contact surfaces.
Static friction acts to prevent objects from sliding.
Kinetic friction acts to make sliding objects slow down. Sometimes
called Dynamic friction.
Frictional Forces
max
s s
f = μ N
d d
f = μ N
17. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 17
Tension
An ideal cord has zero mass, does not stretch,
and the tension is the same throughout the cord.
This is the force transmitted through a “rope”
from one end to the other.
18. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 18
Example (text problem 4.77): A pulley is hung from the ceiling by a rope.
A block of mass M is suspended by another rope that passes over the
pulley and is attached to the wall. The rope fastened to the wall makes a
right angle with the wall. Neglect the masses of the rope and the pulley.
Find the tension in the rope from which the pulley hangs and the angle .
FBD for the
mass M
w
T
x
y
Mg
w
T
w
T
Fy
0
Apply Newton’s 2nd
Law to the mass M.
19. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 19
FBD for the pulley:
0
sin
0
cos
T
F
F
T
F
F
y
x
Apply Newton’s 2nd Law:
sin
cos F
F
T
This statement is true
only when = 45 and
Mg
T
F 2
2
Example continued:
x
y
T
F
T
20. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 20
Gravitational Forces
2
2
1
r
M
GM
F
Gravity is the force between two masses. Gravity is a
long-range force. No contact is needed between the
bodies. The force of gravity is always attractive!
r is the distance between the two masses
M1 and M2 and G = 6.671011 Nm2/kg2.
M2
r
M1
F21 F12
.
12
21 F
F
21. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 21
Let M1 = ME = mass of the Earth. 2
2
M
r
GM
F E
Here F = the force the Earth exerts on mass M2. This is the
force known as weight, w.
.
2
2
2
gM
M
r
GM
w
E
E
2
2
m/s
8
.
9
N/kg
8
.
9
where
E
E
r
GM
g
Near the surface of
the Earth
km
6400
kg
10
98
.
5
E
24
E
r
M
Gravitational Forces
22. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 22
What is the direction of g?
Note that
m
F
g
is the gravitational force per unit mass. This is called
the gravitational field strength. It is also referred to as
the acceleration due to gravity.
What is the direction of w?
Gravitational Forces
23. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 23
Example: What is the weight of a 100 kg astronaut on the
surface of the Earth (force of the Earth on the astronaut)?
How about in low Earth orbit? This is an orbit about 300
km above the surface of the Earth.
On Earth: N
980
mg
w
In low Earth orbit:
N
890
)
( 2
h
R
GM
m
r
mg
w
E
E
o
The weight is reduced by about 10%.
The astronaut is NOT weightless!
Gravitational Forces
24. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 24
Applying Newton’s Second Law
a
F m
The one equation everyone remembers!
This equation is just the tip of the “iceberg” of the mechanics
problem. The student will need to anlyze the forces in the
problem and sum the force vector components to build the
left hand side of the equation.
Sumof the forces
acting on the objects
in the system
“m” is the
System
Mass
“a” is the
System
Response
25. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 25
Example: A force of 10.0 N is applied to the right on block 1.
Assume a frictionless surface. The masses are m1 = 3.00 kg
and m2 = 1.00 kg.
Find the tension in the cord connecting the two blocks as
shown.
F
block 2 block 1
Assume that the rope stays taut so that both blocks
have the same acceleration.
Applying Newton’s Second Law
26. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 26
FBD for block 2:
T F
w1
N1
x
y
x
T
w2
N2
y
FBD for block 1:
0
1
1
1
w
N
F
a
m
T
F
F
y
x
0
2
2
2
w
N
F
a
m
T
F
y
x
Apply Newton’s 2nd Law to each block:
27. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 27
a
m
T
F 1
a
m
T 2
To solve for T, a must be eliminated. Solve for a in (2)
and substitute in (1).
(1)
(2)
Example continued:
These two equations contain
the unknowns: a and T.
N
5
.
2
kg
1
kg
3
1
N
10
1
1
2
1
2
1
2
1
2
1
1
m
m
F
T
T
m
m
T
m
T
m
F
m
T
m
a
m
T
F
28. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 28
Pick Your System Carefully
x
T
w2
N2
y
T F
w1
N1
x
y
Include both objects in the system. Now when you sum
the x-components of the forces the tensions cancel. In
addition, since there is no friction, y-components do not
contribute to the motion.
29. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 29
Apparent Weight
Stand on a bathroom scale.
FBD for the
person: Apply Newton’s 2nd Law:
y
y
y
ma
mg
N
ma
w
N
F
w
N
x
y
30. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 30
The normal force is the force the scale exerts on you. By
Newton’s 3rd Law this is also the force (magnitude only)
you exert on the scale. A scale will read the normal force.
y
a
g
m
N
is what the scale reads.
When ay = 0, N = mg. The scale reads your true weight.
When ay 0, N > mg or N < mg.
Apparent Weight
In free fall ay = -g and N = 0. The person is weightless.
31. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 31
Example (text problem 4.128):
A woman of mass 51 kg is standing in an elevator. The elevator
pushes up on her feet with 408 newtons of force.
What is the acceleration of the elevator?
FBD for
woman:
y
y
y
ma
mg
N
ma
w
N
F
Apply Newton’s 2nd Law: (1)
w
N
x
y
Apparent Weight
32. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 32
Solving (1) for ay:
2
m/s
8
.
1
m
mg
N
ay
The elevator could be (1) traveling upward with decreasing
speed, or (2) traveling downward with increasing speed.
The change in velocity is DOWNWARD.
Given: N = 408 newtons, m = 51 kg, g = 9.8 m/s2
Unknown: ay
Example continued:
Apparent Weight
33. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 33
N
mg
F
Free Body Diagram
34. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 34
N
mg
a
F m
This is not a methodolgy to solve for the acceleration. It is just graphically
demonstrating that the net force is ma
35. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 35
N mg
mg
N
Same problem but the applied force is angled up
36. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 36
mg N
The normal force, N, is smaller in this case because the upward angled
applied force reduces the effective weight of the sled.
39. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 39
Equilibrium Problem
This is an example of three-vector equilibrium problem. It lends itself
to a simple solution because the vector sum of the three vectors
closes on itself (equilibrium) and forms a triangle
40. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 40
Milk Carton
Max static friction force
Non-slip limit on applied force
45. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 45
Hanging Picture
T1
mg
60o
30o
T2
0
1
0
2
cos(60 )
sin(60 )
T mg
T mg
• Since this turned out to be a right
triangle the simple trig functions are
that is needed to find a solution.
• If the triangle was not a right triangle
then the Law of Sines would have
been needed.
56. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 56
Force Summary
Friction
Opposes motion
Proportional to normal
force
Non-conservative
Static & dynamic
Normal Forces
Perpendicular to surface
at point of contact.
Magnitude needed to
maintain equilibrium
Tension
No mass
No stretching
Pulleys
Massless
No friction (bearing)
Tension in rope
continuously changes
direction
57. MFMcGraw PHY 1401- Ch 04b - Revised: 6/9/2010 57
Summary
• Newton’s Three Laws of Motion
• Drawing free body diagrams
• Contact forces versus long-range forces
• Different forces (gravity, friction, normal, tension,
air resistance)
• Application of Newton’s Second Law