Systems of Objects with Friction Practice Problems

Two wooden blocks are connected using an inelastic wire. The blocks are placed on a horizontal floor. The mass of block P is m_P while block Q has a mass m_Q. You pull the blocks to the left using a horizontal force F, giving the blocks a constant velocity. The coefficient of kinetic friction between both blocks and the surface is μ_k. Determine the tension in the wire connecting the blocks in terms of m_P, m_Q, and μ_k with the help of one or more free-body diagrams.

Two wooden blocks are connected using an inelastic wire. The mass of block P is m_P while block Q has a mass m_Q. The blocks are placed on a horizontal bench. You pull the blocks to the left using a horizontal force F, giving the blocks a constant velocity. The blocks experience the same coefficient of kinetic friction, μ_k. Determine the magnitude of F in terms of m_P, m_Q, and μ_k with the help of one or more free-body diagrams. 

The figure shows an iron slab of mass 4.0 kg attached to a box having a mass of 5.0 kg via a massless string. The pulley connecting them has a mass of 150 g and a radius of 10 cm. Calculate the magnitude of acceleration experienced by the iron slab if it has a force of 25 N applied toward the left. Also, calculate the magnitude of tension(s) in different parts of the string. Consider the pulley and the horizontal surface to be frictionless.

Two porters are transporting a 250 kg luggage box towards the train waiting at the platform. One of the porters pulls it with a rope from the front with a force of 280 N while the other pushes it from behind with a force of 245 N.  Determine the coefficient of kinetic friction experienced by the luggage box if the box moves with a constant speed.

Mike is working as a helper in an appliance showroom. He is trying to pull a 25 kg refrigerator with a force of 125 N but he is unable to move it. Determine the force of friction acting on the refrigerator if the coefficient of static friction between the refrigerator and the showroom floor is 0.60.

A box of mass 3.0 kg is attached to an iron ball having mass 3.5 kg through a massless string passing over a frictionless pulley. Consider the system is initially at rest when the iron ball is suddenly released. Determine how much tension is developed in the string and also the acceleration experienced by the box.

Consider an arrangement of massless and frictionless pulleys used to connect a bag weighing 4.0 kg to a block of 1.5 kg through a massless string as shown in the figure. Determine the magnitude of the acceleration of the 1.5 kg block.

A 2.0 kg book rests on the rough, sloping surface of a wooden wedge of mass 5.0 kg, which itself lies on a frictionless ice surface as shown in the diagram below. If the coefficient of static friction between the book and the wooden wedge is μ=0.4 and $\theta$ = 25°, determine the minimum horizontal force F applied to the wooden wedge that will cause the book to start sliding up the incline.

A crate of mass m is connected to a stone weighing 5.0 kg through a massless string and a frictionless pulley as shown in the figure. Determine the value of 'm' that will keep the system moving at a constant speed if μ_k = 0.18 and μ_s = 0.42 are the coefficients of friction between the crate and the surface.

A 2.0 kg book is on top of a 3.0 kg book placed on the floor. If the acceleration of the 3.0 kg book is a = 1.2 m/s², what is the required minimum coefficient of friction μ between the books for the book on top to not slide off? (Assume μ = μ_s = μ_k)

A 30.0-kg box rests on a surface, connected to a hanging 1.50-kg bag via a pulley system as shown in the diagram. The coefficient of static friction between the box and the surface is 0.35, while the coefficient of kinetic friction is 0.20. If sugar is slowly placed into the bag until the system just begins to move, determine the mass of sugar added to the bag.

In the arrangement shown, a 20.0 kg crate is linked to an empty sack, with a mass of 0.80 kg, by a rope and a frictionless pulley system. The coefficients of static friction and kinetic friction between the crate and the surface are 0.38 and 0.18 respectively. The sack is incrementally filled with grains until the system is in motion. If the total mass of the sack at this instant is 7.60 kg, determine the magnitude of the system's acceleration.

A 4.0 kg crate is moving at an acceleration of 1.5 m/s² on a horizontal floor. Above it, there is a 2.5 kg book. From experimentation, it is found that the book doesn't slide off on the crate for the minimum value of μ = 0.15 between the book and the crate. Assuming μ = μ_s = μ_k, calculate the acceleration of the book relative to the floor if μ is one-third of this value.

A 3.0 kg crate is on a 5.0 kg crate that is sliding on the horizontal floor at an acceleration of 1.1 m/s². It was found that for the minimum value of μ = 0.11 between the two crates, the crate on top wouldn't slide off on the crate at the bottom. If μ is only one-third of this value, what is the acceleration of the 3.0 kg crate relative to the 5.0 kg crate? (Assume μ = μ_s = μ_k)