Force and Dynamics

DYNAMICSThis branch of mechanics deals with the causes of motion.

Contents: Forces & Effect of forces .Free body diagram.Laws of motion.Momentum &it’s conservation.Impulse.

ForcesWhat change the state of object is called "force”.

It can be a push/ a pull/ a twist.

A force is recognised by the effect or effects that it produces.

Effect of forces

Application of force can---Deform (i.e. change its shape)Speed upSlow DownChange direction

“Free body Diagrams

A free body diagram is the one in which-• the object is represented as a small rectangle

irrespective of its size or shape.• all the forces acting on the object as the arrows or

lines.• Length of the arrows will give the magnitude of the

forces.• The direction of the arrows give the direction of the

forces.• All the arrows should come from the center of

mass of the body.

Free body force diagrams

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Consider a man on a sloping table:Reaction (a contact force) is perpendicular to the surface. Friction (a tangential contact force) goes up the slope. Let’s combine the forces…

Resultant force is zero, so no

acceleration

Weight = mgThe length of the lines represent the relative magnitude of the forces.The lines point in the direction of the force.The forces act from the centre of mass of the bodyThe arrows should come from the centre of mass of the body.

Examples :

T- represents the tension forces

Different types of forces

Weight

Tension

Drag force

Spring force

Friction

Normal force

GRAVITY or WEIGHT

Gravity is a force that pulls objects downwards towards the centre of the earth.Think what happens when you throw a ball up into the air.   The ball goes up in the air and then falls down again.  Think what happens when you jump up into the air.   You soon come down again to earth.     Think what happens to ripe fruits such as apples that grow on trees.   They will  fall to the ground unless they are picked first.      All of these happen because of the force we call gravity

Drag forceA drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is the relative velocity between the body and the fluid. 

AIR RESISTANCE

Air resistance pushes against things which are moving. Air resistance pushes against a moving car and slows it down. Air resistance pushes against falling objects and slows them down.  

UPTHRUST

◎Upthrust is the force that pushes an object up and makes it seem to lose weight in a fluid.

◎It is the force which is responsible in making the object float or sink in a liquid.

FRICTION

Friction is the resistance between two surfaces that are in contact with each other.  The friction force opposes the motion of the object.There are two types of friction- static and kinetic friction.Static friction is the frictional force applied by a surface till the object slides over the other.Dynamic or kinetic friction is the frictional force applied by a surface on a moving object.

FN is the normal force

Tension forceThe tension is the force which is transmitted through a string, rope, or wire when it is pulled tight by forces acting from each end. The tensional force is directed along the wire and pulls equally on the objects on either end of the wire.

Spring force

The spring force is the force exerted by a compressed or stretched spring upon any object which is attached to it. An object which compresses or stretches a spring is always acted upon by a restoring force which brings the object to its rest or stable position. For most springs (specifically, for those which are said to obey "Hooke's Law"), the magnitude of the force is directly proportional to the amount of stretch or compression.

Normal reactive force

The normal force is the support force exerted upon an object which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects which are in contact with each other.

A bit of history of forces

Aristotle is the first one to give systematic idea about forces

and motion in the physical world.

There is natural, violent, and local motion; rectilinear and circular motion Speed is proportional to motive force, and inversely proportional to resistance. Velocity = a constant x F/R  

Nothing moves unless you push it.  [it is moved by a mover]

Galileo's contributions

Galileo was deeply influenced by Archimedes principles of statics (the theory of equilibrium) which he expanded on for his discussion of moving bodies. Through his use of mathematics and physical experimentation, Galileo was able to formulate the Law of Fall in 1604, which is related to the Law of Inertia which he first formulated in 1612. These laws stand in marked contradiction to Aristotelian physics and all that was accepted up to then. From this period on, Galileo made distinct efforts to refute Aristotelian theory.

English physicist and mathematician, goes the credit for being the first to introduce the concepts of mass and force in mechanics and to formulate the laws governing motion. These laws are commonly called Newton’s laws of motion and constitute the principles of dynamics.

Newtonian mechanics

Newton’s first Law or Law of Inertia

◎An object that is not moving will not move until a net force acts upon it.

◎An object that is in uniform motion moves in the same direction and at the same speed unless an external unbalanced force acts on it.

Newton’s first Law or Law of Inertia

Condition for an object to be equilibrium

An object is said to be in equilibrium when all the forces acting on it cancels out or the net force acting on it is zero.

Newton’s 2nd Law:Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).

