Mechanics
Mechanics is a branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements also it deals with matter and investigates energy.Mechanics is divided into three branches:1- Statics2- Kinematics3- Dynamics
In this slide we will discuss Dynamics.04/11/2023 1IB Physics (IC NL)
Dynamics The branch of mechanics that is
concerned with the effects of forces on the motion of a body or system of bodies, especially of forces that do not originate within the system itself. That is the external forces and not the internal ones.
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Internal forces These forces generate inside the body due
to the interaction between the particles, atoms, molecules or even inside the nucleus.
Forces that originate within the object itself
They cannot change the object’s velocity
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Types of forces In nature we have four fundamental
forces and all the other forces that you know undergo these four which are in order of strength:
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Strong force The Strong Force - This force binds
neutrons and protons together in the cores of atoms and is a short range force.
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Electromagnetic force Electromagnetic - This acts
between electrically charged particles. Electricity, magnetism, and light are all produced by this force and it has an infinite range.
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Weak forces
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Weak Force - This causes Beta decay (the conversion of a neutron to a proton, an electron and an antineutrino) and various particles (the "strange" ones) are formed by strong interactions but decay via weak interactions. Like the strong force, the weak force is also short range.
IB Physics (IC NL)
Gravitational force Gravitational - This force acts
between all masses in the universe and it has infinite range.
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Table of strength
Interaction Relative strength
Range
Strong 1038 10-15
electromagnetic 1036 ∞
Weak 1025 10-18
gravitational 1 ∞
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Unit two: forces
In our IB, forces are to be studied from a basic part of view and concerned with external forces; later we might go to forces related to the four preceding forces. External force
Any force that results from the interaction between the object and its environment
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External Forces Def: force is a mechanical action capable of: i. moving a body initially at rest. ii. Changing the motion of a body. iii. Deforming a body. Usually think of a force as a push or pull Vector quantity May be a contact force or a field force
Contact forces result from physical contact between two objects
Field forces act between disconnected objects Also called “action at a distance”
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Contact and Field Forces
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Newton’s First Law If a body is at rest it remains at
rest, if it is moving with uniform motion it keeps its uniform motion unless acted upon by an external force. The net force is defined as the vector
sum of all the external forces exerted on the object
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Equilibrium An object either at rest or moving
with a constant velocity is said to be in equilibrium
The net force acting on the object is zero (since the acceleration is zero)
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Condition of equilibrium
0
extF
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Inertia Is the tendency of an object to
resist any attempt to change its state of motion.
An object's inertia is directly proportional to its mass; the heavier an object is, the more inertia it has. Hence, a body's mass measures its inertia.
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Mass
Is the quantity of matter found in a body.
Scalar quantity SI unit is kg
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Seat Belt Device Illustration of how one
type of seat belt operates involving the inertia of a block
It protects you when inertia keeps you moving if the driver suddenly applies the brakes.
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Newton’s Second Law If a body is subjected to a force this body
accelerates. The force and the acceleration are directly proportional and in the same direction.
F and a are both vectors
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Units of Force
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SI unit of force is the Newton (N)
1 N = 1 kg.m.s-2
Sir Isaac Newton 1642 – 1727 Formulated basic
concepts and laws of mechanics
Universal Gravitation
Calculus Light and optics
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Horse and Barge
The barge mass is 2.00X103 kg
q1 = 30.0o
q2 = 45.0o
Values of the forces F1 and F2 are each 600 N
Find the x and y resultant forces and associated accelerations
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Gravitational Force Mutual force of
attraction between any two objects
Expressed by Newton’s Law of Universal Gravitation:
221
g r
mmGF
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G = 6.67 x 10-11 SI
Weight The magnitude of the gravitational
force acting on an object of mass m near the Earth’s surface is called the weight w of the object w = m g is a special case of Newton’s
Second Law g is the acceleration due to gravity or
gravitational field strength. g can also be found from the Law of
Universal Gravitation
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More about weight Weight is not an inherent property of
an object mass is an inherent property or mass is
invariant. Weight depends upon location. Weight changes with g g= 9.81ms-2 in Paris, 9.83ms-2 at the
pole and 9.78ms-2 at the equator.
