A constant force of magnitude 5.75 N is exerted on an object. The force's direction is 57.5° counterclockwise from the positive x axis in the xy plane, and the object's displacement is

Δr = (4.8i − 2.2j + 1.7k) m.
Calculate the work done by this force.

J

Fx = 5.75 cos 57.5

Fy = 5.75 sin 57.5
Fz = 0
F = Fx i + Fy j + 0 k
D= 4.8 i - 2.2 j + 1.7 k

F dot D = (5.75 cos 57.5) * 4.8 - (5.75 sin 57.5 * 2.2) + 0 * 1.7 Joules

xy plane, but directions are i,j. Goodness, you are headed for a breakdown. Lets work in the i,j plane

work=force dot distance
force=5.75cos57.5deg i +5.75sin57.5deg j=3.09i + 4.85j
work= (3.09i + 4.85j). (4.8i − 2.2j + 1.7k) =3.09*4.8+4.85*(-2.2) + 0= you do it.
check my math, typing math is not my thing.

To calculate the work done by a force, we can use the formula:

Work = Force * Displacement * cos(theta)

where:
- Force is the magnitude of the force applied,
- Displacement is the magnitude of the displacement vector, and
- Theta is the angle between the force vector and the displacement vector.

Given:
- Force = 5.75 N
- Displacement = |Δr| = sqrt(4.8^2 + (-2.2)^2 + 1.7^2) = 5.52 m (using the Pythagorean theorem)
- Theta = 57.5°

Now, let's calculate the work done:

Work = 5.75 N * 5.52 m * cos(57.5°)

To calculate the cosine of 57.5°, you can use either a scientific calculator or online trigonometric calculators.

Cos(57.5°) = 0.5646 (approximately)

Now, substitute the values into the formula:

Work = 5.75 N * 5.52 m * 0.5646

Work ≈ 17.68 J

Therefore, the work done by the force is approximately 17.68 Joules (J).