91Ó°ÊÓ

When objects slide against each other, there is a resistance called friction. Kinetic friction is the specific type of friction that acts on moving objects. It opposes the direction of motion and is always less than or equal to the force applied. In our exercise, the kinetic frictional force between the collie's bed box and the floor amounts to \(5.0 \text{ N}\). This force attempts to stop the box from moving as the collie drags it along.

Friction depends on both the nature of the surfaces in contact and how hard they press against each other. This interaction creates a force which we calculate using the frictional force formula:
\[f_{\text{friction}} = \mu_k \times N\]
where \(\mu_k\) is the coefficient of kinetic friction and \(N\) is the normal force, or the force perpendicular to the surfaces.

• Kinetic friction acts horizontally in this case.
• The collie's applied force must be larger than the frictional force for movement.
• As the object continues to move, kinetic friction transforms some mechanical energy into thermal energy.

Thermal energy is the energy that comes from heat. When we talk about friction converting into thermal energy, we're touching upon the transformation of energy from mechanical to heat. This happens because as surfaces slide over each other, microscopic irregularities cause energy to be lost in the form of heat. In our scenario, as the collie drags the box, the kinetic friction of \(5.0 \text{ N}\) results in an increase in thermal energy.


The increase in this energy can be calculated using the work done by the frictional force. Here the transformation of work into thermal energy is quantified:
\[\Delta E_{\text{thermal}} = 5.0 \text{ N} \times 0.70 \text{ m} = 3.5 \text{ J}\]

• Thermal energy increase is equal to the work done by friction.
• Friction continuously converts mechanical energy into heat.
• This is why surfaces often get warm when rubbed together.

In the world of physics, work is done when a force causes displacement. The equation \(W = F \cdot d \cdot \cos(\theta)\) helps us determine how much work is performed. In this example, the collie's force of \(8.0 \text{ N}\) is at an angle of \(0^{\circ}\) with the direction of movement, meaning all the force effectively contributes to the displacement of the box.

The work done by the collie's force is:
\[W = 8.0 \text{ N} \times 0.70 \text{ m} \times 1 = 5.6 \text{ J}\]

Things to remember about work:

• Work is only done when there is displacement in the direction of force.
• An angle \(\theta = 0^{\circ}\) simplifies calculations because \(\cos(0) = 1\).
• The concept of work helps us measure the energy transferred by forces.