Let's break down the problem systematically:

Given:

• Mass of the box ($m$) = 60 kg
• Angle of slope ($\theta$) = 8.0°
• Acceleration due to gravity ($g$) = 9.8 m/s²

1. Work done on the box by the force of gravity:

The work done by gravity is the force of gravity acting on the box in the direction of displacement. On an inclined plane, gravity can be split into two components:

• One parallel to the surface: $F_{\text{gravity, parallel}} = mg \sin(\theta)$
• One perpendicular to the surface: $F_{\text{gravity, perpendicular}} = mg \cos(\theta)$

The work done by gravity depends on the displacement of the box in the direction of the force. Since the truck moves with constant velocity, we assume no vertical displacement of the box (no change in height), and thus the displacement along the ramp is purely horizontal. As such, we only consider the component of gravity parallel to the slope.

The formula for work done by gravity is: $W_{\text{gravity}} = F_{\text{gravity, parallel}} \times d$ Where $d$ is the displacement. Since the box is stationary relative to the truck (due to static friction), there is no displacement along the slope, and hence the work done by gravity on the box is zero: $W_{\text{gravity}} = 0 \text{ J}$

2. Work done on the box by the normal force:

The normal force acts perpendicular to the surface. Since the displacement of the box is parallel to the surface and the normal force is perpendicular to it, the angle between the force and displacement is 90°. The work done by a force is calculated as: $W = F \cdot d \cdot \cos(\theta)$ For the normal force, $\theta = 90^\circ$, and $\cos(90^\circ) = 0$. Therefore, the work done by the normal force is: $W_{\text{normal}} = 0 \text{ J}$

3. Work done on the box by the force of friction:

The static friction force prevents the box from sliding, but since the box is not moving relative to the truck, the displacement is zero. The work done by friction is: $W_{\text{friction}} = F_{\text{friction}} \times d$ Since the box is not moving, $d = 0$, so: $W_{\text{friction}} = 0 \text{ J}$

Final Answers:

• Work done by gravity: $0 \, \text{J}$
• Work done by normal force: $0 \, \text{J}$
• Work done by friction: $0 \, \text{J}$

Since there is no displacement in the direction of these forces, the work done by all of them is zero.

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Would you like a more detailed explanation of any of the steps or concepts involved? Here are some related questions you may find useful:

1. How does static friction prevent the box from moving?
2. What is the difference between static and kinetic friction in this context?
3. How does the angle of the incline affect the forces on the box?
4. How would the work done by gravity change if the box were sliding?
5. How is the force of static friction calculated in a situation like this?

Tip: Work is defined as a force causing displacement. When there's no displacement in the direction of the force, no work is done!