New Info Flashcards
If power = Fv, but velocity is constant and mass constant (definition is a constant force being applied to produce velocity) how is power being used
Power used to counter resistive forces to produce a constant force that results in a constsnt velocity
- so against the air resistance friction etc
Integration trig rules
Sec 2 = tan
If codec involved = -
Cosec 2 = - cot
Tan sec = sec
Cot cosec = -cosec
If sec then sec
If cosec then cosec but - rule
Bruv integration if it is staurolite something 1- need to use what
A TRIGNOMETRIC FUNCTION , so it simplifies to cos2 or something saaureoot thst, rearrange change the limits or leave it etc
Simple harmonic motion, if we have firce , how can we equate that to a simple harmonic motion equation ti find omega
Remember f = ma, make a = to the rest of the equation 😭
Equate coefficients
Remember to find minimum or max something, differentiate and
Set to 0, find this x coordinate , second differentiate if there’s two find max min find y coordinate, that’s max
Make an equation with a variable x and siffenrkste !
Flip don’t hit the griddy, when deriving snells law what essentially doing + relate to running swimming question
Basically said that light would always take the quickest path based in mediums to get form a to b, we don’t know that for a fact so what we did is called a distance that is optimum x and rest d-x
Found equations for overlap time, and said we ldukd differentiate this and equal to 0 to find the optimal x value that would give us smallest time
But upon rearrange we realise this is so similar to snells law
Running we can use the idea that refractive index is ratio if speed of light/ speed of whatever
So if running was speed of light, the. Refractive index of running is 1
And so refractive index of swimming is running / swimming
And now we have snells law
Dot product work
Cimmutive and distributive
Also dot products can cancel out
And dot of thr same angle is 0 so cos 0 is one and it becomes MAGENTIC sqaure
Minimum potential energy argument
Okay so the ladder can actually exist anywhere, this is because it’s gpe is the same in any position so nothing is changing
When the man gets on,s he introduces some rotational acceleration which caused the ladder to move. Every time however he had to correct himself so that his centre of mass is inline with the weight of the circular so no more rotational EQUILIBIRUM but he can’t do thst oerfectl every time.
So every step he takes it moves back a bit
When he is half way it is almost heoxjitnsl.
As a result he can never reach the roof
Reaction force when accelerating CANNOT = weight
Describe lift scene
Reaction force must change so there is a resultant force and acceleration is felt , otherwise no resultant force
When a lift is accelerating decelerating, two things are happening
The person is also accelerating and decelerating
The lift is also accelerating and decelerating
Both at the same rate
Ok calm with the lift, in order for that to happen the tension dynamically changes
And for the man the reaction dynamically changes
All with the same acceleration value!
Remember scale reads normal, so accelerating downwards causes less normal mand so less weight
Explain what’s happening with earth rotating
What assumptions
Earth is rotating with centripetal accelrwtion, and thus anyone on it, towards centre of axis , centre of circular motion
So as accelerating there, mv2/r is resultant force = mg - R As you accelerating that direction
Might be components but this is why your normal is less and weight too
But if at poles, no rotation , so no resultant force acceleration so your mg = normal and weight is more real heavier!
Assumptions are that earth uniform mass disruption sk gravitational force is felt everywhere the same, + speheric,a earth
Weigh least wt equator because of rotation
Just remember Rhett centr
Two force is always just the force in same direction as centre
So anything else if no accelrwtion in those planes CANCEL EACH OFHER OUT
Don’t lack don’t lack we just said accelrwtion means normal = anything to do with weight oringall,
Without friction btw
So on banked surface, the normal actual,y is the one who provides the centripetal accelrwtion force, not weight, and component of normal = mg so thst fkrces verticslly resolve to 0 so there is no accelrwtion. Here
This gives you equations of nsin and n cos theta.
Yh so normal force supports weight AND centripetal force
Therefore normal greater and heavier
With friction this will change = brriction given to max as static as mew R will have components in the mv2 /r direction and y direction, giving rise to different simultaneous
Put them together and show,d have equation using r and mew and theta that’s it
MAGENTIC field will exert a
Force on a kcijg charge, and this experiences CIRCULAR MOTION, because force vector always perpendicular to the direction of the velocity vector
Normal force sn not be negative ever
And remember that velocity depends on the big planet not the tint thing
Series
Arithmetic is a + (n-1)d
Sum is 1/2n (2a + n-1 d or a + l
Geometric is
A r ^n-1
Sum is a(1-r^n)
/ 1-r
Infinity is a/1-r
Remember for power questions alone find infidual resistances and do it separately
Then find ratio
