A uniform cube of side length $\mathbf{8}\mathbf{.0}\mathbf{\text{\hspace{0.17em}cm}}$ rests on a horizontal floor.The coefficient of static friction between cube and floor is m. A horizontal pull $\overrightarrow{\mathbf{P}}$ is applied perpendicular to one of the vertical faces of the cube, at a distance $\mathbf{7}\mathbf{.0}\mathbf{\text{\hspace{0.17em}cm}}$ above the floor on the vertical midline of the cube face. The magnitude of $\overrightarrow{\mathbf{P}}$ is gradually increased. During that increase, for what values of$\mathbf{\text{μ}}$ will the cube eventually (a) begin to slide and (b) begin to tip? (Hint: At the onset of tipping, where is the normal force located?)

In Fig. 12-25, suppose the length L of the uniform bar is $\mathbf{3}\mathbf{.00}\mathbf{\text{\hspace{0.17em}m}}$ and its weight is $\mathbf{200}\mathbf{\text{\hspace{0.17em}N}}$Also, let the block’s weight $\mathit{W}\mathbf{=}\mathbf{}\mathbf{300}\mathbf{\text{\hspace{0.17em}N}}$ and the angle $\mathit{\theta }\mathbf{=}\mathbf{}\mathbf{30}\mathbf{.0}\mathbf{°}$ . The wire can withstand a maximum tension of $\mathbf{500}\mathbf{\text{\hspace{0.17em}N}}$ .(a)What is the maximum possible distance x before the wire breaks? With the block placed at this maximum x, what are the(b) horizontal and (c) vertical components of the force on the bar from the hinge at A?

In Fig. 12-47, a nonuniform bar is suspended at rest in a horizontal position by two massless cords. One cord makes the angle$\mathit{\theta }\mathbf{=}\mathbf{}\mathbf{36}\mathbf{.}\mathbf{9}\mathbf{°}$ with the vertical; the other makes the angle $\mathit{\varphi }\mathbf{=}\mathbf{53}\mathbf{.1}\mathbf{°}$with the vertical. If the length $\mathit{L}$ of the bar is$\mathbf{6}\mathbf{.}\mathbf{10}\mathbf{}\mathit{m}$, compute the distance$\mathit{x}$ from the left end of the bar to its center of mass.

In Fig. 12-82, a uniform beam of length $\mathbf{12}\mathbf{.0}\mathbf{\text{\hspace{0.17em}m}}$ is supported by a horizontal cable and a hinge at angle $\mathbf{\text{θ}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{50.0}\mathbf{°}$. The tension in the cable is $\mathbf{400}\mathbf{\text{\hspace{0.17em}N}}$ .

In unit-vector notation, what are

(a) the gravitational force on the beam and

(b) the force on the beam from the hinge?

The system in Fig. 12-77 is in equilibrium. The angles are ${\mathbf{\text{θ}}}_{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{60}\mathbf{\text{°}}$and ${\mathbf{\text{θ}}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{20}\mathbf{\text{°}}$, and the ball has mass $\mathbf{\text{M}}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{.0}\mathbf{\text{\hspace{0.17em}kg}}$ . What is the tension in (a) string ab and (b) string bc?

Question: A horizontal aluminum rod 4.8 cm in diameter projects 5.3 cm from a wall. An 1200kg object is suspended from the end of the rod. The shear modulus of aluminum is $\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{10}}\mathbf{}\mathit{N}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$ .(a) Neglecting the rod’s mass, find the shear stress on the rod, and (b) Neglecting the rod’s mass, find the vertical deflection of the end of the rod.