Question

1. (8 pts) A particle starts at the point (0, 1) and moves along the semicircle r=v1-y to (0, -1). Find the work done on this particle by the force field F(x, y) = (3y. -3x).

Answer 1

The particle moving along a semicircle from (0, 1) to (0, -1) under the force field F(x, y) = (3y, -3x) requires calculating the work done on the particle and the final answer is 6

To find the work done on the particle, we need to integrate the dot product of the force field F and the displacement vector along the path. Let's parameterize the semicircle path by setting
`y = 1 - x^2`and calculate the corresponding x-values.

Substituting this into the force field, we get
`F(x) = (3(1 - x^2), -3x)`. Now, let's calculate the displacement vector d