State to examples of zero work.

When we talk about "zero work," we're referring to situations where no net work is done on an object, despite forces being applied. This concept is important in physics, particularly in mechanics. Let’s break down two clear examples to illustrate this idea.

Example 1: Object at Rest

Imagine you have a heavy box sitting on the floor. If you push on the box with a force, but it doesn’t move, the work done on the box is zero. In physics, work is defined as the product of force and displacement in the direction of the force. Since the box hasn’t moved, the displacement is zero. Therefore, the work done can be calculated as:

• Work (W) = Force (F) × Displacement (d) × cos(θ)

In this case, even though you are exerting force, the displacement (d) is zero, leading to:

• W = F × 0 = 0

Example 2: Circular Motion

Consider a car driving around a circular track at a constant speed. The engine exerts a force to keep the car moving, but this force is directed towards the center of the circle, while the car's displacement is tangential to the circle. The angle (θ) between the force and the displacement is 90 degrees. Since the cosine of 90 degrees is zero, the work done by the centripetal force is also zero:

• W = F × d × cos(90°) = F × d × 0 = 0

In both examples, even though forces are acting, the lack of displacement means that no work is done. This principle is crucial for understanding energy transfer and the behavior of objects in various physical situations.