Final answer:
The resultant work done on the toolbox when dragged with a tension of 85 N at an angle of 28° over a distance of 40 m, with a constant friction force of 25 N, is 2061.07 joules.
Step-by-step explanation:
The question asks for the resultant work done on a toolbox as it is dragged a horizontal distance by a rope with tension. To find the resultant work, we need to consider both the work done by the tension in the rope and the work done against friction.
The work done by the tension can be found using the formula:
Work = Force × Distance × cos(θ)
Where Force is the tension in the rope, Distance is the horizontal distance moved, and θ is the angle of the rope with the horizontal.
Substituting the given values:
Work = 85 N × 40 m × cos(28°) = 3061.07 J (approx)
Now, we must subtract the work done against friction, which is calculated as:
Work = Friction Force × Distance
Work = 25 N × 40 m = 1000 J
Therefore, the resultant work done on the toolbox is the work done by tension minus the work done against friction:
Resultant Work = 3061.07 J - 1000 J = 2061.07 J