Final answer:
The work done by the gravitational force on the box is -120 Joules as gravity acts downward while displacement is upward along the plane. The work done is calculated using the cosine of the angle between the force and displacement direction, which is negative in this case due to opposing directions.
This correct answer is d.
Step-by-step explanation:
The question asks for the work done by the weight of a 40-N box being pulled along an inclined plane. Work done by a force is calculated using the formula W = F × d × cos(θ), where F is the force, d is the distance, and θ is the angle between the force and the direction of displacement.
In this case, the angle to consider is the complement of the plane's incline since the weight acts vertically downward. This angle is 90 degrees - 37 degrees, which is 53 degrees.
The gravitational force (the weight of the box) is acting downward, while the displacement is upward along the plane. Since the force of gravity only has a component along the incline (not perpendicular to it), we do not need to consider the normal force component for work done by gravity. The work done by the weight of the box can be calculated as:
W = 40 N × 5.0 m × cos(53°)
Convert the angle to radians if necessary and calculate the cosine:
cos(53°) = cos(53 · (π/180)) = 0.6 (approx)
W = 40 N × 5.0 m × 0.6 = 120 J
The work done by gravity will be negative since gravity is doing negative work against the direction of the displacement (which is upwards on the incline). Therefore, the answer is -120 Joules, which can be written in scientific notation as -1.2 x 10² J.
This correct answer is d.