When work is done by friction, in what form in energy "lost"?

It becomes heat.

When work is done by friction, the energy that is "lost" or converted into a less useful form is primarily dissipated in the form of thermal energy.

Friction is a force that opposes the relative motion between two surfaces in contact. When an object slides or rolls over a surface with friction, the microscopic irregularities on both surfaces interact, causing resistance and generating heat. This heat energy is the primary form in which the energy is lost.

To understand how this happens, we can use the concept of mechanical work. Work is defined as the transfer of energy that occurs when a force is applied to an object and causes it to move in the direction of the force. When an object is subjected to frictional forces, such as when you rub your hands together, the work done by friction opposes the applied force and results in a decrease in the object's mechanical energy.

To calculate the work done by friction, you can use the equation:

Work = force of friction x displacement x cosine(angle between force and displacement)

Typically, the force of friction is multiplied by the distance over which the object moves or the displacement. The angle between the force and displacement is used to account for any variations in direction. By calculating the work done, you can determine the amount of mechanical energy lost due to friction.

However, it is important to note that although the mechanical energy may appear to be lost, the total energy of the system is conserved according to the law of conservation of energy. The energy lost to friction is transformed into thermal energy, causing an increase in the temperature of the objects involved.