Block $B$ in the figure shown below weighs $750 \mathrm{N}$. The coefficient of static friction between the block and table is $0.25$ and angle $\theta$ is $30°$. Assume that the cord between $B$ and the knot is horizontal. Find the maximum weight of block $A$ for which the system will be stationary.

Figure shows the three crates being pushed over a concrete floor by a horizontal force $\overrightarrow{F}$ of magnitude $425 \mathrm{N}$. The masses of the crates are $m_1=30.0 \mathrm{kg}, m_2=10.0 \mathrm{kg}$ and $m_3=20.0 \mathrm{kg}$. The coefficient of kinetic friction between the floor and each of the crates is $0.700.$(a) What is the magnitude of the force $F_{32}$ $3$ on crate $2?$ from crate  (b) If the crates then slide onto a polished floor, where the coefficient of kinetic friction is less than $0.700,$ is magnitude $F_{32}$ more than, less than or the same as it was when the coefficient was $0.700?$   

In the figure shown below, block lies on a $20 \mathrm{kg}$ trolley that can roll across a floor on frictionless bearings. Between the block and the trolley, the coefficient of kinetic friction is $0.20$and the coefficient of static friction is $0.25.$ When a horizontal $2.0 \mathrm{N}$ force is applied to the block, what are the magnitudes of (a) the frictional force between the block and the trolley and (b) the acceleration of the trolley?

In the figure shown below, two blocks are connected over a pulley. The mass of block $A$ is $15 \mathrm{kg}$ and the coefficient of kinetic friction between $A$ and the incline is $0.20.$ Angle $\text{θ}$ of the incline is $30°$. Block $A$ slides up the incline at constant speed. What is the mass of block $B$?

In the figure shown above, block $A$ of mass $2.0 \mathrm{kg}$, block $B$ of $3.0 \mathrm{kg}$ and block $C$ of $6.0 \mathrm{kg}$ are connected by strings of negligible mass that run over pulleys of negligible mass and friction. The coefficient of kinetic friction between block $B$ and the table is $0.40$.  When the system is released, the blocks move. What is the magnitude of their acceleration?

A toy chest and its contents have a combined weight of $200 \mathrm{N}$. The coefficient of static friction between toy chest and floor is $0.47$. The child in figure attempts to move the chest across the floor by pulling on an attached rope. (a) If $\text{θ}=42°$, what is the magnitude of the force $\overrightarrow{F}$ that the child must exert on the rope to put the chest on the verge of moving? (b) Write an expression for the magnitude force required to put the chest on the verge of moving as a function of the angle $\text{θ}$. Determine (c) the value of $\text{θ}$ for which $F$ is a minimum and (d) that minimum magnitude.

In the figure shown, two blocks in contact slide down an inclined plane $AC$ of inclination ${30}^{\mathrm{o}}$. The coefficient of kinetic friction between the$2.0 \mathrm{kg}$ block and the incline is ${\mu }_1=0.20$ and that between the $4.0 \mathrm{kg}$ block and the incline is ${\mu }_2= 0.30$. Find the magnitude of the acceleration.

A block is pushed across a floor by a constant force that is applied at downward angle $\text{θ}$. Figure gives the acceleration magnitude $a$ versus a range of values for the coefficient of kinetic friction ${\mu }_k$ between block and floor: $a_1=3.0 \mathrm{m} {\mathrm{s}}^{-2}$, ${\mu }_{k2}=0.20,\text{ and }{\mu }_{k3}\mathrm{ =}0.40.$ What is the value of $\text{θ}$?