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Sunday, March 8, 2009
K.E. = 1/2 m v squared
If you was the scientist to discover the K.E. formula starting from the fact that K.E. is proportional to the velocity to a power by the mass. Illustrate your steps to lead to the above formula.
if a body of mass m, starts from rest ans is acted by a steady force F, which gives a uniform acceleration a. if the velocity of that body is v that travells through a distance s, then, using v sq= 2as or a=v.sq/2s
sub. F=ma
F= m(v2/2s)
or Fs= 1/2mv2
and Fs is the work done to abody to give a velocity v, therefore its equal to K.E= 1/2mv2
in simple trems hellscream it is like a stone at rest and u are pushing it with a force F and form the formula if u have force and mass u get acceleration F=ma then u can talk about velocity over the particular distance u pushed the rock. so using the formula V^2=2as ..... eqn 1
if u rearrange it and make 'a' the subject u get a=V^2/2s ..... eqn 2
so now taking that F=ma you can substitute 'a' with eqn 2 F=mV^2/2s but work done is force "F" by distance "s"
so Fs= 1/2 mV^2
and well hence Fs is the work done to abody to give a velocity v, therefore its equal to K.E= 1/2mv2
well people this is kinda wierd because I think the man who found this out was a little unsure himself of what he created because if what renjisan says is correct and what poopsiepumkinpie says about just a matter of substitution, I mean I'm no scientist but why is it that he figured out that formula if it it based on other people's discovery because poopsiepumkinpie knows how to get it so it wasn't all that of a big deal but still we cant do without it and it is just simply mathematically based..........
well we koow that f=ma velocity = v^2=u^2-2as where kinetic energy is the energy produced by a moving object therefore a moving object has velocity and a mass this leads to the the formula f=ma v^2=u^2-2as the a woula cancle of this leads to the object having ah costant acceleration kinetic energy =1/2 m v since the 2 will turn to 1/2 mass is the object mass and velocity is the final velocity - the initial velocity wgich is how the u cancles of
well force, which is mass x acceleration, is associated with velocity since velocity is dependent on a force to move the object to the distance over a given amount of time. force is directly porportional to velocity because the more force applied is the faster the mass of body will travel. kinetic energy deals with motion of objects which is 1/2 mv^2...here you see that the force dependent velocity is set to a power and multiplied by the mass of the object.
i feel it is.corect me if i am wrong!!! since force is mass by acceleration and velocity is rate of change of accelration with respect to time. then the KINETIC ENEGRY is the energy created by the an object moving with a velocity. kinetic enegry is due to an object in motion.
I dont understand how math "hate or love it" got his answer. wat did he do with distance travelled in the formular Fs = (mv^2)/2 i dont understand thathow u can go from the equation above to KE=(mv^2)/2
yes ah understand what u sayin but where the 2as from the formula v^2=u^2-2as went if is so then the object has a constant acceleration an a particular direction so therefore the object is doing a form of displacement then
you see small man. FS is force x distance= energy. the units can prove this as you can see force is measured in newtons(N) and distance is measure in Meters. the units will give newton meters(Nm) when they are multiplied. the unit of 1 joule is equilivent to 1Nm therefore it can be stated that Fs is the same as kenitic energy(KE)
the question has an unknown variable which is a power and logs are said to be powers so you would have to use logs to get the unknown power
it also said that the K.E is proportional to the mass multiply by velocity by an unknown power
so to make K.E equal to mv^x we have to multiply by a constant represented by K
so the equation become K.E = Kmv^x
but now we have to unknown variables but we realize K is a constant so no matter the other values K is the same
so if we get two kinetic energy with corresponding mass and velocity readings we get [mv^x]1 = [mv^x]2
so [logm + xlogv]1 = [logm + xlogv]2 [xlogv]1 - [xlogv]2 = [logm]2 - [logm]1 we then solve for x after we get x we just sub for x in equation and get K
since kinetic energy is velocity due to a force the 2 formulas are user force=ma velocity = v^2=u^2-2as ke=1/2from the u^2 mass the mass of the object to be moved and the velocit it will travel due to the force acting on it newtons law states that for every action there is an equal but opposite reaction therefore the opposite reaction is the movement of the object
i think poopsie explained this question quite well, the equation reveals that the KE of an object is directly proportional to the square of its speed. therefore if the speed increased twice the KE would increase by a factor of 4
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yes finally
ReplyDeleteif a body of mass m, starts from rest ans is acted by a steady force F, which gives a uniform acceleration a. if the velocity of that body is v that travells through a distance s, then, using v sq= 2as or
ReplyDeletea=v.sq/2s
sub. F=ma
F= m(v2/2s)
or Fs= 1/2mv2
and Fs is the work done to abody to give a velocity v, therefore its equal to K.E= 1/2mv2
poopsie...u kind of lost me there a lil bit...lol
ReplyDeletein simple trems hellscream it is like a stone at rest and u are pushing it with a force F and form the formula if u have force and mass u get acceleration F=ma
ReplyDeletethen u can talk about velocity over the particular distance u pushed the rock. so using the formula V^2=2as ..... eqn 1
if u rearrange it and make 'a' the subject u get
a=V^2/2s ..... eqn 2
so now taking that F=ma you can substitute 'a' with eqn 2
F=mV^2/2s
but work done is force "F" by distance "s"
so Fs= 1/2 mV^2
and well hence Fs is the work done to abody to give a velocity v, therefore its equal to K.E= 1/2mv2
hellscream its just a matter of substituting the two formulas..
