Dynamics

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.

04/11/2023 2IB Physics (IC NL)

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


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:


Strong force The Strong Force - This force binds

neutrons and protons together in the cores of atoms and is a short range force.


http://imagine.gsfc.nasa.gov/docs/dict_jp.html


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.



Weak forces

04/11/2023 7

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)

http://imagine.gsfc.nasa.gov/docs/dict_ei.html

Gravitational force Gravitational - This force acts

between all masses in the universe and it has infinite range.



Table of strength

Interaction Relative strength

Range

Strong 1038 10-15

electromagnetic 1036 ∞

Weak 1025 10-18

gravitational 1 ∞


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


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”


Contact and Field Forces


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


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)


Condition of equilibrium

0

extF


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.


Mass

Is the quantity of matter found in a body.

Scalar quantity SI unit is kg


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.


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


Units of Force


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


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


Gravitational Force Mutual force of

attraction between any two objects

Expressed by Newton’s Law of Universal Gravitation:

221

g r

mmGF


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


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.


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


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


More Action-Reaction pairs

is the force the

Earth exerts on the object

is the force the object exerts on the earth


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


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


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


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


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.


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


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)


Equilibrium revisited.

Easier to work with the equation in terms of its components:

This could be extended to three dimensions


Equilibrium Example – Free Body Diagrams


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


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


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?


Multiple Objects – Example, cont.


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


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


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


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


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


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


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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Dynamics

Education