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As a matter of fact, this velocity profile is typical of any vehicle, which is first accelerated, then run with minimum acceleration or even zero acceleration and finally brought to rest with constant deceleration.

We work out an example for studying motion under variable force, which is similar to the earlier example except that force is now dependent on time.

Problem : A block of mass “m” is pulled by a string on a smooth horizontal surface with force F = kt, where “k” is a constant. The string maintains an angle “θ” with horizontal. Find the time when block breaks off from the surface.

Unbalanced force system

Solution : Here, important thing is to know the meaning of "breaking off". It means that physical contact between two surfaces is broken off. In that condition, the normal force should disappear as there is no contact between block and surface.

Since normal force is directed vertically up, we need to analyze forces in y-direction only so that we could apply the condition corresponding to "breaking off".

Free body diagram of the block

Free body diagram

F y = N + k t sin θ - m g = 0 N = m g - k t sin θ

Now, let t = t B (break off time) when N = 0 (breaking off condition)

0 = m g - k t B sin θ k t B sin θ = m g t B = m g k sin θ

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Motional mechanism of animals

According to laws of motion, motion of a body is not possible by the application of internal force. On the other hand, animals move around using internal muscular force. This is not a contradiction, but an intelligent maneuvering on the part of animals, which use internal muscular force to generate external force on them.

Let us take the case of our own movement. So long we stand upright, applying weight on the ground in vertical direction; there is no motion.

Motion of a human being

To move forward (say), we need to press back the surface at an angle. The ground applies an equal and opposite force (say, reaction of the ground). The reaction of the surface is an external force for our body. The horizontal component of the reaction force moves our body forward, whereas the vertical force balances our weight.

Elements of body system

The underlying frame work of the analysis of force systems in inertial frame of reference is now almost complete. There is nothing new as far as application of laws of motion is concerned. But, there is a big “but” with respect to details of various elements of body systems that we consider during study of motion. These elements typically are block, string, incline, pulleys and spring.

The whole gamut of analysis in dynamics requires systemic approach to answer following questions :

  • what are the forces ?
  • which of them are external forces ?
  • does friction is part of the external force system ?
  • whether forces are collinear, coplanar or three-dimensional ?
  • are forces balanced or unbalanced ?
  • are the forces time dependent ?
  • is the motion taking place in inertial frame or accelerated frame ?
  • what would be the appropriate coordinate system for analysis ?
  • what are the characteristics of system elements ?

It is not very difficult to realize that our job is half done if we are able to classify the system in hand based on the answers to above questions. Though, we have listed the system elements at the end of the list, we shall soon realize that a great deal of our effort in getting answers to questions 1, 2, 4 and 8 are largely determined by the elements involved, while the rest are situation specific.

We have briefly described system elements like block, string, pulley etc. In subsequent modules, we shall emphasize details of these and other elements.

Questions & Answers

what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Good
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply
A balloon is released from the ground which rises vertically up with acceleration 1.4m/sec^2.a ball is released from the balloon 20 second after the balloon has left the ground. The maximum height reached by the ball from the ground is
Lucky Reply
work done by frictional force formula
Sudeer Reply
Torque
Misthu Reply
Why are we takingspherical surface area in case of solid sphere
Saswat Reply
In all situatuons, what can I generalize?
Cart Reply
the body travels the distance of d=( 14+- 0.2)m in t=( 4.0 +- 0.3) s calculate it's velocity with error limit find Percentage error
Clinton Reply
Explain it ?Fy=?sN?mg=0?N=mg?s
Admire Reply

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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