This document discusses kinetics of particles and Newton's laws of motion. It introduces the concept of equation of motion relating the forces acting on a particle to its acceleration. Equations of motion are developed for rectangular, normal-tangential, and cylindrical coordinate systems. Examples are provided to demonstrate solving equations of motion for particles undergoing accelerated motion under various force conditions in different coordinate systems.
The basis for kinetics is Newton's second law, which states that when an unbalanced force acts on a particle, the particle will accelerate in the direction of the force with a magnitude that is proportional to the force.
The basis for kinetics is Newton's second law, which states that when an unbalanced force acts on a particle, the particle will accelerate in the direction of the force with a magnitude that is proportional to the force.
Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical En...Transweb Global Inc
Strength of Materials is a branch of applied mechanics that deals with behavior of solid bodies subjected to various forces. This may also be known as Mechanics of Materials or mechanics of solids. Copy the link given below and paste it in new browser window to get more information on Stress in Bar of Uniformly Tapering Rectangular Cross Section:- http://www.transtutors.com/homework-help/mechanical-engineering/simple-stresses-and-strain/stress-in-bar-of-uniformly-tapering-rectangular-cross-section.aspx
Stress in Bar of Uniformly Tapering Rectangular Cross Section | Mechanical En...Transweb Global Inc
Strength of Materials is a branch of applied mechanics that deals with behavior of solid bodies subjected to various forces. This may also be known as Mechanics of Materials or mechanics of solids. Copy the link given below and paste it in new browser window to get more information on Stress in Bar of Uniformly Tapering Rectangular Cross Section:- http://www.transtutors.com/homework-help/mechanical-engineering/simple-stresses-and-strain/stress-in-bar-of-uniformly-tapering-rectangular-cross-section.aspx
Week 3 OverviewLast week, we covered multiple forces acting on.docxmelbruce90096
Week 3 Overview
Last week, we covered multiple forces acting on an object. This week we will cover motion in two dimensions, inclined planes, circular motion, and rotation.
Forces in Two Dimensions (1 of 2)
So far you have dealt with single forces acting on a body or more than two forces that act parallel to each other. But in real life situations more than one force may act on a body. How are Newton's laws applied to such cases? We will restrict the forces to two dimensions.
Since force and acceleration are vectors, Newton's law can be applied independently to the X and Y-axes of a coordinate system. For a given problem you can choose a suitable coordinate system. But once a coordinate system is chosen, we have to stick with it for that problem. The example that follows shows how to find the acceleration of a body when two forces act on it at right angles to each other.
Forces in Two Dimensions (2 of 2)
To find the resultant acceleration we draw an arrow OA of length 3 units along the X-axis and then an arrow AB of length 4 units along the Y-axis. The resultant acceleration is the arrow OB with the length of 5 units. Therefore, the acceleration is 5 m/s2 in the direction of OB. Also when you measure the angle AOB with a protractor, we find it to be 53°.
The acceleration caused by the two forces is 5 m/s2 at an angle of 53°.
Uniform Circular Motion
When an object travels in a circular path at a constant speed, its motion is referred to as uniform circular motion, and the object is accelerated towards the center of the circle. If the radius of the circular path is r, the magnitude of this acceleration is ac = v2 / r, where v is its speed and ac is called the centripetal acceleration. A centripetal force is responsible for the centripetal acceleration, which constantly pulls the object towards the center of the circular path. There cannot be any circular motion without a centripetal force.
Banking
When there is a sharp turn in the road or when a turn has to be taken at a high speed as in a racetrack, the outer part of the road or the track is raised from the inner part of the track. This is called banking. It provides additional centripetal force to a turning vehicle so that it doesn't skid.
The angle of banking is kept just right so that it provides all the centripetal force required and a motorist does not have to depend on the friction force at all.
Inclined Planes
Forces on an Inclined Plane
The inclined plane is a device that reduces the force needed to lift objects. Consider the forces acting on a block on an inclined surface. The inclined surface exerts a normal force FN on the block that is perpendicular to the incline. The force of gravity, FG, points downward. If there is no friction, the net force, Fnet, acting on the block is the resultant of FN and FG. By Newton's second law the net force must point down the incline because the block moves only along the incline and not perpendicular to it.
The vector triangle shows .
Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
this project is basically based "motion", the way it's directly or indirectly linked to us. Viewing this power point presentation will enable you to study as a whole in descriptive way.In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame n If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
Hope you will like it and feedbacks are welcomed.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
2. KINETICS OF A PARTICLE:
FORCE & ACCELERATION
• Newton’s Second Law of Motion
• Equation of Motion
• Equation of Motion: Rectangular Components
• Equation of Motion: Normal & Tangential Components
• Equation of Motion: Cylindrical Components
3. NEWTON’S LAWS OF MOTION
FIRST LAW:
A particle originally at rest, or moving in a straight line with a constant
velocity, will remain in this state provided the particle is not subjected to an
unbalanced force
SECOND LAW:
A particle acted upon by an unbalanced force F experiences an acceleration a
that has the same direction as the force and a magnitude that is directly
proportional to the force.
