91Ó°ÊÓ

Kinetic friction is the force that opposes the motion between two surfaces in contact. It acts in the opposite direction to the movement of the object. This force is crucial to consider in any physical scenario where there is relative motion, such as a block sliding on a floor. The magnitude of kinetic friction can be calculated using the formula:

• \( f_k = \mu_k \times N \)
• where \( \mu_k \) is the coefficient of kinetic friction, and \( N \) is the normal force.

For instance, if the block has a mass of \( 4.00 \, \text{kg} \), the normal force \( N \) can be calculated using the weight of the block, which is mass times the gravitational acceleration \( g \), resulting in \( N = 4.00 \, \text{kg} \times 9.80 \, \text{m/s}^2 = 39.2 \, \text{N} \). If the coefficient of kinetic friction is \( 0.600 \), then the frictional force \( f_k = 0.600 \times 39.2 \, \text{N} = 23.52 \, \text{N} \). This force resists the block's motion across the floor, converting part of the force's work into heat.

Thermal energy refers to the energy that is generated and transferred as heat within a system. It arises due to the molecular activity within substances and is a result of processes such as friction. When a block slides across a surface, part of the mechanical work is converted to thermal energy due to kinetic friction.
The increase in thermal energy can be computed by assessing the total work done against friction. In our scenario, where work done against friction is \( 70.56 \, \text{J} \), if the block's thermal energy increases by \( 40.0 \, \text{J} \), the rest is absorbed by the floor.
To find out how much thermal energy goes to the floor, simply subtract the block's increase from the total work done against friction:

• Floor's thermal energy increase = Total work done against friction - Block's thermal energy increase
• \( = 70.56 \, \text{J} - 40.0 \, \text{J} = 30.56 \, \text{J} \)

This distribution of energy into heat highlights the inevitable conversion of mechanical energy in frictional systems.

A horizontal force is a force applied parallel to the surface of interaction, such as a force applied to push a block across a floor. In the exercise, this force was given as \( 35.0 \, \text{N} \). This value represents how much force is applied in the direction of the block's movement.

• To calculate the work done by this force, use the formula:
• \( W = F \times d \times \cos{\theta} \)

For a horizontal force, the angle \( \theta \) between the force and displacement is \( 0^\circ \), resulting in \( \cos{0^\circ} = 1 \). Hence, the work done is simply the product of the force magnitude and the displacement:

• \( W = 35.0 \, \text{N} \times 3.00 \, \text{m} \times 1 = 105.0 \, \text{J} \)

This concept is crucial in understanding how forces exert energies into movements, thereby affecting objects within their path and converting some of this exerted energy into other forms, like kinetic or thermal energy.