91Ó°ÊÓ

In physics, the normal force is the support force exerted upon an object in contact with another stable object. It acts perpendicular to the surface of contact. For an object resting on a horizontal surface with no additional vertical forces, the normal force equals the gravitational force. However, when additional vertical forces are applied, like in our exercise, we must adjust this calculation:

• When a downward force is applied to an object, it increases the normal force (like adding weight to a box).
• When an upward force is applied, it decreases the normal force (like slightly lifting the box).

In the given problem, we have the force of gravity calculated as \( F_g = mg = 2.5 \text{ kg} \times 9.8 \text{ m/s}^2 = 24.5 \text{ N} \). Depending on the vertical force \( \vec{P} \) applied (8 N, 10 N, or 12 N respectively), this normal force changes. Remember, normal force is crucial as it influences both static and kinetic friction.

Static friction is a force that keeps an object at rest when a force is applied to it. It's the friction present before an object begins to slide. It adapts to the applied force up to a maximum value. The maximum static friction force \( f_s \) can be calculated using:

\[ f_s = \mu_s \times N \]

Where \( \mu_s \) is the coefficient of static friction, and \( N \) is the normal force.

In our example, with different \( \vec{P} \) values:

• For \( \mathbf{P = 8.0 \text{ N}} \), the maximum static friction is 6.6 N.
• For \( \mathbf{P = 10.0 \text{ N}} \), \( f_s \) is 5.8 N.
• For \( \mathbf{P = 12.0 \text{ N}} \), \( f_s \) is 5.0 N.

Static friction will match any applied horizontal force up to this calculated limit. If the applied force exceeds this limit, the object will start to move, and kinetic friction will take over.

Kinetic friction occurs when two objects are moving relative to each other with surfaces in contact. Unlike static friction, kinetic friction doesn't adjust. It has a constant value when objects are sliding against each other. For kinetic friction, the force \( f_k \) is given by:

\[ f_k = \mu_k \times N \]

Here, \( \mu_k \) is the coefficient of kinetic friction. For this problem, we favor kinetic friction only when the horizontal force \( \vec{F} \) is higher than the maximum static friction \( f_s \). Once this threshold is surpassed, the object enters motion, and kinetic friction is considered.

• In scenarios with \( \mathbf{P = 10.0 \text{ N}} \) and \( \mathbf{P = 12.0 \text{ N}} \), where the horizontal force is greater than the static friction, kinetic friction calculations become necessary.

Remember, kinetic friction tends to be less than static friction, which explains why sliding an object into motion often takes less force after it starts moving compared to the force required to start the movement.