Incline

A 3.0 m long wooden plank is used to push a cargo box with a mass of $m = 200$ kg up onto a platform that is 1.3 m high. The coefficient of kinetic friction between the box and the plank is 0.3. The box is pushed at a constant speed.

As shown in Figure, a wooden wedge ABC with mass $M=10$ kg is stationary on a rough horizontal ground. A block with mass $m=1.0$ kg starts to slide down from rest on the inclined surface of the wedge, which has an angle $\theta = 30^\circ$. When the block has slid a distance $s=1.4$ m, its velocity is $v=1.4$ m/s. Throughout this process, the wedge does not move. The gravitational acceleration is $g=10$ m/s². The coefficient of kinetic friction between the wedge and the ground is given as $\mu=0.02$, though this information might not be necessary for the primary calculation.

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.

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 $\tan\theta > \mu_B$.

A crate of mass $m$ is pushed at a constant speed up a frictionless ramp inclined at an angle $\theta$ to the horizontal. The crate is pushed by a horizontal force $\vec{F}$.

A block of mass $m_1$ on a horizontal frictionless surface is connected by a massless cord over a massless, frictionless pulley to a block of mass $m_2$ on a frictionless plane inclined at an angle $\theta$. A horizontal force $\vec{F}$ is applied to $m_1$.

A block of mass $m_1$ on a frictionless horizontal surface is connected by a massless cord over a frictionless, massless pulley to a second block of mass $m_2$ on a frictionless plane tilted at an angle $\theta$. A force $\vec{F}$ is applied to $m_2$, directed up the incline.

A block of mass $m_1$ on a frictionless inclined surface is connected to a hanging block of mass $m_2$ by a cord running over a massless, frictionless pulley. The incline has an angle $\beta$. An upward force of magnitude $F$ acts on mass $m_2$, which has a downward acceleration of magnitude $a$.

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 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.