It can be summerized as-The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.

F = Δp / Δt.

Newton’s third law

For every action there is an equal and opposite re-action.

The equal and opposite forces do not act on the same body!

p = mvm=massv=velocity

Momentum of a body is

defined as the mass of the

body multiplied by its velocity

It is a vector quantity. It’s

units are kg m s-1 or Ns

Linear Momentum

It is the amount of motion contained in the body.

How hard is it to stop a moving object?

To stop an object, we have to apply a force over a period of time. This is called ImpulseImpulse = FΔt Units: N∙sF = force (N)Δt = time elapsed (s)

Using Newton’s 2nd Law we getF Δt = m ΔvWhich means Impulse = change in momentum

The area under force – time graph gives impulse. It is also equal to change in momentum.

Figure 1 represents the uniform force acting on the object , while figure 2 represent a varying force acting on the object

Let’s think!!!!

An egg dropped on a tile floor breaks, but an egg dropped on a pillow does not. Why?

What causes an egg break or not break?

FΔt= mΔv

In these two cases- mass of the egg and change in speed is the same.If time increases for this change according to equation Δt goes up, and so compensate the left hand side force has to decrease, F decreases. So when dropped on a pillow, the egg starts to slow down as soon as it touches it. A pillow increases the time the egg takes to stops.

Would you rather be in a head on collision with an identical car, travelling at the same speed as you, or a brick wall? Assume in both situations you come to a complete stop.

One more challenge.

The answer is…

It Doesn’t Matter!!!!FΔt= mΔvΔt, m, and Δv are the same these two cases ! The time it takes you to stop depends on your car, m is the mass of your car, and Δv depends on how fast you were initially travelling.

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Conservation of Momentum

Or in any collision or explosion momentum is conserved (provided that there are no external forces).

When bodies in a system interact the total momentum remains constant provided no external force acts on the system.

WORK ,POWER AND ENERGY

CONTENTS:- WORK

WORK DONE BY DIFFERENT FORCESENERGYFORMS OF ENERGYPOWER

WORK

Work is not energy.Work is a means of transferring energy by a

force applied on an object.If the object does not move or the force is not

in the direction of the motion then the force is not transferring energy to the object or we say “the force is not doing work on the object.”

It provide a link between force and energy.

Work done by a force-

To calculate work done on an object, we need:

The ForceThe average magnitude of the force The direction of the forceThe DisplacementThe magnitude of the change of positionThe direction of the change of position

Place your screenshot here

Simulation-

http://www.ck12.org/assessment/tools/geometry-tool/plix.html?eId=SCI.PHY.232&questionId=54b828535aa4136113ee4ff2&artifactID=2002923&backUrl=http%3A//www.ck12.org/search/%3Fq%3Dwork%2520done%26source%3Dck12%26grade%3D12%23interactive

Videohttps://www.youtube.com/watch?v=WTfLrIEaRHA

https://www.youtube.com/watch?v=d6MhIBpmJnE

Work – Energy principle

Work done = Energy stored

https://www.youtube.com/watch?v=30o4omX5qfo

Work done by different forces

Work done in stretching a springWork done by gravity

https://www.youtube.com/watch?v=moJbleVsqyo

Work done from a force- displacement graph

Work done= Area under force – displacement graph

Energy◎Energy is the capacity to do work.

When work is done on the object, the energy level of the object increases while, when work is done by the object the energy level of the object decreases.

Different forms of energy

Kinetic energy is the energy an object possesses due to its motion.

Potential energyGravitational potential energy is energy an object receives due to its height.To calculate change in Gravitational Potential energy, we use the formula:

Elastic Potential energy

Elastic potential energy is potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.

www.hyperphysics.com

www.slideshare.net%2Fmaiiiiiiiiiiiiiiiiiiiiii%2Fkinetic-and-potential-energy&psig=AFQjCNGaJ1Y3GGy05Q_-n7pZztVEuOvFfQ&ust=1455534563741107

Energy Transformations- Roller coaster

https://fzxxprj.wikispaces.com/How+does+Law+of+conservation+apply+to+a+Roller+Coaster

PowerRate of doing work is known as power of the object.Unit of power is J s-1 or Watt (W)It is a scalar quantity.

P

Power

http://www.physicsclassroom.com/class/energy/Lesson-1/Power

Efficiency

http://www.bbc.co.uk/schools/gcsebitesize/science/aqa_pre_2011/energy/heatrev6.shtml