ReplyDeleterenjisan u look smart i think i kind ah understand what u saying, but it still not to clear, ill have to research dat.
ReplyDeletewell people this is kinda wierd because I think the man who found this out was a little unsure himself of what he created because if what renjisan says is correct and what poopsiepumkinpie says about just a matter of substitution, I mean I'm no scientist but why is it that he figured out that formula if it it based on other people's discovery because poopsiepumkinpie knows how to get it so it wasn't all that of a big deal but still we cant do without it and it is just simply mathematically based..........
ReplyDeletewell we koow that f=ma
ReplyDeletevelocity = v^2=u^2-2as
where kinetic energy is the energy produced by a moving object therefore a moving object has velocity and a mass this leads to the the formula f=ma
v^2=u^2-2as the a woula cancle of this leads to the object having ah costant acceleration kinetic energy =1/2 m v since the 2 will turn to 1/2 mass is the object mass and velocity is the final velocity - the initial velocity wgich is how the u cancles of
well force, which is mass x acceleration, is associated with velocity since velocity is dependent on a force to move the object to the distance over a given amount of time. force is directly porportional to velocity because the more force applied is the faster the mass of body will travel.
ReplyDeletekinetic energy deals with motion of objects which is 1/2 mv^2...here you see that the force dependent velocity is set to a power and multiplied by the mass of the object.
i feel it is.corect me if i am wrong!!! since force is mass by acceleration and velocity is rate of change of accelration with respect to time.
ReplyDeletethen the KINETIC ENEGRY is the energy created by the an object moving with a velocity. kinetic enegry is due to an object in motion.
mass = m, mass of an object.
ReplyDeleteacceleration = a
final velocity = v
initial velocity = u
distance travelled = s
force = F
If an object of mass, m starts from rest and reaches a final velocity v, in a time t, then a force has been acted upon the body of
Force = Mass x Acceleration
F = ma ........ (1)
From the eqution v^2 = u^2 + 2as .......(2)
u = 0
v2 = 2as
a = v^2/2s .........(3)
sub (3) into (1)
F = m(v^2/2s)
Fs = (mv^2)/2
Where Force x Distance travelled = Work Done
which is energy.
Kinetic Energy = (mv^2)/2
so saying that k.e is poportional to the velocity to the power by a mass.
ReplyDeleteI dont understand how math "hate or love it" got his answer. wat did he do with distance travelled in the formular
ReplyDeleteFs = (mv^2)/2
i dont understand thathow u can go from the equation above to KE=(mv^2)/2
ANYONE CAN EXPLAIN FOR ME PLZ?
yes ah understand what u sayin but where the 2as from the formula v^2=u^2-2as went if is so then the object has a constant acceleration an a particular direction so therefore the object is doing a form of displacement then
ReplyDeleteyou see small man. FS is force x distance=
ReplyDeleteenergy. the units can prove this as you can see force is measured in newtons(N) and distance is measure in Meters. the units will give newton meters(Nm) when they are multiplied. the unit of 1 joule is equilivent to 1Nm therefore it can be stated that Fs is the same as kenitic energy(KE)
the question has an unknown variable which is a power and logs are said to be powers
ReplyDeleteso you would have to use logs to get the unknown power
it also said that the K.E is proportional to the mass multiply by velocity by an unknown power
so to make K.E equal to mv^x we have to multiply by a constant
represented by K
so the equation become K.E = Kmv^x
but now we have to unknown variables
but we realize K is a constant so no matter the other values K is the same
so if we get two kinetic energy with corresponding mass and velocity readings
we get
[mv^x]1 = [mv^x]2
so
[logm + xlogv]1 = [logm + xlogv]2
[xlogv]1 - [xlogv]2 = [logm]2 - [logm]1
we then solve
for x
after we get x
we just sub for x in equation
and get K
sorry i forgot K.E in the equation so it should read K = K.E/[mv^x]
ReplyDeletesince kinetic energy is velocity due to a force the 2 formulas are user
ReplyDeleteforce=ma
velocity = v^2=u^2-2as
ke=1/2from the u^2
mass the mass of the object to be moved
and the velocit it will travel due to the force acting on it
newtons law states that for every action there is an equal but opposite reaction therefore the opposite reaction is the movement of the object
i think poopsie explained this question quite well, the equation reveals that the KE of an object is directly proportional to the square of its speed. therefore if the speed increased twice the KE would increase by a factor of 4
ReplyDelete