Friction

Two objects, A and B, with masses $m_A$ and $m_B$ respectively, are connected by a massless string over a frictionless, massless pulley as shown in the diagram. Object B rests on a horizontal table with a coefficient of kinetic friction $\mu$. The system is initially held at rest with the string taut and is then released.

Two blocks of mass $m_1$ and $m_2$ are connected by a massless string. They slide down a plane inclined at an angle $\alpha$ to the horizontal. The coefficients of kinetic friction between the blocks and the plane are $\mu_1$ and $\mu_2$ respectively. Block $m_1$ is positioned downslope from block $m_2$.

A block of mass $m$ is pushed across a floor by a constant force $\vec{F}$ applied at a downward angle $\theta$. The provided graph shows the block's acceleration magnitude $a$ as a linear function of the coefficient of kinetic friction $\mu_k$. The line passes through the points $(0, a_1)$, $(\mu_{k2}, 0)$, and $(\mu_{k3}, -a_1)$, where it can be deduced that $\mu_{k3} = 2\mu_{k2}$.

A horizontal force $\vec{F}$ pushes a block of weight $W$ against a vertical wall. The block is initially at rest. The coefficient of static friction between the wall and the block is $\mu_s$. The coordinate system is defined with the x-axis horizontal (positive in the direction of $\vec{F}$) and the y-axis vertical (positive upwards).

Two boxes of mass $m_1$ and $m_2$ are in contact on a horizontal surface. A horizontal force $\vec{F}$ is applied to the first box, $m_1$. The frictional forces on the boxes are $f_1$ and $f_2$, respectively.

An initially stationary box of total weight $W$ is to be pulled across a floor by a cable. The tension in the cable cannot exceed a maximum value $T_{max}$. The coefficient of static friction between the box and the floor is $\mu_s$.

A sled is held on an inclined plane by a cord pulling up the plane. The sled is on the verge of moving up the plane. The magnitude $F$ of the cord's force is a linear function of the coefficient of static friction $\mu_s$. The data shows that the force is $F_1$ when $\mu_s = 0$, and the force is $F_2$ when $\mu_s = \mu_{s2}$.

Three blocks with masses $m_1$, $m_2$, and $m_3$ are connected by ropes and pulleys as shown. Block 2 rests on a horizontal table. Assume the ropes and pulleys are massless and frictionless, and that $m_3 > m_1$. When the system is released from rest, it accelerates with a magnitude $a$.

As shown in the figure, two books, A and B, are interleaved page by page. The coefficient of static friction between pages is $\mu = 0.3$. The mass of each page is $m = 5$ g, and each book has $N=200$ pages. Book A is held stationary. A horizontal force $F$ is applied to pull out book B.

A block of mass $m$ is pushed along a horizontal floor by a constant applied force of magnitude $F$. The block starts from rest and its speed increases linearly with time, reaching a speed $v_s$ at time $t_s$.