Static Friction: Videos & Practice Problems

Static friction occurs when an object is at rest, opposing the force trying to initiate movement. It is defined by the equation $f{s}_{max}=\mu s_{}N$, where N is the normal force. The coefficient of static friction is typically greater than that of kinetic friction. If the applied force exceeds the maximum static friction, the object begins to move, transitioning to kinetic friction, calculated as $f{k}_{}=\mu k_{}N$.

Static Friction & Equilibrium

Static friction is a crucial concept in physics that differs from kinetic friction in its application and behavior. While kinetic friction occurs when an object is in motion, static friction acts on objects that are at rest, preventing them from starting to move. This type of friction is essential for understanding how forces interact with stationary objects.

When you apply a force to a stationary object, such as a heavy book on a table, static friction works to oppose the direction in which the object would move if there were no friction. For instance, if you push the book to the right, static friction acts to the left, countering your push. The force of static friction can be calculated using the formula:

$$f_s \leq \mu_s \cdot N$$

where f_s is the static friction force, μ_s is the coefficient of static friction, and N is the normal force acting on the object. The coefficient of static friction is typically greater than that of kinetic friction, indicating that it generally requires more force to initiate movement than to maintain it once the object is in motion.

To determine whether an object will remain at rest or start moving, compare the applied force to the maximum static friction force, denoted as f_{s max}. If the applied force is less than or equal to f_{s max}, the object will not move, and static friction will adjust to match the applied force, ensuring the object remains stationary. Conversely, if the applied force exceeds f_{s max}, the object will begin to move, and the frictional force will transition to kinetic friction, calculated using:

$$f_k = \mu_k \cdot N$$

In practical scenarios, such as pushing a block with known coefficients of static and kinetic friction, you can analyze the forces at play. For example, if a 5.1 kg block is at rest and you apply a force of 20 N, the static friction force will equal 20 N, as it balances the applied force. However, if you increase the applied force to 40 N, which exceeds the maximum static friction of 30 N, the block will start moving, and the frictional force will then be calculated using the kinetic friction formula.

Understanding the transition from static to kinetic friction is vital in physics, as it illustrates how forces interact with objects at rest and in motion. This knowledge is applicable in various real-world situations, from everyday activities to engineering and design.

Static & Kinetic Friction

To analyze the forces acting on a 5.1-kilogram block, we consider two scenarios: the force required to initiate movement and the force needed to maintain constant speed. In both cases, we start by identifying the forces involved, including the weight force (mg) and the normal force.

In the first scenario, when attempting to get the block moving, the relevant friction is static friction. The maximum static friction force, denoted as \( f_{s \text{ max}} \), can be calculated using the equation:

\( f_{s \text{ max}} = \mu_s \cdot N \)

Here, \( \mu_s \) is the coefficient of static friction, and \( N \) is the normal force, which for a horizontal surface is equal to the weight of the block, \( mg \). Thus, we can express the force needed to start moving the block as:

\( f = \mu_s \cdot mg \)

Substituting the values, where \( \mu_s = 0.7 \), \( m = 5.1 \, \text{kg} \), and \( g = 9.8 \, \text{m/s}^2 \), we find:

\( f = 0.7 \cdot 5.1 \cdot 9.8 = 35 \, \text{N} \)

This means a force of at least 35 Newtons is required to initiate movement.

In the second scenario, once the block is in motion at a constant speed, the relevant friction is kinetic friction. The force needed to keep the block moving can be calculated using the equation:

\( f_k = \mu_k \cdot N \)

Where \( \mu_k \) is the coefficient of kinetic friction. The force required to maintain constant speed is given by:

\( f = \mu_k \cdot mg \)

Using \( \mu_k = 0.5 \), we calculate:

\( f = 0.5 \cdot 5.1 \cdot 9.8 = 25 \, \text{N} \)

Thus, only 25 Newtons are needed to keep the block moving at a constant speed. This illustrates an important principle: the coefficient of static friction (\( \mu_s \)) is always greater than the coefficient of kinetic friction (\( \mu_k \)), meaning it is generally harder to start moving an object than to keep it in motion. This concept is commonly observed in everyday experiences, such as pushing heavy objects.

