Question

The block moves up an incline with constant speed. What is the total work WtotalWtotalW_total done on the block by all forces as the block moves a distance LLL

Answer 1

External force W₁ = F L

Friction force W₂ = - fr L

weight component W₃ = - mg sin θ L

Y Axis Force W=0

Step-by-step explanation:

When the block rises up the plane with constant velocity, it implies that the sum of the forces is zero.

For these exercises it is indicated to create a reference system with the x axis parallel to the plane and the y axis perpendicular

let's write the equations of translational equilibrium in given exercise

X axis

F - fr -Wₓ = 0

F = fr + Wₓ

the components of the weight can be found using trigonometry

Wₓ = W sin θ

`W_(y)` = W cos θ

let's look for the work of these three forces

W = F x cos θ

External force

W₁ = F L

since the displacement and the force have the same direction

Friction force

W₂ = - fr L

since the friction force is in the opposite direction to the displacement

For the weight component

W₃ = - mg sin θ L

because the weight component is contrary to displacement

Y Axis

N- Wy = 0

in this case the forces are perpendicular to the displacement, the angle is 90º and the cosine 90 = 0

therefore work is worth zero