In the study of friction, the magnitude of sliding friction between two solid surfaces is generally how related to the magnitude of static friction between the same surfaces?

Introduction / Context:
Friction is the resistive force that opposes relative motion between two surfaces in contact. There are different types of friction, including static friction, which acts when surfaces are at rest relative to each other, and sliding or kinetic friction, which acts when surfaces are already moving. The question asks you to compare the magnitude of sliding friction with static friction for the same pair of surfaces. This comparison is very important in understanding why it is harder to start moving a heavy object than to keep it moving once it has started.

Given Data / Assumptions:

• Two solid surfaces are in contact under a given normal reaction.
• Static friction acts just before motion begins.
• Sliding friction acts when one surface is moving relative to the other.
• We assume ordinary dry surfaces, not special lubricated or highly unusual materials.

Concept / Approach:
Static friction adjusts itself to match the applied force up to a maximum value called limiting friction. To start motion, the applied force must exceed this maximum static friction. Once motion begins, the frictional force drops slightly to a lower, almost constant value known as sliding or kinetic friction. For most pairs of surfaces, the coefficient of static friction is slightly higher than the coefficient of sliding friction. Therefore, the maximum static friction is greater than sliding friction. This is why it feels harder to set a heavy box in motion than to push it along the floor after it has started moving.

Step-by-Step Solution:
Step 1: Recall that static friction acts when there is no relative motion, and it increases with applied force up to a maximum value.Step 2: The maximum value of static friction is sometimes called limiting friction.Step 3: Once the applied force exceeds this limiting value, the object starts to move and sliding friction acts.Step 4: Experimental results show that the sliding frictional force is usually slightly less than the limiting static friction force for the same surfaces.Step 5: Therefore, sliding friction is smaller than static friction, making option D correct.

Verification / Alternative check:
You can verify this by thinking about practical experience. When you try to push a heavy cupboard, you feel a strong resistance at the start. After it begins to slide, maintaining the same speed seems easier, because the resistive force has decreased. Engineers also use different coefficients for static and kinetic friction in calculations. The typical relationship is that the coefficient of static friction is slightly greater than the coefficient of sliding friction, confirming that the sliding frictional force is smaller in magnitude than the maximum static friction.

Why Other Options Are Wrong:
Option A, stating that sliding friction is double the static friction, is incorrect and does not match experimental evidence. Option B claims both are exactly the same, which contradicts the established difference between limiting static friction and kinetic friction. Option C suggests that sliding friction is greater than static friction, which would make objects harder to move once they start, but this does not match everyday observation. Only option D correctly states that sliding friction is smaller than static friction for the same surfaces.

Common Pitfalls:
Some learners misread the question and compare sliding friction to normal static friction instead of the maximum static friction, which can cause confusion. Others mix up the direction of the inequality and think that motion should increase friction. Remember that nature often resists the start of motion more strongly than the continuation of motion. Keeping this physical interpretation in mind helps you recall that static friction is usually higher, and sliding friction is slightly reduced once motion begins.

Final Answer:
Smaller than the static friction