Friction

A triangular wooden block ABC rests on a rough horizontal surface. On its two rough inclined surfaces, two blocks with masses $m_1$ and $m_2$ ($m_1 > m_2$) are placed, as shown in Figure. The angles of inclination are $\theta_1$ and $\theta_2$. The entire system, consisting of the triangular block and the two smaller blocks, is at rest.

An inclined plane has a length $L=5$ m and height $H=3$ m. At the bottom, there is an object A with mass $m=5$ kg. The coefficient of kinetic friction between A and the plane is $\mu=0.3$. A horizontal force $F=100$ N pushes A, causing it to move up the incline from rest. After A has moved a distance $s_0=2$ m along the incline, the force F is removed. Assume $g=10$ m/s².

A block weighing 22 N is held at rest against a vertical wall by a horizontal force $\vec{F}$ of magnitude 60 N. The coefficient of static friction between the wall and the block is 0.55, and the coefficient of kinetic friction between them is 0.38. In six experiments, a second force $\vec{P}$ is applied to the block, directed parallel to the wall.

Two blocks, A and B, with masses $m_A$ and $m_B$ and coefficients of kinetic friction $\mu_A$ and $\mu_B$ respectively, are connected by a light rod. They slide down an inclined plane with an angle of inclination $\theta$ together, as shown in the figure. It is assumed that the condition for sliding down is met, i.e., $\tan\theta > \mu_A$ and $\tan\theta > \mu_B$.

An object of mass $m$ is placed on the conical surface of an umbrella. The cone surface makes an angle $\theta$ with the horizontal. The umbrella rotates about its vertical axis with a constant angular velocity $\omega$. The object is at a horizontal distance $r$ from the axis of rotation.

In Figure below, a 5.0 kg block is sent sliding up a plane inclined at $\theta = 37^\circ$ while a horizontal force $\vec{F}$ of magnitude 50 N acts on it. The coefficient of kinetic friction between block and plane is 0.30. The block's initial speed is 4.0 m/s.

A circular curve of highway is designed for traffic moving at 60 km/h. Assume the traffic consists of cars without negative lift.

A crate of mass $m$ slides down an inclined trough. The trough is V-shaped with a right-angled cross-section and is inclined at an angle $\theta$ with respect to the horizontal. The coefficient of kinetic friction between the crate and the trough is $\mu_k$.

Two blocks of mass $m_1$ and $m_2$ are connected by a massless string and rest on a horizontal surface with a coefficient of kinetic friction $\mu_k$. A force $\vec{F}$ is applied to block $m_2$ at an angle $\theta$ below the horizontal, causing the system to accelerate.