Final answer:
To calculate the work done by the worker, the horizontal force applied must be resolved into a component parallel to the ramp's incline, then multiplied by the distance moved. However, the question lacks the value for the horizontal force, making it impossible to complete the calculation.
Step-by-step explanation:
To determine the amount of work done by the worker on the box as it is pushed up a frictionless ramp, we need to calculate the component of the force that is parallel to the ramp, since the box is pushed horizontally. Since the ramp is inclined at an angle of 7.1 degrees with respect to the x axis, we will use the angle to find the parallel component of the force. The work done (W) is the product of this force component and the distance moved up the ramp (3.7 m), which can be calculated using the equation W = Fcos(θ)d, where F is the force applied, θ is the angle of the incline, and d is the distance.
However, without knowing the applied horizontal force, we cannot provide the exact work done in this scenario. If the question had provided the applied horizontal force, we could have continued with the calculation as follows:
First, resolve the horizontal force into a component parallel to the incline (Fparallel = F * cos(θ)).
Then compute the work done: W = Fparallel * d.