Friction

An object of mass $m$ starts from rest at the top of a fixed inclined plane of height $h$ and angle of inclination $\theta$. The coefficient of kinetic friction between the object and the plane is $\mu$.

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.

An object of mass $m$ is on a plane inclined at an angle $\theta$ to the horizontal. The coefficient of static friction between the object and the plane is $\mu$. A horizontal pushing force $F$ is applied to the object, and it remains stationary.

As shown in Figure, a motorcycle is turning on a slope with an inclination angle of $\alpha$. The coefficient of static friction between the motorcycle and the slope is $\mu$. The radius of the circular track is $R$.

As shown in Figure, a small block is placed on a fixed inclined plane with an inclination angle of $\theta$. The coefficient of friction between the block and the plane is given as $\mu = \tan\varphi$, where $\varphi$ is a fixed angle. A force $F$ is applied to the block at an angle $\beta$ with respect to the inclined plane, pulling it upwards along the plane.

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.

As shown in Figure, two objects, A and B, have masses $m_A$ and $m_B$. They are in contact along a smooth surface that makes an angle $\alpha$ with the horizontal. Both blocks are on a horizontal surface, and the coefficient of kinetic friction between each block and the ground is $\mu$. A horizontal force $F$ pushes block A, causing A and B to accelerate together.

A small object is initially at the bottom of a slope inclined at an angle $\alpha$ with the horizontal. It is projected upward along the slope with an initial velocity $v_0$, and reaches the maximum height. It then slides downward and returns to the initial position with final velocity $v_1$. The coefficient of sliding friction between the object and the slope surface is $\mu$.

Two blocks of mass $m$ and $M$ are in contact on a frictionless horizontal surface. A horizontal force $\vec{F}$ is applied to the smaller block of mass $m$. The coefficient of static friction between the blocks is $\mu_s$.