Final answer:
The work done by a force of 68 N acting at an angle of 30 degrees above the horizontal on an object that slides 76 m is approximately 4468 joules, rounded to the nearest whole number.
Step-by-step explanation:
To calculate the work done by a force acting on an object at an angle, we must consider only the component of the force that acts in the direction of displacement. Since the force is applied at an angle of 30 degrees above the horizontal, we need to use the cosine of that angle to find the horizontal component of the force, which is the direction of the displacement.
The formula to calculate work when force and displacement are in the same direction is Work = Force × Displacement × cos(θ), where θ is the angle between the force and the direction of displacement.
In this specific example, the horizontal component of the force is (68 N) × cos(30°), and the displacement is 76 m. Thus:
- Horizontal component of force = 68 N × cos(30°) = 68 N × (√{3}/2) ≈ 58.79 N
- Work done = 58.79 N × 76 m ≈ 4468 joules
When reported to the nearest whole number, the work done is approximately 4468.