(a) A force F = (3xî + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x-direction from the origin to x = 5.18 m. Find the work W = F · dr done by the force on the object (in J). J (b) What If? Find the work W = F · dr done by the force on the object (in J) if it moves from the origin to (5.18 m, 5.18 m) along a straight-line path making an angle of 45.0° with the positive x-axis. J Is the work done by this force dependent on the path taken between the initial and final points? dependent independent

Relax

Respuesta :

Answer:

W = 53.6648 J

Explanation:

W = ∫ F * dr

F = < 4*x i , 3*y j > Newtons

dr = < dx, 0 >

Take the dot product:

F * dr = 4* x * dx

Now replacing numeric

W = ∫ 4 * x * dx , ║ x = ( 0 m ⇒ 5.18 m )

W = ¹ / ₂ * (4 N/m) * x ²  

W = (2 N/m) * (5.18 m)²

W = 53.6648 J