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Flash Animations for MECHANICS learning




Forces and Measurement


01. Dynamometer | measurement of forces


02. Mass vs Weight   


03. How to draw forces   


04. Relationship between mass & weight | Earth, Moon, Mars


05. Buoyancy | Archimedes principle   


06. Equilibrium with three forces : Exercise 1   


07. Equilibrium with three forces : Exercise 2   


08. Lorentz force | application | rail gun | right hand rule  


09. Lorentz force | application | electric motor   


10. Lorentz force | application | speaker   




11. Frame of reference   


12. Need for speed, but less a limit | the game   


13. Stopping distance : analyzing braking behavior  


14. Speed/Time diagram   


15. Speed/Distance diagram   


16. Distance/Time diagram      


17. Acceleration/Time & Speed/Time diagrams


18. Uniform movement | Chronophotography     


19. Accelerated movement | Chronophotography     


20. Launched object trajectory     


21. Trajectory of a launched object | Chronophotography 


22. Center of mass trajectory     


23. 3 forces | uniform rectilinear movement | law of inertia 


Newton's laws of motion


24. Newton's first law | law of inertia   


25. Newton's second law | F = m.a       


26. Newton's third law | law of action-reaction     
























27. Simple gravity pendulum   


28. Simple gravity pendulum | MCQ   


29. Simple gravity pendulum|Velocity & force vectors


30. Vertical pendulum | {mass+spring} system   


31. Horizontal pendulum | {mass+spring} system   


32. Horizontal pendulum | Theoretical   




33. Transverse wave speed | rope   


34. Longitudinal wave speed | spring   


35. Transverse periodic wave | rope   


36. Longitudinal periodic wave | spring   


37. Transverse periodic wave | rope | ACTIVITY   


38. Longitudinal periodic wave | spring | ACTIVITY   


39. Transverse wave | two disturbances crossing   


40. Transverse wave | reflection on a fixed obstacle   




41. Pendulum | Experimental activity   


42. Simple gravity pendulum|Energy transfer|Ep|Ek|Em   


43. Work kinetic energy theorem   


44. Conversion of energy : hydroelectric dam   


45. Kinetic energy | the scooter   


46. Roller coaster | Russians mountains | Em = Ek + Ep    


47. Electric motor EFFICIENCY    







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- Gravitational Interaction


Brief presentation of the solar system

Attractive action exerted by remote /
- The Sun on each planet;
- A planet on an object close to it;
- An object to another object because of their mass.
Gravity is an attractive interaction between two objects that have mass, it depends on their distance.

Gravitation governs the whole universe (solar system, stars and galaxies).


Weight and mass

Remote action exerted by the Earth on an object in its neighborhood: weight of a body.
The weight P and the mass m of an object are two quantities of different kinds and they are proportional.
The unit of weight is the newton (N).
The relationship of proportionality is expressed by P = mg

An object has:
- An energy position close to the Earth;
- Energy of motion called kinetic energy.
The sum of its kinetic energy of position and is its mechanical energy.
Conservation of energy during a fall.


- Kinetic energy and road safety


The kinetic energy: the relationship giving the kinetic energy of a solid translation is:
Ec = 1 / 2 m.v².
The kinetic energy is measured in joules (J).
The braking distance is growing faster than the speed.


- The Universe in motion and time

- Movements and forces


Relativity of motion


Principle of inertia

Effects of a force on the motion of a body. Role of body mass

Statement of the principle of inertia for a terrestrial observer, "every body perseveres in its state of rest or uniform motion if the forces acting on it cancel out"

Universal gravitation

The gravitational interaction between two bodies.

Gravity result of gravity.
Comparison of the weight of one body on earth and the moon.

Trajectory of a projectile.
Interpretation of the movement of the Moon (or satellite) by extrapolating the motion of a projectile.

- The fundamental interactions


- Elementary Particles

The constituents of matter: neutrons, protons, electrons.
Elementary charge.


- Fundamental interactions

- The mass and the gravitational interaction, Newton's law.
- Expenses and electrical interaction, Coulomb's law, direction, meaning, value:
 F =
Kqq'/d2 with k = 9x109  IS
Electrification phenomena.
Insulators. Drivers; charge carriers: electrons and ions
- The nucleon and the strong interaction.
Two interactions at work in the kernel: the Coulomb repulsion between protons offset up to uranium, in an attractive interaction of intense but short range.


- Interactions and cohesion of the material at various scales

astronomical scale
atomic scale and human
across the nucleus.



