91Ó°ÊÓ

Kinetic friction is the force that opposes the motion when one object slides over another. This type of frictional force acts in the opposite direction to the motion of the object. It depends on two main factors:

• The nature of the surfaces in contact
• The normal force pressing the two surfaces together

In the context of the problem, kinetic friction acts to oppose the motion of the box as it is pushed across the warehouse floor. The formula for calculating the force of kinetic friction is given by:
\[ f_k = \mu_k \cdot N \]where:

• \( f_k \) is the kinetic friction force
• \( \mu_k \) is the coefficient of kinetic friction
• \( N \) is the normal force, which is typically the weight of the object if on a horizontal surface \( N = m \cdot g \)

The coefficient of kinetic friction is a dimensionless value that describes how easily one object will slide over another. It varies between different material pairs and needs experimental methods for determination, as calculated in this exercise.

The work-energy principle is a fundamental concept in physics that relates the net work done on an object to its change in kinetic energy. This principle can be expressed as follows:
\[ W_{net} = \Delta KE \]where:

• \( W_{net} \) is the net work done on the object
• \( \Delta KE \) is the change in the object’s kinetic energy

When the worker exerts a force on the box, he does work that changes the box's kinetic energy from zero (since it starts from a rest position) to its final kinetic energy determined by its velocity and mass.
In this exercise, it has been determined that the work completed by the worker (minus the work lost to friction) corresponds precisely to the change in kinetic energy of the box, showing how effectively energy has been transferred from the worker's effort into the motion of the box.

Kinetic energy is the energy of an object due to its motion. The formula to calculate kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]where:

• \( KE \) is the kinetic energy
• \( m \) is the mass of the object
• \( v \) is the velocity of the object

The change in kinetic energy \( \Delta KE \) is calculated as the difference between the final kinetic energy \( KE_f \) and the initial kinetic energy \( KE_i \). In this exercise, the initial kinetic energy was zero because the box started from rest. As the box moved under the influence of the worker's force, its kinetic energy increased by 20 J (joules) because of the additional speed it acquired.

The coefficient of friction is a measure of how much force is required to move one object over another. It is represented by \( \mu \), and can be separated into static (\( \mu_s \)) and kinetic (\( \mu_k \)) coefficients. The kinetic coefficient of friction applies to surfaces in relative motion, like the box sliding on the floor, which is relevant in this exercise.
The formula relating the coefficient of kinetic friction to the frictional force is:\[ \mu_k = \frac{f_k}{N} \]where:

• \( \mu_k \) is the coefficient of kinetic friction
• \( f_k \) is the frictional force
• \( N \) is the normal force

In the scenario given, the coefficient of kinetic friction \( \mu_k \) was calculated to be approximately 0.18, indicating a moderate level of friction between the box and the warehouse floor. This value is critical for understanding how much force is necessary to keep the box moving at a given speed.