Systems of Objects on Inclined Planes with Friction Practice Problems

The figure below depicts two boxes connected to each other by a massless string. Determine the magnitude of the tension force in the string if the motion of the boxes is downwards on the inclined plane.

As shown in the figure, a block of mass 2.0 kg is attached to another block weighing 750 g through a massless string. The coefficients of static and dynamic friction between the block and incline are 0.45 and 0.25 respectively. The block on the inclined surface is pulled up to the top of the plane. At this point determine whether the block will remain steady or move downwards on the inclined plane.

The figure shows a 250 g slab placed on a 950 g frictionless wedge structure. The whole assembly rests on level ground. Determine the normal reaction experienced by the wedge if the slab was sliding downwards on the inclined structure.

A wooden block (block W) and a metallic block (block M) are tied together by a lightweight cord and slide down an inclined plane at an angle $\theta=30^{\circ}$ to the horizontal. The masses of the blocks are $m_W=m_M=5.0\ kg$. The coefficients of friction for the wooden and metallic blocks are $\mu_{W}=0.25$ and $\mu_{M}=0.35$, respectively. Calculate the acceleration of the system as the blocks slide down the incline.

A box of textbooks (box T) and a crate of laboratory equipment (crate L) are connected by a durable nylon rope and slide down an inclined plane at an angle $θ=45°$ to the horizontal. The masses of both boxes are $m_{T}=m_{L}=10.0\operatorname{kg}$. The coefficients of friction for the box and the crate are $μ_T=0.30$ and $\mu_{L}=0.40$, respectively. Calculate the tension in the rope as the system slides down the incline.