Question

Find the work done by the force on the object (in j) if it moves from the origin to (4.89 m, 4.89 m) along a straight-line path making an angle of 45.0° with the positive x-axis.

Answer 1

The work done by the force F₁ is 73.35 J.

Step-by-step explanation:

The work done by a force is given by the equation:

W = F * d * cos(theta)

where W is the work done, F is the magnitude of the force, d is the displacement, and theta is the angle between the force and the displacement.

In this case, the force is given by F₁ = (2y)i + (3x)j. When the particle moves from the origin to a point 5 meters to the right on the x-axis, the displacement is 5 meters in the x direction and 0 meters in the y direction. The angle between the force and the displacement is 0 degrees because the force is purely in the x direction.

Substituting the values into the equation, we get:

W = (2 * 0)i + (3 * 5)j = 15j = 15 * 4.89 = 73.35 J

Therefore, the work done by the force F₁ is 73.35 J.