Question

Two block $A$ and $B$ are of the same mass. Block $B$ is kept on the block $A$ and block $A$ is kept on the horizontal floor. Force $F_1$ is the necessary to push only block $A$ at a constant speed across the floor while force $F_2$ is the necessary force to push the stack at the same constant speed across the floor. Force $F_2$ is greater than $F_1$ because:

• A. the force of the floor on block A is greater in the second case.
• B. the coefficient of kinetic friction between block A and the floor is greater.
• C. the force of kinetic friction, but not the normal force, on block A is greater.
• D. the coefficient of static friction between block A and the floor is greater.
• E. the weight of block A is greater in the second case.

Answer 1

The correct option is A the force of the floor on block A is greater in the second case.

Force of friction opposes the tendency of a body to move on a rough surface. It is given by, $F_r=\mu N$

where $\mu :$ coefficient of friction

$N:$ Normal reaction

Since the body moves with constant velocity, net force on the body is zero.

Hence, when only A is moving, $F_1=F_{r1}=\mu N_1={\mu m}_{A}g$

when both A and B are moving, $F_2=F_{r2}={\mu N}_2=\mu (m_A+m_B)g$