On a cold day, Ming rubs her hands together to warm them up....

On a cold day, Ming rubs her hands together to warm them up. She presses her hands together with a force of $5.0 \mathrm{N} .$ Each time she rubs them back and forth they move a distance of $16 \mathrm{cm}$ with a coefficient of kinetic friction of $0.45 .$ Assuming no heat flow to the surroundings, after she has rubbed her hands back and forth eight times, by how much has the internal energy of her hands increased?

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Key Concepts

Normal Force in Friction Calculations

The normal force is the perpendicular force exerted by surfaces in contact and is critical in determining the frictional force. Since kinetic friction is calculated as the product of the coefficient of friction and the normal force, understanding the role of the normal force is essential in analyzing frictional heating.

Energy Conversion through Friction

This concept describes the process by which mechanical work is converted into thermal energy due to friction. As surfaces slide against one another, the energy lost from the mechanical work is absorbed as heat, raising the internal energy of the materials involved.

Kinetic Friction

Kinetic friction is the resistive force acting between surfaces in relative motion. It is proportional to the normal force and is quantified by the coefficient of kinetic friction. The work done by kinetic friction converts mechanical energy into thermal energy, increasing the internal energy of the objects in contact.

Work-Energy Principle

This concept relates mechanical work to changes in energy. When a force is applied over a distance, it does work on an object, which can be converted from kinetic energy into other forms. In contexts like friction, the work done against friction is transformed into internal energy or heat.

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