- Forces, work and energy





- Motion of a rigid body

1. Vector speed of a point of the solid
2. Centre of inertia of a solid
3. Translational motion of a solid
4. Movement of a solid rotation around a fixed axis, angular velocity


- Forces acting on a macroscopic solid

Actions on a solid examples of effects (maintaining balance, setting in motion of translation, rotation, deformation)


- An approach to Newton's laws applied to the center of inertia

1st law : The principle of inertia
This principle is true that in some benchmarks
These repositories are called Galilean.
Second law : Appearance Semi-Quantitative comparison of the sum of the forces and the variation of the velocity vector of center of mass in a Galilean.
Third law : The principle of reciprocal actions




Magnetic field


Action of a magnet, a current, a very short needle.
Magnetic field vector B : direction, meaning, value and unit.
Examples of magnetic field lines, uniform magnetic field.
Superposition of two magnetic fields (vector addition)


Magnetic field created by a current


Proportionality of the field value B and the current in the absence of magnetic media.
Magnetic field created by:
- A straight current;
- A solenoid.


Electromagnetic forces


Laplace's law :

management, direction, value of the force: F = I.l .B.sinα


Electromagnetic coupling


Conversion of electrical energy into mechanical energy. Role of Laplace forces. Observation of the effect associated with the reciprocal motion of a circuit in a magnetic field: conversion of mechanical energy into electrical energy.





- Work of a force

Concepts of work force

Possible effects of a force whose point of application moves.

Working of a constant force

WAB= F.AB = F.AB. cosα

Work unit: the joule (symbol : J).

Expression of the work of the weight of a body.
Engine work, work-resistant.

Power work of one or more forces


- Work: a mode of energy transfer

Work and Kinetic Energy

In a terrestrial reference, experimental study of free fall of a body near the Earth's work weight :

WAB(P) = Δ[(1/2)MVG2 ]

Energy interpretation, definition of the kinetic energy of a solid translation.
Generalization: a solid translation subjected to various forces : (1/2)MV
B2 - (1/2)MVA2= ΣWAB(Fext)


Work and gravitational potential energy

Potential energy of a strong interaction with the Earth ;

Special case situations are located near the Earth.

Relationship : Epp = Mgz .

Conversion of potential energy into kinetic energy in the case of free fall.


Work and internal energy

Some other effects of work received (elastic deformation, temperature rise, changes in physico-chemical).
Concept of internal energy.


- Heat transfer

Work can produce a given rise in temperature of a body. A similar rise in temperature can be achieved by transfer of energy in another form: heat transfer; microscopic appearance.
Other mode of energy transfer: radiation.

- To produce sounds, listen


Production of sound by musical instruments

Vibrating mechanical system associated with a system for coupling with the air
- Illustration by simple
- For a few real instruments


Vibration modes

Vibration of a rope stretched between two fixed points

Highlighting modes of vibration by sinusoidal excitation: fundamental mode, harmonic quantification of their frequency.
Nodes and antinodes of vibration.

Free oscillations of a plucked string or struck: interpretation of the sound emitted by the superposition of these modes.


Vibration of a column of air

Highlighting modes of vibration by sinusoidal excitation.
Simplified model of excitation of a column of air through a reed or a bevel : selection of frequencies emitted by the length of the air column.


Wave interpretation.
Reflection on a single fixed obstacle

Observing the reflection of a wave on a fixed obstacle; qualitative interpretation of the shape of the reflected wave.
For a sine wave incident.
Wave: superposition of the incident wave and sine wave reflected from a fixed obstacle.


Reflections on two fixed obstacles: quantification of observed modes.

Wave of any shape between two fixed obstacles: recurrent imposed by the distance L between the two fixed points and the speed v, the period is 2L/v.

Standing wave between two fixed obstacles: quantification methods ; relation 2L = nλ (n integer); justification of own frequencies :

 nn = nV/2L.


Transposition to a column of air excited by a loudspeaker

Qualitative observation of the phenomenon.


Musical acoustics and physics of sound
Audible frequency range, sensitivity of the ear.
Pitch of a sound and fundamental frequency, timbre: the importance of harmonics and their attack transients and extinction.
Loudness, intensity reference :

I0 = 10-12W/m2.

Sound level: the decibel sound,

L = 10 log10(I/I0)


Range: octaves, tempered scale.


- Temporal evolution of mechanical systems


Newtonian mechanics

Qualitative connection between ΣFext and ΔvG.

Comparison ΔvG corresponding to equal intervals of time for forces of different values (result of the activity).

Introduction ΔvG /Δt

Acceleration :

aG = lim Δt à 0 (ΔvG /Δt) = dvG/dt ;

acceleration vector (direction, sense, value).

