A particle is moved along a path A B - B C - C D - D E - E F - F A , as shown in figure, in presence of a force F → = α y i ^ + 2 α x j ^ N , where x and y are in meter and α = - 1 N / m - 1 . The work done on the particle by this force F → will be ____ Joule.

Step-by-step solution

d w = F → ⋅ d r → d w = a y d x + 2 a x d y Now, total work done in whole path is given by, W = W A B + W B C + W C D + W D E + W E F + W F A A → B , y = 1 , d y = 0 , W A → B = ∫ α y d x = α ⋅ 1 ∫ 0 1 d x = α B → C , x = 1 , d x = 0 , W B → C = 2 α ⋅ 1 ∫ 1 0.5 d y = - 2 α 0.5 = - α C → D , y = 0.5 , d y = 0 , W C → D = ∫ 1 0.5 α y d x = α ⋅ 1 2 ∫ 1 0.5 d x = - α 4 D → E , x = 0.5 , d x = 0 , W D → E = 2 α ∫ x d y = 2 α ⋅ 1 2 ∫ 1 0.5 d y = - α 2 E → F , y = 0 , d y = 0 , W E F = 0 F → A , x = 0 , d x = 0 , W E → A