Question

Note: This is NOT a physics question. This is an integral calculus question

WORK:

i need someone to explain to me how to get F(x) in \[W = \int_a^b F(x) dx\] this is my only problem =_= i get that a is the initial distance and b is the final distance and that F(x) is probably the force..but how can i express force as a function o.O

Answer 1

Newtonian force is given by \( m \large \frac{d^2x}{dt^2} \). That should be the net force, hence, a function of x (one dimensional resulting force, that is). More precisely, \[ W = \int_{a}^{b} F .dr \]Where r is the unit vector in the direction of the resulting force.

Answer 2

dr is the unit vector, my bad there.

Answer 3

is that F dot

Answer 4

Generally, it will be a constant force or given in the exercise. And, yes, dot dr. Both are vectors. To find the general force from scratch you will have to solve some differential equations (or by Lagrangian method or by Newton's).

Answer 5

uhmm okay? o.O i think we're only in integral calculus still....

Answer 6

So, you will have the force function or you will consider it constant. :-)

Answer 7

Those pesky pull on a ice cube, and stuff like that.

Answer 8

ill guess i'll just see some demonstrations and look for a pattern :/ but according to your equatin i guess it would be \[W = \int_a^b m \frac{d^2s}{dt^2} dx\] right?

Answer 9

since F(x) = m times d^2s/dt^2

Answer 10

No, if you are only doing integral calculus, it will always be \[ W = F \int_{a}^{b} dx \]Since F will be constant. It may not look constant, maybe you will have to apply Newton's law, do some vector addition, stuff like that, but it should reduce to that. Or you will have something like, take F(x) = cosx in the exercise.

Answer 11

and dx would be...?

Answer 12

Just dx. The very basic example is this:Taking the box from a point A to a point B. Since the direction of moviment is the same as the force, Fb - Fa is the correct answer. Another example: If the body moves only in the x-direction, then we have to take only the x-component of the force vector and the result would be \( F_{x} b - F_{x} a \)