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In physics, the concept of work is all about the action of forces on an object. When a force is applied to an object causing it to move, work is done. The amount of work depends on both the force applied and the distance over which it is applied.

The formula to calculate work is:

• \( W = F \times d \times \cos(\theta) \)
• where \( W \) is the work, \( F \) is the force applied, \( d \) is the distance moved, and \( \theta \) is the angle between the force and the direction of movement.

In the given exercise, the worker's push is horizontal and thus parallel to the crate’s movement, making \( \theta = 0\) and \( \cos(0) = 1\). Therefore, the work done by the worker's force can be directly calculated by multiplying the force by the distance moved by the crate. The worker exerts a force of 73.5 N to move the crate 4.5 m, resulting in a work of 330.75 J.

Understanding how work is calculated helps in comprehending how energy changes form when forces are applied.

When an object moves at a constant velocity, its speed and direction remain unchanged. In physics, this indicates that the net force acting on the object is zero.

For the factory worker pushing the crate, this means that the force he applies is exactly balanced by the frictional force opposing the motion.

• This results in no acceleration or deceleration.
• For the crate in this problem, a constant velocity is achieved when the worker's force equals the force of kinetic friction.

With constant velocity, it is crucial to understand that the forces are balanced. The applied force counteracts the opposing frictional force exactly, maintaining the crate's steady movement across the floor.

This ensures that concepts like acceleration don't come into play, simplifying the problem to focus strictly on resistance—namely friction.

The normal force is crucial in understanding any object resting or moving along a surface. It is the perpendicular force exerted by a surface to support the weight of the object resting on it. In simpler terms, it acts as a balancing force preventing objects from sinking into the surface.

For a crate on a level floor, the normal force is equal to the gravitational force acting on the crate since there's no vertical motion.

• Calculated as \( F_n = mg = 30.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \), or 294 N for this problem.
• This force balances out with the downward pull of gravity on the crate.

Remember, the normal force acts perpendicular to the surface, and since it does not do any work (as it does not cause displacement in its direction), the work done by the normal force in moving the crate is zero.

The concept of net work is best understood with the idea of summing up all work done by forces acting on an object. In essence, it’s about how these forces either boost or dampen the object's energy.

For the crate being pushed, we consider:

• The positive work done by the worker's push: 330.75 J
• The negative work done by friction: -330.75 J
• Zero work by both the normal force and gravity

Adding these together gives a net work of zero, indicating an energy balance in the system.

Net work being zero makes sense as the crate moves at a constant velocity. Since the work inputs balance the outputs, no extra energy is needed to keep the crate moving once balanced forces are applied. This principle is essential in understanding energy conservation and how different forces interact in real-life movements.