Previous Problem List Next(1 point)Let F be the radial force field F zi +to (10, 100). (Compare your answers!)Find the work done by this force along the following to curves both which go from (0,0A. If C1 is the parabola:t, y , 0 t10, then F.dr-B. If C2 is the straight line segment:10t2, y-100r2, 0st1, then F.drC2
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Previous Problem List Next (1 point) Let F be the radial force field F zi + to (10, 100). (Compare your answers!) Find the work done by this force along the following to curves both which go from (0,0 A. If C1 is the parabola: t, y , 0 t10, then F.dr- B. If C2 is the straight line segment: 10t2, y-100r2, 0st1, then F.dr C2
A.
Given radial force field F = xi + yj
For Parabola C1, x,y coordinates are x = t , y = t2
Parabola r(t) = t i + t2 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*t2)dt = (t + 2t3)dt
Now integrate with respect to t in the interval 0 to 10
The work done is...
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