91影视

Figure 12-50 shows a $\mathbf{70}\mathbf{\text{鈥�}}\mathbf{}\mathit{k}\mathit{g}$climber hanging by only the crimp holdof one hand on the edge of a shallow horizontal ledge in a rock wall. (The fingers are pressed down to gain purchase.) Her feet touch the rock wall at distance$\mathit{H}\mathbf{=}\mathbf{}\mathbf{2}\mathbf{.0}\mathbf{\text{鈥�}}\mathit{m}$directly below her crimped fingers but do not provide any support. Her center of mass is distance $\mathit{a}\mathbf{=}\mathbf{}\mathbf{0}\mathbf{.20}\mathbf{\text{鈥�}}\mathit{m}$from the wall. Assume that the force from the ledge supporting her fingers is equally shared by the four fingers. What are the values of the(a) horizontal component F_hand (b) vertical component F_vof the force on eachfingertip?

In Fig. 12-51, a uniform plank, with a lengthLof $\mathbf{6}\mathbf{.10}\mathbf{\text{鈥�}}\mathit{m}$ and a weight of$\mathbf{445}\mathbf{\text{鈥�}}\mathit{N}$ , rests on the ground and against a frictionless roller at the top of a wall of height $\mathit{h}\mathbf{=}\mathbf{3}\mathbf{.05}\mathbf{\text{鈥�}}\mathit{m}$. The plank remains in equilibrium for any value of $\mathit{胃}\mathbf{鈮�}\mathbf{70}\mathbf{掳}$ but slips if $\mathit{胃}\mathbf{<}\mathbf{70}\mathbf{掳}$. Find the coefficient of static friction between the plank and the ground.

In Fig 12-52, uniform beams A and B are attached to a wall with hinges and loosely bolted together (there is no torque of one on the other). Beam A has length${\mathit{L}}_{\mathbf{A}}\mathbf{=}\mathbf{2}\mathbf{.40}\mathbf{\text{鈥尘}}$ and mass$\mathbf{54}\mathbf{.0}\mathbf{\text{鈥�}}\mathit{k}\mathit{g}$; beamBhas mass$\mathbf{68}\mathbf{.0}\mathbf{\text{鈥�}}\mathbf{}\mathit{k}\mathit{g}$. The two hinge points are separated by distance$\mathit{d}\mathbf{=}\mathbf{1}\mathbf{.80}\mathbf{}\mathit{m}$.In unit-vector notation, what is the force on(a) beamAdue to its hinge? (b) beamAdue to the bolt? (c) beamBdue to its hinge? And (d) beamBdue to the bolt?

For the stepladder shown in the Figure, sides$\mathit{A}\mathit{C}$and $\mathit{C}\mathit{E}$ are each $\mathbf{2}\mathbf{.44}\mathit{m}$ long and hinged at . Bar is a tie-rod $\mathbf{0}\mathbf{.762}\mathit{m}$long, halfway up. A man weighing $\mathbf{854}\mathbf{\text{N}}$climbs $\mathbf{1}\mathbf{.80}\mathit{m}$ along the ladder. Assuming that the floor is frictionless and neglecting the mass of the ladder.Find

(a)the tension in the tie-rod and the magnitudes of the forces on the ladder from the floor at

(b) Aand

(c) E . (Hint: Isolate parts of the ladder in applying the equilibrium conditions.)

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Question: In Fig. 12-26, a uniform sphere of mass m = 0.85 m and radius r = 4.2 mis held in place by a massless rope attached to a frictionless wall a distance L = 8.0 cm above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall.

Figure 12-17 shows four overhead views of rotating uniform disks that are sliding across a frictionless floor. Three forces, of magnitude F, 2F, or 3F, act on each disk, either at the rim, at the center, or halfway between rim and center. The force vectors rotate along with the disks, and, in the 鈥渟napshots鈥� of Fig. 12-17, point left or right. Which disks are in equilibrium?

Figure (a) shows a horizontal uniform beam of mass${\mathbf{m}}_{\mathbf{b}}$and length$\mathbf{L}$that is supported on the left by a hinge attached to a wall and on theright by a cable at angle $\mathbf{胃}$ with the horizontal. A package of mass ${\mathbf{m}}_{\mathbf{p}}$ is positioned on the beam at a distance $\mathbf{x}$ from the left end. The total mass is${\mathbf{m}}_{\mathbf{b}}\mathbf{+}{\mathbf{m}}_{\mathbf{p}}\mathbf{=}\mathbf{61.22}\mathbf{\text{kg}}$. Figure (b) gives the tension $\mathbf{\text{T}}$ in the cable as a function of the package鈥檚 position given as a fraction $\mathbf{x}\mathbf{/}\mathbf{L}$ of the beam length. The scale of the $\mathbf{T}$ axis is set by ${\mathbf{T}}_{\mathbf{a}}\mathbf{=}\mathbf{500}\mathbf{\text{N}}$ and ${\mathit{T}}_{\mathbf{b}}\mathbf{=}\mathbf{700}\mathbf{\text{N}}$.

(a) Evaluate angle$\mathbf{\text{胃}}$ ,

(b) Evaluate mass${\mathbf{\text{m}}}_{\mathbf{b}}$ , and

(c) Evaluate mass ${\mathbf{\text{m}}}_{\mathbf{p}}$.

A crate, in the form of a cube with edge lengths of $\mathbf{1}\mathbf{.2}\mathbf{\text{m}}$ , contains a piece of machinery; the center of mass of the crate and its contents is located $\mathbf{\text{0.30m}}$above the crate鈥檚 geometrical center. The crate rests on a ramp that makes an angle $\mathbf{\text{胃}}$with the horizontal. As$\mathbf{\text{胃}}$ is increased from zero, an angle will be reached at which the crate will either tip over or start to slide down the ramp. If the coefficient of static friction${\mathbf{渭}}_{\mathbf{s}}$ between ramp and crate is $\mathbf{0}\mathbf{.}\mathbf{60}$(a) Does the crate tip or slide? And (b) at what angle $\mathbf{胃}$does the crate tip or slide occur? (c) If${\mathbf{渭}}_{\mathbf{s}}\mathbf{=}\mathbf{0.70}$,does the crate tip or slide? And (d) If${\mathbf{渭}}_{\mathbf{s}}\mathbf{=}\mathbf{0}\mathbf{.70}$,at what angle u does the crate tip or slide occur?

Question: A horizontal aluminum rod 4.8 cmin diameter projects 5.3 cm from a wall. An1200kgobject is suspended from the end of the rod. The shear modulus of aluminum is$\mathbf{3}\mathbf{.}\mathbf{0}\mathbf{脳}{\mathbf{10}}^{\mathbf{10}}\mathbf{}\mathit{N}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$ .(a) Neglecting the rod鈥檚 mass, find the shear stress on the rod, and (b) Neglecting the rod鈥檚 mass, find the vertical deflection of the end of the rod.

Question: Figure 12-55 shows the stress鈥搒train curve for a material. The scale of the stress axis is set by,s = 300 in units of${\mathbf{10}}^{\mathbf{6}}\mathit{N}\mathbf{/}{\mathit{m}}^{\mathbf{2}}$. (a) What is the Young鈥檚 modulus? And (b) What is the approximate yield strength for this material?

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