A tow rope, parallel to the water, pulls a water skier...

A tow rope, parallel to the water, pulls a water skier directly behind a boat with constant velocity for a distance of $65 \mathrm{~m}$ before the skier falls. The tension in the rope is $120 \mathrm{~N}$. (a) Is the work done on the skier by the rope positive, negative, or zero? Explain. (b) Calculate the work done by the rope on the skier.

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Key Concepts

Work (Physics)

Work is the process by which energy is transferred by a force acting over a displacement. It is defined mathematically as the dot product of the force and displacement vectors, which takes into account the magnitudes of the vectors and the cosine of the angle between them.

Dot Product

The dot product is a mathematical operation that multiplies two vectors to yield a scalar. In the context of work, it incorporates both the magnitude of the force, the displacement, and the cosine of the angle between them, determining whether the work is positive, negative, or zero.

Force

Force is a vector quantity that represents a push or pull acting upon an object. When a constant force, such as tension, acts in the direction of the object's displacement, it can transfer energy to the object, doing positive work.

Displacement

Displacement refers to the change in position of an object. It is a vector quantity that, in the calculation of work, must be considered in both magnitude and direction relative to the force applied.

Positive Work

Positive work occurs when the force applied to an object and the displacement of the object are in the same direction. In such cases, energy is added to the object, usually resulting in an increase in its kinetic energy.

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