An object with an initial kinetic energy of 15 J is acted upon simultaneously by two constant forces F ₁ = (2 i + 3 j - k ) N and F ₂ = (4 i - j + 2 k ) N . Under the influence of these forces, the object moves from an initial point A(1, 2, -1) m to a final point B(3, 4, 2) m . The final kinetic energy of the object is

Step-by-step solution

First, find the net force acting on the object by adding the individual forces: F _ net = F ₁ + F ₂ F _ net = (2 i + 3 j - k ) + (4 i - j + 2 k ) = (6 i + 2 j + k ) N Next, determine the displacement vector by subtracting the initial position coordinates from the final position coordinates: r = r _B - r _A r = (3 - 1) i + (4 - 2) j + (2 - (-1)) k = (2 i + 2 j + 3 k ) m Calculate the net work done using the dot product of net force and displacement: W = F _ net r W = (6)(2) + (2)(2) + (1)(3) = 12 + 4 + 3 = 19 J Fina