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.

A mass $m$ on a horizontal surface is attached to two fixed walls by two identical springs, each with spring constant $k$. The coefficient of friction (static and kinetic) is $\mu$. The mass is released from rest at a displacement $x_0$. An "oscillation process" is defined as a half-cycle (e.g., moving from the rightmost to the leftmost point).

An object of mass $m$ on a horizontal surface with friction coefficient $\mu$ is subject to a restoring force $F=-kx$. There is a perfectly elastic wall at the origin $x=0$. The object is released from rest at $x=x_1 > 0$. Let $x_s = \mu mg/k$ be the magnitude of the displacement where the spring force equals the friction force.

Two cylinders of different radii, $R$ and $r$, rotate in opposite directions about parallel horizontal axes with the same angular velocity $\omega$. The axes are separated by a distance $L$. At $t=0$, a uniform plank of mass $M$ is placed horizontally on the rollers, with its center of mass (CM) initially above the axis of one of the cylinders. The coefficient of kinetic friction is $\mu$. The top surfaces of the rollers move inwards.

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 $\mu_s = \mu_{s2}$.