Final answer:
The work done by gravity on the box as it is pulled up the incline is -29,447.68 J, indicating that gravity is doing negative work against the displacement.
Step-by-step explanation:
To calculate the work done by gravity as the box moves up the incline, we can use the formula for work, W = F × d × cos(θ), where F is the force parallel to the direction of displacement, d is the displacement, and θ is the angle between the force and the displacement direction.
Since gravity acts downward, the angle between the force of gravity and the direction of displacement is 180° - 30° = 150°. The force of gravity (Fg) can be calculated using Fg = m × g, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s²).
The work done by gravity on the box is as follows:
- Calculate the force of gravity: Fg = 347 kg × 9.8 m/s² = 3400.6 N.
- Determine the angle: θ = 150°.
- Calculate the work done by gravity: W = 3400.6 N × 8.00 m × cos(150°).
Now we need to calculate the cosine of 150° which is -√3/2. The negative sign indicates that gravity does work in the direction opposite to the displacement.
Therefore, W = 3400.6 N × 8.00 m × -√3/2.
Finally, the work done by gravity is: W = -29,447.68 J (negative sign indicates work is done against the direction of displacement).