Preventing a Block From Moving

To analyze the scenario of a 15-kilogram block at rest on a flat surface, we need to determine the downward force required to prevent the block from moving when a horizontal force of 300 N is applied. The key concept here is the role of static friction, which must counteract the applied force to keep the block stationary.

First, we establish a free body diagram for the block. The forces acting on the block include its weight (mg), the applied downward force (F_down), the normal force (N), and the applied horizontal force (F = 300 N). The weight of the block can be calculated using the formula:

mg = 15 kg × 9.8 m/s² = 147 N.

Since the block is not moving vertically, the sum of the vertical forces must equal zero. This gives us the equation:

ΣF_y = N - mg - F_down = 0.

Rearranging this, we find:

F_down = N - mg.

Next, we need to consider the horizontal forces. The static frictional force (F_s) must equal the applied force to prevent movement. The maximum static friction can be expressed as:

F_{s max} = μ_s × N,

where μ_s is the coefficient of static friction. Given that the applied force is 300 N, we set:

F_{s max} = 300 N.

From this, we can solve for the normal force:

N = F_{s max} / μ_s = 300 N / 0.7 ≈ 428.57 N.

Now that we have the normal force, we can substitute it back into our equation for F_down:

F_down = N - mg = 428.57 N - 147 N ≈ 281.57 N.

Rounding this value, we find that the required downward force to keep the block from moving is approximately 282 N. This calculation illustrates the balance of forces necessary to maintain static equilibrium in the presence of an applied force.

A 36N force is needed to start a 7.0 kg box moving across the floor. If the 36.0 N force continues, the box accelerates at 0.70 m/s². What are the coefficients of static and kinetic friction?

• A. μs = 0.52 ; μk = 0.64
• B. μs = 0.64 ; μk = 0.64
• C. μs = 0.52 ; μk = 0.45
• D. μs = 0.45 ; μk = 0.32

Answer: (C)

Here’s what students ask on this topic:

What is static friction and how does it differ from kinetic friction?

Static friction occurs when an object is at rest and opposes the force trying to initiate movement. It is defined by the equation $f_s={\mu }_{s}N$, where $N$ is the normal force. Kinetic friction, on the other hand, occurs when an object is already in motion and is defined by $f_k={\mu }_{k}N$. The coefficient of static friction (${\mu }_s$) is typically greater than that of kinetic friction (${\mu }_k$), meaning it takes more force to start moving an object than to keep it moving.

How do you calculate the maximum static friction force?

The maximum static friction force can be calculated using the equation $f_s={\mu }_{s}N$, where ${\mu }_s$ is the coefficient of static friction and $N$ is the normal force. The normal force is usually the weight of the object, calculated as $mg$, where $m$ is the mass of the object and $g$ is the acceleration due to gravity (approximately 9.8 m/s²).

What happens when the applied force exceeds the maximum static friction?

When the applied force exceeds the maximum static friction, the object begins to move. At this point, the friction force transitions from static friction to kinetic friction. The kinetic friction force is then calculated using the equation $f_k={\mu }_{k}N$, where ${\mu }_k$ is the coefficient of kinetic friction and $N$ is the normal force.

Why is the coefficient of static friction usually greater than the coefficient of kinetic friction?

The coefficient of static friction is usually greater than the coefficient of kinetic friction because it generally takes more force to overcome the initial resistance to motion (static friction) than to keep an object moving (kinetic friction). This is due to the microscopic interactions and interlocking between the surfaces in contact, which are more pronounced when the object is at rest.

How do you determine whether to use static or kinetic friction in a problem?

To determine whether to use static or kinetic friction in a problem, you need to compare the applied force to the maximum static friction force. If the applied force is less than or equal to the maximum static friction force, the object remains at rest, and you use static friction. If the applied force exceeds the maximum static friction force, the object starts to move, and you switch to using kinetic friction.