If the perpendicular components
and
of a vector
are known, then
can also be found analytically. To find the magnitude
and direction
of a vector from its perpendicular components
and
, we use the following relationships:
Note that the equation
is just the Pythagorean theorem relating the legs of a right triangle to the length of the hypotenuse. For example, if
and
are 9 and 5 blocks, respectively, then
blocks, again consistent with the example of the person walking in a city. Finally, the direction is
, as before.
Determining vectors and vector components with analytical methods
Equations
and
are used to find the perpendicular components of a vector—that is, to go from
and
to
and
. Equations
and
are used to find a vector from its perpendicular components—that is, to go from
and
to
and
. Both processes are crucial to analytical methods of vector addition and subtraction.
Adding vectors using analytical methods
To see how to add vectors using perpendicular components, consider
[link] , in which the vectors
and
are added to produce the resultant
.
If
and
represent two legs of a walk (two displacements), then
is the total displacement. The person taking the walk ends up at the tip of
There are many ways to arrive at the same point. In particular, the person could have walked first in the
x -direction and then in the
y -direction. Those paths are the
x - and
y -components of the resultant,
and
. If we know
and
, we can find
and
using the equations
and
. When you use the analytical method of vector addition, you can determine the components or the magnitude and direction of a vector.
Step 1.Identify the x- and y-axes that will be used in the problem. Then, find the components of each vector to be added along the chosen perpendicular axes . Use the equations
and
to find the components. In
[link] , these components are
,
,
, and
. The angles that vectors
and
make with the
x -axis are
and
, respectively.
Step 2.Find the components of the resultant along each axis by adding the components of the individual vectors along that axis . That is, as shown in
[link] ,
and
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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