An object is placed on an inclined plane which forms an angle B = 18º with the horizontal. An external force F of magnitude 14.3 N is applied to the object. The force F acts in a direction which forms an angle A = 62º with the horizontal. As a result of the force F, the object moves a distance of 0.8 m along the inclined plane. What work was done by the source of force F?

I tried solving this using by drawing it out, using trig and newton's laws to calculate Fx and Fy and used these values to calculate work in x-direction and y-direction.

Finally I used Workx and Workx to find overall work with pythagoras....is this correct?

I got 6.21J as the work

No on the workx +worky. Work is not a vector. You just add them as scalars.

To find the work done by the source of force F, we need to calculate the dot product of the force and the displacement.

The dot product of two vectors A and B is given by the equation: A · B = |A| * |B| * cos(θ)

Where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.

In this case, the force F has a magnitude of 14.3 N and forms an angle A = 62º with the horizontal. The displacement is the distance moved by the object along the inclined plane, which is given as 0.8 m.

Now, let's break down the force F into its horizontal and vertical components. The horizontal component can be found using the equation: F_horizontal = F * cos(A). Similarly, the vertical component of the force can be found using the equation: F_vertical = F * sin(A).

To calculate the horizontal and vertical components of force F, we substitute the given values into the equations:

F_horizontal = 14.3 N * cos(62º)
F_horizontal = 14.3 N * 0.454 (rounded to three decimal places)
F_horizontal = 6.486 N

F_vertical = 14.3 N * sin(62º)
F_vertical = 14.3 N * 0.891 (rounded to three decimal places)
F_vertical = 12.734 N

Now, since the inclined plane forms an angle B = 18º with the horizontal, we can calculate the horizontal and vertical displacements along the inclined plane. The horizontal displacement is given by: displacement_horizontal = displacement * cos(B), and the vertical displacement is given by: displacement_vertical = displacement * sin(B).

Let's substitute the given values to calculate the horizontal and vertical displacements:

displacement_horizontal = 0.8 m * cos(18º)
displacement_horizontal = 0.8 m * 0.951 (rounded to three decimal places)
displacement_horizontal = 0.7616 m

displacement_vertical = 0.8 m * sin(18º)
displacement_vertical = 0.8 m * 0.309 (rounded to three decimal places)
displacement_vertical = 0.2472 m

Finally, we can find the work done by the source of force F using the dot product formula: work = F_horizontal * displacement_horizontal + F_vertical * displacement_vertical.

Substituting the known values:

work = 6.486 N * 0.7616 m + 12.734 N * 0.2472 m
work = 4.938176 N·m + 3.1446488 N·m
work ≈ 8.08 N·m

Therefore, the work done by the source of force F is approximately 8.08 N·m.