Role of the mass.
Newton's second law applied to the center of inertia.
Importance of the choice of the reference in the study of motion of the center of inertia of a solid: Galilean.
Newton's third law: law of reciprocal actions.


Case Study

Vertically falling of an solid object

Force of gravity, the notion of uniform gravity field.

- Fall vertical friction

Application of Newton's second law of motion to a vertical drop: forces applied to the solid (weight, buoyancy, fluid friction force) differential equation of motion resolution by an iterative numerical method, the original scheme and asymptotic regime ( called "permanent"), speed limit; notion of characteristic time.

- Vertical free fall

Uniformly accelerated rectilinear motion, acceleration independent of the mass of the object.
Analytical solution of the differential equation of motion importance of initial conditions.


Plane movements

- Movements of projectiles in a uniform gravitational field

Application of Newton's second law to the movement of center of mass of a projectile in a uniform gravitational field in the case where friction can be neglected.
Parametric equations hours.
Equation of the trajectory.
Importance of initial conditions.


- Satellites and Planets

Kepler's laws (circular or elliptical path).
Heliocentric and geocentric reference systems.
Study of a uniform circular motion, velocity, acceleration vector, normal acceleration.
Statement of the law of universal gravitation for objects whose mass distribution is spherically symmetric and the distance to their large size (recall).
Application of Newton's second law of inertia at the center of a satellite or a planet: centripetal force, radial acceleration, modeling the movement of the centers of inertia of the satellites and planets using a circular motion and uniform applications ( period of revolution, speed, altitude, geostationary satellite).
Qualitative interpretation of weightlessness in the case of a satellite in uniform circular motion.


Oscillating systems

Presentation of various mechanical oscillating systems

Pendulum weight, simple and robust system clock-spring free oscillation : equilibrium position, deviation from equilibrium, X angle, amplitude, damping (pseudo-periodic regime, aperiodic regime), pseudo-isochronous period and small oscillations, natural period.
Expression of the natural period of a pendulum simple justification for the form of expression by dimensional analysis.


The {object-spring} mechanism

Return force exerted by a spring.

Study dynamics of the system "solid" : choice of repository, balance of forces, under the second law of Newton, differential equation, analytical solution in the case of zero friction. Natural period.


Introduction to the temporal evolution of systems


Present, through the documents most diverse real-life situations where the time evolution is of particular importance: seismic waves, mechanical vibrations, movements swings, Earth-Moon laser, increasing the speed of transport (Train high speed), increasing the clock frequency of computers, time scale of plate tectonics, and launch a rocket into orbit satellites, the Mir space station falling, parachute jumping and the elastic, improving sports performance, etc..


- Propagation of a wave


Mechanical waves progressive



From the examples given in operation generate the following definition of a mechanical wave:
"Called the phenomenon of mechanical wave propagation of a disturbance in a medium without material transport".
Longitudinal waves, transverse.
Sound waves as longitudinal waves of compression-expansion.
General properties of waves:
- A wave propagates from the source in all directions available to them.
- The disturbance is transmitted from place to place, transfer of energy without transporting matter.
- The speed of propagation of a wave is a property of the medium.
- Two waves can cross without disturbing each other.


One-dimensional wave

Notion of one-dimensional wave.
Notion of delay: the disturbance at the point M at time t is that which previously existed at a point M 'at

t' = t - τ : with τ = M'M/v, τ is the delay and v the speed (for non-dispersive media)..


Mechanical progressive periodic wave


Notion of periodic wave.
Temporal frequency, period, spatial periodicity.
Sine wave, period, frequency, wavelength, ; relationship :

 λ = v .T = v /N

Diffraction in the case of sine wave : experimental demonstration.
Influence of the size of the aperture or obstacle on the observed phenomenon.
Dispersal : evidence of the influence of frequency on the speed of the wave on the surface of the water dispersion medium term.



- The time evolution of systems and the measurement of time


This part is considered a revised year-end, around the time measurement. It has no theoretical knowledge or skills due new. The examples are not exhaustive and the teacher is free to expand.
How to measure time?
- From a radioactive decay (age of the Earth, age of cave paintings ...)
- From periodic phenomena
. maintained electrical oscillator (LC oscillator)
. movements of the stars
. rotation of the Earth
. pendulum clocks
. atomic clocks: definition of the second.
• Measure length to determine length
- From the propagation of a mechanical wave (ultrasonic range finder, ultrasound, sonar ...)
- From the propagation of light waves (laser ranging, Earth-Moon distance ...)
- The meter defined from the second and the speed of light
- The meter and the seconds pendulum
- History of the measurement of longitude
• Measure length to determine a speed
- Measure the speed of sound
- Measuring the speed of light