THIRD LAW:
The mutual forces of action and reaction between two particles are equal,
opposite and collinear.
4. NEWTON’S LAWS OF MOTION
• The first and third laws are extensively used during statics
• However, Newton’s second law of motion forms the basis for most of the
dynamics concepts, since this law relates the accelerated motion of the particle
to the forces that act on it.
• If the mass of the particle is ‘m’, Newton’s second law of motion may be
written in mathematical form as:
F = ma
• This equation is referred to as the equation of motion
Newton’s Law of Gravitational Attraction:
• Newton’s law of Gravitational Attraction may be expressed mathematically as:
F = [G m1 m2]/r2
where F = Force of attraction between two particles
G = Universal constant of gravitation, 66.73x10-12
m3
/kg.s2
m1 m2 = mass of each of the two particles
r = distance between the centers of the two particles
5. EQUATION OF MOTION
• The equation of motion is:
F = ma
• Consider a particle P which has a mass m and is subjected to the action of two
forces F1 and F2
• We can graphically account for the magnitude and direction of each force acting
on the particle by drawing the particle’s free body diagram
• Since the resultant of these forces produces the vector ma, its magnitude and
direction can be represented graphically on the kinetic diagram
6. EQUATION OF MOTION FOR A SYSTEM OF PARTICLES
• The equation of motion for a system of particles can be
written as:
ΣF = maG
• i.e. the sum of the external forces acting on the system of
particles is equal to the total mass of the particles times the
acceleration of its center of mass G.
7. EQUATION OF MOTION: Rectangular Coordinates
• When a particle is moving relative to an inertial x, y, z frame of reference, the
forces acting on the particle as well as its acceleration may be expressed in terms
of their i, j, and k components as:
∑ F = m a
∑ Fx i + ∑ Fy j + ∑ Fz k = m( ax i + ay j + az k)
• For this equation to be satisfied, the respective i, j and k components on the left
side must be equal to the corresponding components on the right side.
8. EQUATION OF MOTION: Rectangular Coordinates
Examples:
13.1, 13.2, 13.3, 13.4,13.5
Fundamental Problems:
F13.1, F13.5
Practice Problems:
13.10, 13.14, 13.16, 13.27, 13.33
9. EXAMPLE 13-1
The 50kg crate shown rests on a horizontal plane for
which the coefficient of kinetic friction is 0.3 If the crate
is subjected to a 400N towing force as shown, determine
the velocity of the crate in 3s starting from rest.
10. EXAMPLE 13-4
A smooth 2 kg collar shown is attached to a spring having a stiffness
k = 3N/m and an unstretched length of 0.75 m. If the collar is
released from rest at A, determine its acceleration and the normal
force of the rod on the collar at the instant y = 1m.
11. PROBLEM 13-16
The man pushes on the 60lb crate with a force F. The force is always
directed down at 30º from the horizontal as shown, and its
magnitude is increased until the crate begins to slide. Determine the
crate’s initial acceleration if the static coefficient of friction is 0.6 and
kinetic coefficient of friction is 0.3
12. PROBLEM 13-27
Determine the required mass of block A so that when it is released
from rest it moves the 5kg block B 0.75m up along the smooth incline
plane in t=2s. Neglect the mass of the pulleys and the cords.
13. EQUATION OF MOTION: Normal & Tangential Coordinates
• When a particle moves over a curved path which is known, the equation of motion
for the particle may be written in the tangential, normal and binormal directions.
i.e.
∑ F = m a
∑ Ft ut + ∑ Fn un + ∑ Fb ub = mat + man
• Here ∑ Fn , ∑ Ft and ∑ Fb represent the sums of all the force components acting
on the particle in the normal, tangential and binormal directions respectively.
• Since there is no motion of the particle in the binormal direction as the particle is
constrained to move along the path, so the above equation may be written as:
∑ Ft = m at
∑ Fn = m an
∑ Fb = 0
14. EQUATION OF MOTION: Normal & Tangential Coordinates
• Since at = dv/dt represents the time rate of change in magnitude of
velocity, so if ∑Ft acts in the direction of motion, the particle’s speed will
increase, whereas, if it acts in opposite direction, the particle will slow
down.
• Similarly an = v2
/ρ represents the time rate of change the velocity’s
direction. Since this vector always acts in the positive n direction i.e.
towards the path’s center of curvature, then ∑Fn, which causes an, also acts
in this direction
• In particular, when the particle is constrained to travel in a circular path
with constant speed, there is a normal force exerted on the particle by the
constraint. As this force is always directed towards the center of the path,
it is often referred to as centripetal force.
