Friction Between Two Objects and Relative Motion

Problem Statement

A sufficiently long board A of mass $M$ is placed on a smooth horizontal floor. A small object B of mass $m$ is placed near the right end of board A.

There is friction between the contact surfaces of A and B. Let $\mu$ be the coefficient of static friction and $\mu'$ be the coefficient of kinetic friction between them. Let the magnitude of gravitational acceleration be $g$ .

At time $t$ , both A and B are at rest. Then, a constant horizontal force $F$ is applied to board A in the rightward direction.

When force $F$ satisfies a certain condition, object B slides on board A.

Find the distance $L$ that object B slides relative to board A from time $t$ to $t=t_1$ . Assume object B does not fall off board A during time $t_1$ .

Constraints

$M = 3.0 \ \text{kg}$
$m = 2.0 \ \text{kg}$
$\mu = 0.50$
$\mu' = 0.30$
$F = 30 \ \text{N}$
$g = 9.8 \ \text{m/s}^2$
$t_1 = 10 \ \text{s}$

Input Format

Find the distance $L$ that object B slides relative to board A in $\text{m}$ (meters) and give the answer as a positive integer.

Problem Statement

Constraints

Input Format

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