91Ó°ÊÓ

When attempting to move an object like the filing cabinet in our example, understanding how to calculate frictional force is crucial. Frictional force is the force that resists the motion of two surfaces sliding against each other. There are two types of frictional forces, static and kinetic. Here, we focus on calculating the static frictional force that comes into play when the object is initially at rest.
To find the maximum static frictional force, use the formula:

• \( f_{s, \text{max}} = \mu_s \times \text{Weight} \)

where \( f_{s, \text{max}} \) is the maximum static frictional force, \( \mu_s \) is the coefficient of static friction, and "Weight" is the weight of the object, here \( 556 \, \text{N} \).
Plugging the values in, we have:

• \( f_{s, \text{max}} = 0.68 \times 556 = 378.08 \, \text{N} \)

This calculation tells us that the filing cabinet requires a force greater than \( 378.08 \, \text{N} \) to begin moving. If the applied force is less than \( 378.08 \, \text{N} \), the frictional force will equal the applied force, keeping the cabinet at rest.

The coefficient of static friction, denoted as \( \mu_s \), is a dimensionless value that represents the frictional resistance between two stationary objects. This coefficient varies depending on the materials in contact.
For our filing cabinet and floor system, \( \mu_s = 0.68 \). Higher coefficients indicate greater resistance to start moving.
To understand its role, consider how it affects the maximum static friction:

• A greater \( \mu_s \) means the object requires more force to overcome the static friction and start moving.
• It is crucial in determining whether an object will remain stationary or not when a force is applied.

In our scenario, when the applied force is less than \( 378.08 \, \text{N} \), \( \mu_s \) ensures the cabinet doesn't budge by providing sufficient static friction. Only when the force exceeds this threshold does the object begin to move, transitioning from static to kinetic friction.

Once the object starts moving, the friction that acts upon it is known as kinetic friction. The coefficient of kinetic friction, \( \mu_k \), often has a smaller value compared to \( \mu_s \), indicating less resistance to continued motion once the object has started moving.
In our filing cabinet example, \( \mu_k = 0.56 \).
When the applied force surpasses the maximum static friction threshold, kinetic friction takes over. This is seen as:

• The frictional force is calculated as \( f_k = \mu_k \times \text{Weight} \).
• Plugging in the values gives us: \( f_k = 0.56 \times 556 = 311.36 \, \text{N} \).

Now, even though the cabinet moves, this frictional force counteracts to slow down or regulate its motion, making \( \mu_k \) vital in scenarios where constant force is applied to keep the object moving smoothly.