15. EQUATION OF MOTION: Normal & Tangential Coordinates
Examples:
13.6, 13.7, 13.8, 13.9
Fundamental Problems:
F13.7, F13.10
Practice Problems:
13.55, 13.59, 13.62, 13.76
16. EXAMPLE 13-7
The 3kg disk is attached to the end of the cord as shown. The other
end of the cord is attached to a ball-and-socket joint attached at the
center of the platform. If the platform is rotating rapidly, and the
disk is placed on it and released from rest as shown, determine the
time it takes for the disk to reach a speed great enough to break the
cord. The maximum tension the cord can sustain is 100N, and the
coefficient of kinetic friction between the disk and the platform is 0.1
17. EXAMPLE 13-9
The 60-kg skateboarder in Fig below coasts down the smooth
circular track. If he starts from rest when θ = 0°, determine the
magnitude of the normal reaction the track exerts on him when θ =
60°. Neglect his size for the calculation.
18. PROBLEM 13-62
The ball has a mass of 30 kg and a speed v = 4 m/s at the instant it is at
its lowest point, θ = 0°. Determine the tension in the cord and the rate
at which the ball's speed is decreasing at the instant θ = 20°. Neglect the
size of the ball.
19. PROBLEM 13-76
A toboggan and rider have a total mass of 90 kg and travel down
along the smooth slope defined by the equation y=0.08x2
. At the
instant x=10m, the toboggan’s speed is 5m/s. At this instant
determine the rate of increase in speed and the normal force which
the toboggan exerts on the slope. Neglect the size of the toboggan and
rider for calculation.
20. EQUATION OF MOTION: Cylindrical Coordinates
• When all the forces acting on a particle are resolved into cylindrical components
i.e. along the unit vector directions ur, uθ, uz the equation of motion may be
expressed as:
∑ F = m a
∑ Frur+ ∑ Fθuθ+ ∑ Fzuz = m ar ur + m aθ uθ + m az uz
• Consequently, we may write the following three scalar equations of motion:
∑ Fr = m ar
∑ Fθ = m aθ
∑ Fz = m az
• If the particle is constrained to move only in the r-θ plane, then only the first two
of the above equations are used to specify the motion.
21. EQUATION OF MOTION: Cylindrical Coordinates
TANGENTIAL & NORMAL FORCES
• Problems involving cylindrical coordinates requires the determination of the
resultant force components ∑Fr, ∑Fθ, ∑Fzcausing a particle to move with a known
acceleration
• If however, the particle’s accelerated motion is not completely specified at the
given instant, then some information regarding the directions or magnitudes of the
forces acting on the particle must be known or computed in order to solve the
equations of motions.
• Consider a force P causing the particle to move along a path defined by polar
coordinates as r=f(θ)
• The normal force N which the path exerts on the particle is always perpendicular
to the tangent of the path whereas the frictional force F always acts along the
tangent in the opposite direction of motion.
• The direction of N and F can be specified relative to the radial coordinate by
computing the angle Ψ (psi) which is defined between the extended radial line
r=OP and the tangent to the curve.
22. EQUATION OF MOTION: Cylindrical Coordinates
• This angle can be obtained by noting that when the particle is displaced ds along
the path, the component of displacement in the radial direction is dr and the
component of displacement in the transverse direction is r dθ.
• Since these components are mutually perpendicular, the angle Ψ can be
determined from:
tan Ψ = r dθ / dr
or tan Ψ = r / (dr/dθ)
• If Ψ is calculated as a positive quantity, it is measured from the extended radial
line to the tangent in a counter clockwise sense or in the positive direction of θ.
• If it is negative, it is measured in the opposite direction to positive θ.
23. EQUATION OF MOTION: Cylindrical Coordinates
Examples:
13.10, 13.11, 13.12
Fundamental Problems:
F13.14, F13.15
Practice Problems:
13.96, 13.99, 13.105, 13.106,
13.108, 13.109
24. EXAMPLE 13-10
The smooth 0.5-kg double-collar in Fig. can freely slide on arm AB and the
circular guide rod. If the arm rotates with a constant angular velocity of 3
rad/s, determine the force the arm exerts on the collar at the instant θ = 45°.
Motion is in the horizontal plane.
25. EXAMPLE 13-12
A can C, having a mass of 0.5 kg, moves along a grooved horizontal slot
as shown. The slot is in the form of a spiral, which is defined by the
equation r=(0.1θ) m, where θ is in radians. If the arm OA is rotating at a
constant rate of 4 rad/s in the horizontal plane, determine the force it
exerts on the can at the instant θ=π radians. Neglect friction and the size
of the can.
27. PROBLEM 13-108
The 1.5-kg cylinder C travels along the path described by r=(0.6 Sinθ) m. If
arm OA is rotating counterclockwise with constant angular velocity of 3 rad/s,
determine the force exerted by the smooth slot in arm OA on the cylinder at the
instant θ=60°.The spring has a stiffness of 100 N/m and is unstretched when
θ=30°. The cylinder is in contact with only one edge of the slotted arm. Neglect
the size of the cylinder. Motion occurs in the vertical plane.