luggage handler pulls a 20.0 kg suitcase up a ramp inclined at 34.0 ∘ above the horizontal by a force F⃗ of magnitude 165 N that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is μk = 0.300. The suitcase travels 3.90 m along the ramp. Part A Calculate the work done on the suitcase by F⃗. Express your answer with the appropriate units. WF = nothing nothing Request Answer Part B Calculate the work done on the suitcase by the gravitational force. Express your answer with the appropriate units. Ww = nothing nothing

a) W = 643.5 J, b) W = - 427.4 J

Explanation:

a) Work is defined by

W = F. x = F x cos θ

in this case they ask us for the work done by the external force F = 165 N parallel to the ramp, therefore the angle between this force and the displacement is zero

W = F x

let's calculate

W = 165 3.9

W = 643.5 J

b) the work of the gravitational force, which is the weight of the body, in ramp problems the coordinate system is one axis parallel to the plane and the other perpendicular, let's use trigonometry to decompose the weight in these two axes

sin θ = Wₓ / W

cos θ = Wy / W

Wₓ = W sinθ = mg sin θ

Wy = W cos θ

the work carried out by each of these components is even Wₓ, it has to be antiparallel to the displacement, so the angle is zero

W = Wₓ x cos 180

W = - mg sin 34 x

let's calculate

W = - 20 9.8 sin 34 3.9

W = - 427.4 J

The work done by the component perpendicular to the plane is ero because the angle between the displacement and the weight component is 90º, so the cosine is zero.