how do you calculate work? (physics)?

Question

I know that there are two formulas to calculate work

one is an integration of force with respect to displacement
W = 1/2mv^2 - 1/2 mv^2

the other is the dot product of F and displacement.
W = F dot d

what's the difference between these two.? i mean how do you know which one to use? I thought, if the force is not constant I use the first method, and if it is i use the second... if this right/???

What i meant by the first formular is this

Work = 1/2 * M * (V final)^2 - 1/2 * M * (v initial)

this yields work... not zero.. sorry if v final and initial weren't clear

and the other formular is
F dot Displacement...

how do you know which one to use? when you see a questions?
i mean what's the difference if both formulars represent work?

Answer 1

The following equations are the most general expressions for Work:

W = F.s ;Work done by a constant force

W = ∫F.s ;Work done by a varying force
(A varying force meaning that the applied force, F, can change in size and direction)

These formulae are applicable in all classical mechanics situations.

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However, at times, it is useful to find an expression for work in terms of kinetic energy:

Wnet = ∆KE = ½ mv^2 – ½ mu^2 (Work-Energy theorem)

Where Wnet = Work done by a constant net force, v = final velocity, u = initial velocity

Recall that from Newton’s 2nd law that the application of a net force implies that a body is accelerating

So, the Work-Energy theorem is valid only during situations where a body is accelerating.

More importantly though, the Work-energy theorem is applied to situations where using Newton’s 2nd law would be mathematically laborious. For example: a body sliding down an incline where friction is significant

Answer 2

Work Done = Force Applied x Distance Moved

Your first equation would equate to Zero-:
1/2 mv^2 - 1/2 mv^2 = 0

P.S. 1/2 mv^2 is the equation for Newtonian Kinetic Energy

Answer 3

Work in the first equation is the change in Kinetic energy,
KE= 1/ 2 x m x v^2

W= F x D is in Joules
KE is also in Joules
They are both scalar - they are a sincle number and not a vector

F x D = KE1 - KE2

Answer 4

Integrating any force with respecting to displacement will yield the answer. And f.d is easy to used and used when displacement is known.

Answer 5

I can't remember mechanics well now, because i study electronics. but i will tell u a point related to mathematics i think it may help.
any function based on one variable e.g: f(t),g(t)....etc
can be considered a multidimensional vector in and infinite dimensional space.
so when we multiply f(t)*g(t) then integrate
is exactly equivalent to the process of getting their equivalent multidimensional vector dot product.
think in it ,and u'll get ur answer.

Answer 6

Im not sure if this is what your asking: speed = distance traveled/ time elapsed this is done relative to an observer. SI unit is meters per second

Answer 7

there's also W = P (pressure) times delta V (volume)

you use this when you have constant pressure...don't know if that helps