Understanding Friction on Surfaces

This question asks us to evaluate two statements: an assertion about an object slipping on different surfaces and a reason relating slipping to frictional force and surface roughness. Let's analyze each statement carefully.

Analyzing Assertion (A): Object Slipping on Surfaces

Assertion (A) states: "An object slips less on a rough surface than a smooth surface."

Think about your everyday experience. Would it be easier to walk without slipping on a smooth, icy pavement or a rough, concrete path? It's generally easier to avoid slipping on a rough surface like concrete. This is because the interaction between the object (like your shoes) and the surface is different.

On a rough surface, there are more irregularities and points of contact at a microscopic level compared to a smooth surface. These irregularities help "grip" the object, resisting any tendency to slide or slip. Therefore, the assertion that an object slips less on a rough surface seems consistent with observation and basic understanding of how surfaces interact.

Based on this, Assertion (A) appears to be a true statement.

Analyzing Reason (R): Frictional Force and Surface Roughness

Reason (R) states: "When a surface is rough, frictional force increases."

Frictional force is the force that opposes relative motion or the tendency of relative motion between two surfaces in contact. It arises due to the microscopic irregularities, adhesion, and deformation of the surfaces where they touch.

A fundamental principle in the study of friction is that the magnitude of the frictional force depends on the nature of the surfaces in contact and the normal force pressing the surfaces together. The "nature of the surfaces" specifically includes how rough or smooth they are.

Rough surfaces have more interlocking irregularities, which generally leads to a greater resistance to motion between them. This increased resistance is manifested as a larger frictional force. For instance, the coefficient of friction, which is a measure of the friction between two surfaces, is typically higher for rough surfaces than for smooth surfaces.

Therefore, the reason that frictional force increases when a surface is rough is a true statement.

Connecting Assertion (A) and Reason (R)

Now we need to determine if Reason (R) is a correct explanation for Assertion (A). Assertion (A) talks about reduced slipping, and Reason (R) talks about increased frictional force on rough surfaces.

Slipping occurs when the applied force trying to cause motion between the surfaces overcomes the maximum static frictional force (or the kinetic frictional force if motion has started). A larger frictional force provides greater resistance to this relative motion.

Since a rough surface has a higher frictional force (as stated in R), this larger force will more effectively oppose the sliding or slipping of an object on that surface. This means it will be harder for the object to start slipping, or it will slip less easily once it starts moving, compared to a smooth surface where the frictional force is lower.

Thus, the increase in frictional force on a rough surface (R) directly explains why an object slips less on that surface (A). Reason (R) provides the physical mechanism behind the observation stated in Assertion (A).

Conclusion on Assertion and Reason

Both Assertion (A) and Reason (R) are true statements, and Reason (R) correctly explains why Assertion (A) is true. A higher frictional force on rough surfaces is the direct cause for reduced slipping.

Revision Table: Key Friction Concepts

Additional Information: Factors Affecting Friction

While surface roughness is a primary factor influencing the coefficient of friction and thus the frictional force, several other aspects are important to understand about friction:

• Nature of Surfaces: The materials of the surfaces in contact play a crucial role. For example, rubber on concrete has high friction, while ice on ice has very low friction. This includes the microscopic properties beyond just 'roughness'.
• Normal Force: The maximum static friction and the kinetic friction are directly proportional to the normal force pressing the surfaces together. That's why it's harder to slide a heavy box than a light one on the same floor: $\text{frictional force} \propto \text{Normal Force}$. We can write this relationship as $f_s^{\text{max}} = \mu_s N$ for static friction and $f_k = \mu_k N$ for kinetic friction, where $\mu_s$ and $\mu_k$ are the coefficients of static and kinetic friction, respectively, and $N$ is the normal force.
• Area of Contact: Surprisingly, for ideal dry friction, the area of contact between the surfaces does not significantly affect the frictional force, as long as the normal force is constant. This is because increasing the area typically decreases the pressure at each contact point, balancing the increased number of contact points. However, this rule can break down for very smooth surfaces or when adhesion effects are significant.
• Speed: For kinetic friction, the force is generally considered to be nearly independent of the relative speed between the surfaces, although there can be variations at very high or very low speeds.

Understanding these factors helps predict and explain how objects behave when in contact with different surfaces and under varying conditions.