91Ó°ÊÓ

When an object moves with constant velocity, it means that it maintains a steady speed and direction over time.
This implies there is no acceleration happening; the forces acting on the object are balanced. In our scenario, the water skier is being pulled by a boat with a constant velocity.
This constant velocity indicates that the tension in the tow rope exactly counteracts any opposing forces, like water resistance or friction.

• Constant velocity means the net force is zero because initial velocity = final velocity.
• No acceleration is present since acceleration is a change in velocity.

This balance allows us to focus solely on the work done, as the skier maintains a steady pace until they fall.

In physics, force and displacement play vital roles in the concept of work.
Work is defined as the energy transferred when a force acts upon an object to move it over a distance.
The relationship between force and displacement can be calculated using the formula for work: \[ W = F \cdot d \cdot \cos(\theta) \]where:

• \( W \) is the work done in joules.
• \( F \) is the force applied in newtons.
• \( d \) is the displacement in meters.
• \( \theta \) is the angle between the force and the direction of displacement.

In this exercise, the skier moves in the direction of the rope's tension, so \( \theta = 0 \), making \( \cos(0) = 1 \).
This simplifies the calculation, emphasizing the understanding that work is being effectively done because the force used fully aligns with the skier's movement.

Tension is the force exerted along a medium, like a rope or cable, due to the forces acting at each end.
In the case of the water skier, the tension in the rope is constant as the boat pulls them.
This tension provides the necessary force to overcome water resistance and move the skier.

• The given tension here is \( 120 \; \text{N} \).
• It is critical in maintaining the skier's constant velocity.

As the rope remains taut, it ensures a direct and consistent application of force.
When analyzing problems involving tension, it is important to assume that the rope does not stretch and that the force is transmitted uniformly along its length.
This assumption helps us conclude that the skier keeps moving directly behind the boat at a consistent speed until other forces disrupt this balance, like when the skier falls.