91Ó°ÊÓ

Kinetic friction occurs when two surfaces slide against each other. It's a force that opposes the motion of the objects in contact. In our exercise, the kinetic frictional force is what resists the movement of the bed box pulled by the Collie.

The value given for kinetic frictional force is 5.0 N. This force arises due to the interaction between the bed box and the floor surface. The magnitude of this force depends on the nature of the surfaces in contact and their roughness.

Kinetic friction can be calculated if we know the coefficient of kinetic friction (μ_k) and the normal force (N), using the formula:

\[ F_k = \text{μ}_k \times N \]

In this problem, though, we have been directly provided with the kinetic frictional force value, making it straightforward. The key takeaway is that kinetic friction always acts in the direction opposite to that of the movement, reducing the net force causing the motion and thus affecting the work done by other forces in the system.

Work done by a force is a fundamental concept in physics, defined as the product of the force applied and the distance over which it is applied, considering the direction of force.

Mathematically, work (W) is expressed as:

\[ W = F \times d \times \text{cos}(\theta) \]

where F is the force, d is the distance moved, and θ is the angle between the force and direction of motion.

In our exercise, the Collie applies a horizontal force of 8.0 N to move the bed box 0.70 m. Since the force is applied horizontally, θ is 0° and \text{cos}(0°) is 1:

\[ W_{\text{collie}} = 8.0 \text{ N} \times 0.70 \text{ m} \times \text{cos}(0°) = 5.6 \text{ J} \]

This calculation shows the work done by the Collie’s applied force. Notice how important it is to consider the angle of application—if it were different, the work done would change accordingly. The unit of work is the joule (J).

When objects slide against each other, friction not only opposes their movement but also converts kinetic energy into thermal energy. This is why you'll often feel heat when you rub your hands together.

In our problem, as the bed box is dragged across the floor by the Collie, the kinetic frictional force of 5.0 N causes an increase in thermal energy. The work done by this friction force is calculated similarly to the work done by the applied force:

\[ \text{Work done by friction} = \text{F}_{k} \times d \times \text{cos(0°)} \]

Given that \text{F}_{k} = 5.0 \text{ N} and \text{d} = 0.70 \text{ m}, we find:

\[ \text{Work by friction} = 5.0 \text{ N} \times 0.70 \text{ m} \times 1 = 3.5 \text{ J} \]

This 3.5 J is the increase in thermal energy of the bed and floor due to the work done by kinetic friction. The concept here is the conservation of energy, where mechanical work done against friction translates into heat.