Whenever you are faced with adding vectors acting in a straight line (i.e. some directed left and some right, or some acting up and others down) you can use a very simple algebraic technique:
Method: Addition/Subtraction of Vectors in a Straight Line
Choose a positive direction. As an example, for
situations involving displacements in the directions west and east, youmight choose west as your positive direction. In that case,
displacements east are negative.
Next simply add (or subtract) the
magnitude of the vectors using the appropriate signs.
As a final step the direction of the resultant should be included in
words (positive answers are in the positive direction, while negativeresultants are in the negative direction).
Let us consider a few examples.
A tennis ball is rolled towards a wall which is 10 m away from the ball. If after striking the wall the ball rolls a further 2,5 m along the ground away from the wall, calculate algebraically the ball's resultant displacement.
We know that the resultant displacement of the ball
(
${\overrightarrow{x}}_{R}$ ) is equal to the sum of the ball's separate
displacements (
${\overrightarrow{x}}_{1}$ and
${\overrightarrow{x}}_{2}$ ):
Since the motion of the ball is in a straight line (i.e. the ball
moves towards and away from the wall), we can use the method of algebraic additionjust explained.
Let's choose the
positive direction to be towards the wall. This means that the
negative direction is away from the wall.
Finally, in this case
towards the wall is the positive direction , so:
${\overrightarrow{x}}_{R}$ = 7,5 m towards the wall.
Suppose that a tennis ball is thrown horizontally towards a wall at an initial velocity of
$3\phantom{\rule{2pt}{0ex}}\mathrm{m}\xb7\mathrm{s}{}^{-1}$ to the right. After striking the wall, the ball returns to the thrower at
$2\phantom{\rule{2pt}{0ex}}\mathrm{m}\xb7\mathrm{s}{}^{-1}$ . Determine the change in velocity of the ball.
A quick sketch will help us understand the problem.
Remember that velocity is a vector. The change in the velocity of the
ball is equal to the difference between the ball's initial and finalvelocities:
Remember that in this case
towards the wall means a positive velocity , so
away from the wall means a negative velocity :
$\Delta \overrightarrow{v}=5\phantom{\rule{2pt}{0ex}}\mathrm{m}\xb7{\mathrm{s}}^{-1}$ away from the wall.
Questions & Answers
how do you translate this in Algebraic Expressions
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
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.
Privacy Information Security Software Version 1.1a
Good
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is