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Newton’s Third Law If object 1 and object 2 interact, the
force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1.
Another version: for every action there is an equal and opposite reaction.
Equivalent to saying a single isolated force cannot exist
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Newton’s Third Law cont.
F12 may be called the action force and F21 the reaction force
Actually, either force can be the action or the reaction force
The action and reaction forces act on different objects
Point of application is always the center of mass.04/11/2023 27IB Physics (IC NL)
Some Action-Reaction Pairs
is the normal force,
the force the table exerts on the TV
is always perpendicular to the surface
is the reaction – the TV on the table
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More Action-Reaction pairs
is the force the
Earth exerts on the object
is the force the object exerts on the earth
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Forces Acting on an Object Newton’s Law
uses the forces acting on an object
are acting on the
object are acting
on other objects
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Applications of Newton’s Laws Assumptions
Objects behave as particles can ignore rotational motion (for now)
Masses of strings or ropes are negligible
Interested only in the forces acting on the object
can neglect reaction forces
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Free Body Diagram Must identify all the forces acting
on the object of interest Choose an appropriate coordinate
system If the free body diagram is
incorrect, the solution will likely be incorrect
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Free Body Diagram, Example
The force is the tension acting on the box The tension is the
same at all points along the rope
are the forces exerted by the earth and the ground
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Free Body Diagram, final Only forces acting directly on the object are
included in the free body diagram Reaction forces act on other objects and so
are not included The reaction forces do not directly influence
the object’s motion In free body diagrams you can select one
point to be the point of application of all the forces acting on the object.
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Solving Newton’s Second Law Problems Read the problem at least once Draw a picture of the system
Identify the object of primary interest Indicate forces with arrows
Label each force Use labels that bring to mind the
physical quantity involved
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Solving Newton’s Second Law Problems Draw a free body diagram
If additional objects are involved, draw separate free body diagrams for each object
Choose a convenient coordinate system for each object
Apply Newton’s Second Law The x- and y-components should be taken
from the vector equation and written separately
Solve for the unknown(s)
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Equilibrium revisited.
Easier to work with the equation in terms of its components:
This could be extended to three dimensions
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Equilibrium Example – Free Body Diagrams
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Inclined Planes
Choose the coordinate system with x along the incline and y perpendicular to the incline
Replace the force of gravity with its components
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Multiple Objects – Example When you have more than one
object, the problem-solving strategy is applied to each object
Draw free body diagrams for each object
Apply Newton’s Laws to each object
Solve the equations
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Multiple Objects – Example, cont.
A fish weights 40.0 N when at rest. Determine the weight
when a=2.00 m.s-2 up When a=2.00 m.s-2
down What is the weight if the
cable were to break?
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Multiple Objects – Example, cont.
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Forces of Friction(not in IB) When an object is in motion on a
surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions
between the object and its environment
This is resistance is called friction
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More About Friction Friction is proportional to the normal
force The force of static friction is generally
greater than the force of kinetic friction The coefficient of friction (µ) depends on
the surfaces in contact The direction of the frictional force is
opposite to the direction of motion The coefficients of friction are nearly
independent of the area of contact
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Static friction acts to keep the object from moving
If F increases, so does ƒs
If F decreases, so does ƒs
ƒs µ n
Static Friction, ƒs
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Kinetic Friction, ƒk
The force of kinetic friction acts when the object is in motion
ƒk = µ n Variations of the
coefficient with speed will be ignored
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Block on a Ramp, Example
Axes are rotated as usual on an incline
The direction of impending motion would be down the plane
Friction acts up the plane
Opposes the motion Apply Newton’s Laws
and solve equations
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Connected Objects
Apply Newton’s Laws separately to each object
The magnitude of the acceleration of both objects will be the same
The tension is the same in each diagram
Solve the simultaneous equations
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More About Connected Objects Treating the system as one object
allows an alternative method or a check Use only external forces
If treating the system as one object then tension is no more considered and it will be an internal force. The mass is the mass of the system
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