Apply analytical methods of vector algebra to find resultant vectors and to solve vector equations for unknown vectors.
Interpret physical situations in terms of vector expressions.
Vectors can be added together and multiplied by scalars. Vector addition is associative (
[link] ) and commutative (
[link] ), and vector multiplication by a sum of scalars is distributive (
[link] ). Also, scalar multiplication by a sum of vectors is distributive:
In this equation,
is any number (a scalar). For example, a vector antiparallel to vector
can be expressed simply by multiplying
by the scalar
:
Direction of motion
In a Cartesian coordinate system where
denotes geographic east,
denotes geographic north, and
denotes altitude above sea level, a military convoy advances its position through unknown territory with velocity
. If the convoy had to retreat, in what geographic direction would it be moving?
Solution
The velocity vector has the third component
, which says the convoy is climbing at a rate of 100 m/h through mountainous terrain. At the same time, its velocity is 4.0 km/h to the east and 3.0 km/h to the north, so it moves on the ground in direction
north of east. If the convoy had to retreat, its new velocity vector
would have to be antiparallel to
and be in the form
, where
is a positive number. Thus, the velocity of the retreat would be
. The negative sign of the third component indicates the convoy would be descending. The direction angle of the retreat velocity is
south of west. Therefore, the convoy would be moving on the ground in direction
south of west while descending on its way back.
The generalization of the number zero to vector algebra is called the
null vector , denoted by
. All components of the null vector are zero,
, so the null vector has no length and no direction.
Two vectors
and
are
equal vectors if and only if their difference is the null vector:
This vector equation means we must have simultaneously
,
, and
. Hence, we can write
if and only if the corresponding components of vectors
and
are equal:
Two vectors are equal when their corresponding scalar components are equal.
Resolving vectors into their scalar components (i.e., finding their scalar components) and expressing them analytically in vector component form (given by
[link] ) allows us to use vector algebra to find sums or differences of many vectors
analytically (i.e., without using graphical methods). For example, to find the resultant of two vectors
and
, we simply add them component by component, as follows:
In this way, using
[link] , scalar components of the resultant vector
are the sums of corresponding scalar components of vectors
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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