Question

Asked Dec 8, 2018

Step 1

A.

Given radial force field F = xi + yj

For Parabola C_{1}, x,y coordinates are x = t , y = t^{2}

Parabola r(t) = t i + t^{2} j , 0 ≤ t ≤ 10

Apply derivative with respect to t on both sides.

dr(t) = (i + 2tj)dt

F•dr(t) = (xi + yj).(i + 2tj)dt

= (xi.i + 2tyj.j)dt

since i.i = j.j = 1

= (x + 2ty)dt

Also, we have x = t , y = t²

F.dr(t) = (t + 2t*t^{2})dt = (t + 2t^{3})dt

Step 2

Now integrate with respect to t in the interval 0 to 10

Step 3

The work done is...

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