Find the work done by the force field on a particle moving along the given path. from (0,0) to .

Question

Find the work done by the force field  on a particle moving along the given path.   from (0,0) to  .

Quizplus · Accepted Answer

To find the work done by the force field along the given path, we need to compute the line integral of the force field along the path. We can parameterize the path from (0,0) to (1,1) as r(t) = (t,t), 0 <= t <= 1. Then, the line integral becomes: int_C F dot dr = int_0^1 F(r(t)) dot r'(t) dt = int_0^1 <11t^4, 6t^4, 8t^3> dot <1,1> dt (substituting F and r'(t)) = int_0^1 25t^4 + 6t^4 + 8t^3 dt = [5t^5 + 6/5 t^5 + 2t^4]_0^1 = 5 + 6/5 + 2 = 17/5 Therefore, the work done by the force field along the path is 17/5. Comparing this value with the given choices, we see that the answer is E.

Find the Work Done by the Force Field on a Particle