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 with 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: The statement that is incorrect is: The magnitude of the static friction force is always proportional to the external applied force.

Step-by-step solution

Statement a

The statement a) is correct. The magnitude of the kinetic friction force (fk) is given by the equation fk = μk * N, where μk is the coefficient of kinetic friction and N is the normal force. This shows that the magnitude of the kinetic friction force is always proportional to the normal force.

Statement b

The statement b) is correct. The maximum magnitude of the static friction force (fs) is given by the equation fs_max = μs * N, where μs is the coefficient of static friction and N is the normal force. While static friction can vary in magnitude and isn't always equal to its maximum value, the magnitude of the static friction force is always proportional to the normal force.

Statement c

The statement c) is incorrect. The static friction force opposes the external applied force to prevent motion. The magnitude of the static friction force is not always directly proportional to the external applied force. It varies according to the situation and can have values ranging from 0 to its maximum value given by fs_max = μs * N.

Statement d

The statement d) is correct. The direction of the kinetic friction force is always opposite the direction of the relative motion of the object with respect to the surface the object moves on. This is due to the nature of kinetic friction that opposes the motion causing energy dissipation as heat.

Statement e

The statement e) is correct. 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. This force prevents the object from moving and only acts when there is an impending motion.

Conclusion

Out of the given statements, only statement c) is incorrect. Thus, the observations about frictional forces that are incorrect are c) The magnitude of the static friction force is always proportional to the external applied force.

Key concepts

Kinetic Friction

Friction plays a crucial role in everyday physics, dictating how objects move across surfaces. When an object slides over a surface, it experiences a force that opposes its motion, known as kinetic friction. This force arises due to the interactions between the object's surface and the surface it's moving on. The magnitude of kinetic friction is found through the equation \( f_k = \mu_k \times N \), where \({\mu_k}\) represents the coefficient of kinetic friction—a value dependent on the materials in contact—and \({N}\) is the normal force, which is the force perpendicular to the surface exerted by the surface on the object.

It's important to note that kinetic friction does not depend on the velocity or the area of contact but is solely dependent on the types of surfaces involved and the normal force. The directional nature of kinetic friction is straightforward: it always acts in the opposite direction to the relative motion, working to slow down or stop the moving object.

Normal Force

The normal force is a fundamental component when discussing friction as it directly affects the frictional forces an object experiences. This force is perpendicular to the contact surface between two objects. When an object rests on a flat surface, the normal force is typically equal in magnitude to the object's weight, but directed upward. The normal force balances the weight to prevent the object from accelerating through the surface.

In the context of friction, the normal force determines the maximum possible frictional forces (both static and kinetic) that an object can experience on a surface. Uneven surfaces, inclined planes, or external vertical forces can all lead to changes in the normal force, therefore altering the frictional forces felt by the object. For any calculations relating to friction, accurately determining the normal force is essential.

Static Friction

Before an object in contact with a surface begins to move, it is subject to static friction. Contrary to kinetic friction, static friction acts on stationary objects when a force is applied to them, and its value changes depending on the applied force. It automatically adjusts to match the applied force up to its maximum limit, which is given by the formula \( f_{s_{\text{max}}} = \mu_s \times N \), with \({\mu_s}\) being the coefficient of static friction.

Understanding the Upper Limit

Static friction can only go up to a certain maximum value; beyond this point, if the external force continues to increase, the object will begin to slide, and static friction transitions to kinetic friction. The maximum static friction force is the product of the normal force and the coefficient of static friction, both of which are typically given or can be calculated based on the situation.

Coefficient of Friction

The coefficient of friction is a dimensionless number that represents the amount of friction between two surfaces. There are two types of coefficients: static (\({\mu_s}\)) and kinetic (\({\mu_k}\)). These coefficients depend on the nature of both the surfaces in contact. For instance, rubber on concrete has a higher coefficient than ice on steel.

It is essential to understand that these coefficients are empirical values, typically determined through experimentation, rather than derived from theoretical principles. They are crucial for calculating the maximum static friction and the kinetic friction an object experiences. While the coefficient of static friction pertains to the force needed to start the object's motion, the coefficient of kinetic friction relates to the force required to maintain motion once the object has started to slide. As a rule of thumb, \({\mu_s}\) is usually higher than \({\mu_k}\) for a given pair of surfaces, meaning it's generally harder to start moving an object than it is to keep it moving.