if the force depended on the DIRECTION of the VELOCITY(adsbygoogle = window.adsbygoogle || []).push({});

that is [tex] \vec{F} = - F \hat{v} [/tex].

so suppose it was dragged along a path - say from (0,0) to (1,1) i na straight line what is the work done?

It going in a striaght line so we could parametrize the curve into r(t) = (t,t)

and r'(t) = (1,1) right

and thus v hat = (1,1) as well then?

now the problem is the work depends on the direction of the velocity

so then the work done is [tex]W = -F \int_{0}^{1} (1,1) (1,1) dt [/tex] is that right?

ok so lets say it was dragged along the curve y = x^2

then r(t) = (t,t^2)

and r'(t) = (1,2t)

and [tex] \hat{v} = \frac{(1,2t)}{\sqrt{1+4t^2}} [/tex]

ok but what the dirrefetial quantity fo the function here? Is it (t,t^2) dt?

so then is

[tex] W = -F \int_{0}^{1} \frac{(1,2t))}{\sqrt{1+4t^2}} (t,t^2) dt [/tex]

is that right?

Please help!

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# How would you calculate the work done

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