Question

Given the force vector F = (x+ y)ax + (y -x)ay, calculate the work done in moving an object along the parabola x^2= y from point A(1, 1) to point B(2, 4)

Answer 1

Using the given force vector F = (x + y)ax + (y - x)ay and the coordinates of point A(1, 1) and point B(2, 4), we can find the dot product and determine the work done. The work done in this case is 6 units.

Step-by-step explanation:

To calculate the work done in moving an object along a parabola, we first need to find the force vector along the path. In this case, the force vector is given as F = (x + y)ax + (y - x)ay. To find the work done, we need to find the dot product of the force vector and the displacement vector. The displacement vector can be found by subtracting the coordinates of point A from point B. Let's find the dot product using these values:

• Point A(1, 1)
• Point B(2, 4)

The displacement vector, Δr, is (2 - 1)ax + (4 - 1)ay = ax + 3ay. Now we can calculate the dot product: F · Δr = (x + y)(ax) · (ax) + (y - x)(ay) · (ay) = (1 + 3)(ax · ax) + (3 - 1)(ay · ay) = 4 + 2 = 6. Therefore, the work done in moving the object along the parabola from point A to point B is 6 units.