The skateboarder in the figure is coasting down a ramp, and...

The skateboarder in the figure is coasting down a ramp, and there are three forces acting on her: her weight $\overrightarrow{\mathbf{W}}$ (magnitude $=675 \mathrm{N}$ ), a frictional force $\overrightarrow{\mathbf{f}}$ (magnitude $=125 \mathrm{N}$ ) that opposes her motion, and a normal force $\overrightarrow{\mathbf{F}}_{\mathbf{N}}$ (magnitude $=612 \mathrm{N}$ ) Concepts: Part $b$ of the figure shows each force, along with the displacement $\overrightarrow{\mathbf{s}}$ of the skateboarder. By examining these diagrams and without doing any numerical calculations, determine whether the work done by each force is positive, negative, or zero. Provide a reason for each answer. Calculations: Determine the net work done by the three forces when she coasts for a distance of $9.2 \mathrm{m}$

The skateboarder in the figure is coasting down a ramp, and there are three forces acting on her: her weight $\overrightarrow{\mathbf{W}}$ (magnitude $=675 \mathrm{N}$ ), a frictional force $\overrightarrow{\mathbf{f}}$ (magnitude $=125 \mathrm{N}$ ) that opposes her motion, and a normal force $\overrightarrow{\mathbf{F}}_{\mathbf{N}}$ (magnitude $=612 \mathrm{N}$ ) Concepts: Part $b$ of the figure shows each force, along with the displacement $\overrightarrow{\mathbf{s}}$ of the skateboarder. By examining these diagrams and without doing any numerical calculations, determine whether the work done by each force is positive, negative, or zero. Provide a reason for each answer. Calculations: Determine the net work done by the
three forces when she coasts for a distance of $9.2 \mathrm{m}$

Key Concepts

Net Work

Net work is the sum of the individual works done by all forces acting on an object. It determines the overall change in kinetic energy of the object in accordance with the work-energy theorem, thus providing insight into the net energy transfer within the system.

Weight (Gravitational Force)

Weight is the force exerted by gravity on an object, acting vertically downward. When an object moves in a direction that has a component parallel to the gravitational force (such as down an inclined plane), weight does positive work by contributing to the object's motion; if the motion is upward, it does negative work.

Normal Force

The normal force is the perpendicular force exerted by a surface on an object in contact with it. Because its direction is perpendicular to the displacement when the object moves along the surface, the work done by the normal force is zero due to the cosine of 90° being zero.

Friction

Friction is a resistive force that opposes the relative motion between two surfaces in contact. Since it acts opposite to the direction of displacement, it performs negative work, removing energy from the system as the object moves.

Dot Product of Vectors

The dot product is a mathematical operation that gives the component of one vector in the direction of another. In the context of work, it is used to determine the effective contribution of a force in the direction of displacement, indicating positive, negative, or zero work based on the angle between the two vectors.

Work

Work is defined as the dot product of a force and a displacement, which means it depends on the magnitude of the force, the displacement, and the cosine of the angle between them. This concept helps determine whether energy is added to or removed from a system depending on the direction of the force relative to the displacement.

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