Three identical crates are pushed across different surfaces: crate A on ice, crate B on wood, and crate C on concrete. If the normal force is the same for all, rank the crates from least to greatest kinetic frictional force acting on them.

• A. $C,B,A$
• B. $A,C,B$
• C. $B,C,A$
• D. $A,B,C$

Answer: (D)

Verified step by step guidance

1. Recall that the kinetic frictional force \(f_k\) is given by the formula \(f_k = \mu_k N\), where \(\mu_k\) is the coefficient of kinetic friction and \(N\) is the normal force.
2. Since the problem states that the normal force \(N\) is the same for all three crates, the differences in frictional force depend solely on the coefficients of kinetic friction \(\mu_k\) for each surface.
3. Identify the relative values of \(\mu_k\) for the surfaces: ice has the lowest coefficient of kinetic friction, wood has a moderate coefficient, and concrete has the highest coefficient among the three.
4. Rank the crates by their frictional forces from least to greatest by ordering their coefficients: crate A on ice (lowest \(\mu_k\)), crate B on wood (medium \(\mu_k\)), and crate C on concrete (highest \(\mu_k\)).
5. Therefore, the kinetic frictional forces increase in the order: \(A\), \(B\), \(C\).