Final answer:
To calculate the work done by the force on the car, first determine the displacement vector's components using the given magnitude and angle, then perform the dot product of the force and displacement vectors.
Step-by-step explanation:
The question involves calculating the work done by a force on a car, which is a concept from physics. The work done by a force is given by the dot product of the force vector and the displacement vector. Here, we have a force F = (-68.0 N)i + (36.0 N)j and a displacement of 41.0 m in a direction 240.0 degrees counterclockwise from the +x-axis. We can determine the displacement vector in the i and j components using trigonometry:
δi = 41.0m * cos(240°) = 41.0m * (-√3/2)
δj = 41.0m * sin(240°) = 41.0m * (-1/2)
Now we take the dot product of F and δ:
W = F ∙ δ
W = (-68.0 N)i ∙ (δi)i + (36.0 N)j ∙ (δj)j
W = (-68.0 N)(41.0m * (-√3/2)) + (36.0 N)(41.0m * (-1/2))
W = (68.0 N)(20.5m * √3) - (36.0 N)(20.5m)
W = 2396.0 N⋅m * √3 - 738.0 N⋅m
To find the numerical value, you would calculate (2396.0 * √3 - 738.0), remembering to include the direction of the force in respect to the direction of the displacement. The negative sign in the final result contributes to the directional component of the work.