Question

Which of the following observations about the friction force is (are) incorrect? a) The magnitude of the kinetic friction force is always proportional to the normal force b) The magnitude of the static friction force is always proportional to the normal force. c) The magnitude of the static friction force is always proportional to the external applied force. d) The direction of the kinetic friction force is always opposite the direction of the relative motion of the object writh respect to the surface the object moves on. e) The direction of the static friction force is always opposite that of the impending motion of the object relative to the surface it rests on f) All of the above are correct.

Short answer

Answer: C) Static friction force proportionality with external applied force and F) All statements are correct.

Step-by-step solution

A) Kinetic friction force proportionality with normal force.

This statement is true. Kinetic friction force (\(f_k\)) is always proportional to the normal force (\(N\)). The proportionality constant is the coefficient of kinetic friction (\(\mu_k\)). So mathematically, it can be written as \(f_k = \mu_k N\).

B) Static friction force proportionality with normal force.

This statement is also true. The maximum static friction force (\(f_{s,max}\)) is proportional to the normal force (\(N\)). The proportionality constant is the coefficient of static friction (\(\mu_s\)). Mathematically, it can be written as \(f_{s,max} = \mu_s N\). However, it's important to note that the actual static friction force can vary from 0 to the maximum value.

C) Static friction force proportionality with external applied force.

This statement is incorrect. The static friction force is not always proportional to the external applied force. For a given normal force, the static friction force will adjust to balance the applied force up to a maximum value of the static friction force (\(f_{s,max} = \mu_s N\)). Beyond that, the object may start moving due to an external force that exceeds the static friction force.

D) Kinetic friction force direction.

This statement is true. The kinetic friction force always acts in the opposite direction of the relative motion of the object with respect to the surface the object is moving on.

E) Static friction force direction.

This statement is true. The static friction force always acts in the opposite direction of the impending motion of the object relative to the surface it rests on.

F) All statements are correct.

This statement is incorrect. As we have analyzed, statement C is incorrect. Therefore, all the statements are not correct. In conclusion, the incorrect observations about friction force are C) and F).

Key concepts

Kinetic Friction

Kinetic friction is an essential concept when understanding how frictional forces work. This type of friction occurs when two surfaces slide past each other. When we talk about kinetic friction, it is important to remember:

• The kinetic friction force, denoted as \(f_k\), always points in the direction opposite to the movement of the object.
• This force is proportional to the normal force \(N\), with the proportionality constant being the coefficient of kinetic friction \(\mu_k\).

The relationship can be expressed mathematically as \(f_k = \mu_k N\). This equation shows that as the normal force increases, so does the kinetic friction force. It’s crucial to note that the coefficient of kinetic friction \(\mu_k\) is unique for every pair of materials in contact. Factors like surface texture and material type can influence this coefficient. However, \(\mu_k\) remains constant for a given couple of surfaces under consistent conditions.

Static Friction

Static friction is the force that keeps an object at rest when an external force is applied. It is more complex than kinetic friction because it varies depending on the forces acting on the object. Some key points to understand about static friction include:

• The static friction force opposes the direction of potential movement.
• This force adjusts its magnitude to match the applied force until it reaches a maximum value.
• The maximum static friction force \(f_{s,max}\) can be represented by the formula \(f_{s,max} = \mu_s N\), where \(\mu_s\) is the coefficient of static friction.

Remember, static friction does not have a single value. Instead, it ranges from zero to this maximum value, adjusting as necessary to prevent movement until the applied force exceeds \(f_{s,max}\). At this point, the object may begin to slide, and kinetic friction will take over.

Normal Force

Knowing about normal force is crucial to understanding frictional forces. The normal force is a support force exerted by a surface, perpendicular to it, that prevents objects from "falling" into the surface. Here's what you need to know:

• It acts at a 90-degree angle to the contact surface.
• The magnitude of the normal force often equals the weight of the object when on a horizontal surface without additional vertical forces.
• It is influenced by factors such as applied angles, surface inclines, and additional vertical forces.

For friction forces, whether kinetic or static, the normal force plays a pivotal role as it determines the maximum possible friction by dictating the maximum frictional force possible via \(\mu N\). Variations in normal force directly influence the friction experienced between surfaces.

Coefficient of Friction

The coefficient of friction is a dimensionless scalar value that describes the ratio of the force of friction between two bodies and the force pressing them together. There are two types of coefficients of friction: kinetic and static.

• Each pair of contacting materials has its unique coefficient of friction value.
• For kinetic friction, the coefficient is denoted by \(\mu_k\), while for static friction, it is represented as \(\mu_s\).
• The value of \(\mu\) typically ranges between 0 and 1, with larger values indicating higher friction.

This coefficient plays a vital role in the formulas for both static and kinetic friction, as seen in the equations \(f_k = \mu_k N\) and \(f_{s,max} = \mu_s N\). The coefficient of friction is determined experimentally and is crucial when designing systems involving movement and stability.