Equilibrium and elasticity | Practice Problems, Examples & Solutions

Equilibrium

Biochemistry

(Integrates with Chapter 9 ,) Consider the data in Figure 32.49 a. Recast Equation 9.2 to derive a form from which you could calculate the equilibrium electrochemical potential at which no net flow of potassium would occur. This is the Nernst equation. Calculate the equilibrium potential for $\mathrm{K}^{+}$ and also for $\mathrm{Na}^{+},$ assuming $T=$ $37^{\circ} \mathrm{C}$.

The Reception and Transmission of Extracellular Information

03:06

Shriver & Atkins’ Inorganic Chemistry

Using hard-soft concepts, which of the following reactions are predicated to have an equilibrium constant greater than 1 ? Unless otherwise stated, assume gas-phase or hydrocarbon solution and $25^{\circ} \mathrm{C}$
(a) $\mathrm{R}_{3} \mathrm{PBBr}_{3}+\mathrm{R}_{3} \mathrm{NBF}_{3} \rightleftharpoons \mathrm{R}_{3} \mathrm{PRBF}_{3}+\mathrm{R}_{3} \mathrm{NBBr}_{3}$
(b) $\mathrm{SO}_{2}+\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \mathrm{P}: \mathrm{HOC}\left(\mathrm{CH}_{3}\right)_{3} \rightleftharpoons\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{3} \mathrm{PSO}_{2}+\mathrm{HOC}\left(\mathrm{CH}_{3}\right)_{3}$
(c) $\mathrm{CH}_{3} \mathrm{HgI}+\mathrm{HCl} \rightleftharpoons \mathrm{CH}_{3} \mathrm{HgCl}+\mathrm{HI}$
(d) $\left[\mathrm{AgCl}_{2}\right]^{2-(\mathrm{aq})}+2 \mathrm{CN}^{-}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-(a q)}+2 \mathrm{Cl}^{-(a q)}$

Acids and bases

06:47

Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Identify the acid, base, conjugate acid, and conjugate base in the following equilibrium. (Section 7.1).
(a) $\mathrm{HCO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}\left(\mathrm{j} \rightleftharpoons \mathrm{HCO}_{2}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})\right.$
(b) $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{3}^{+}(\mathrm{aq})+\mathrm{OH}^{-(\mathrm{aq})}$
(c) $\mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} \rightleftharpoons \mathrm{HSO}_{4}^{-}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}_{2}^{+}$

Acids and bases

Center of Gravity

124 Practice Problems

01:56

Engineering Mechanics: Statics and Dynamics

Show that the sum of the moments of inertia of a body, $I_{x x}+I_{y y}+I_{z z}$, is independent of the orientation of the $x, y, z$ axes and thus depends only on the location of the origin.

Three-Dimensional Kinetics of a Rigid Body

11:23

Engineering Mechanics: Statics and Dynamics

The plate has a thickness of $0.25 \mathrm{ft}$ and a specific weight of $\gamma=180 \mathrm{lb} / \mathrm{ft}^{3} .$ Determine the location of its center of gravity. Also, find the tension in each of the cords used to support it.

Center of Gravity and Centroid

03:06

Engineering Mechanics: Statics and Dynamics

Locate the center of gravity $\bar{y}$ of the homogeneous rod.

Center of Gravity and Centroid

Rigid-Body Equilibrium

105 Practice Problems

04:16

Engineering Mechanics: Statics and Dynamics

The shaft is supported by a journal bearing at $A$ and a thrust bearing at $B$. Determine the normal force, shear force, and moment at a section passing through (a) point $C$ which is just to the right of the bearing at $A,$ and (b) point $D$ which is just to the left of the 3000 -lb force.

Internal Forces

05:51

Engineering Mechanics: Statics and Dynamics

Determine the internal normal force, shear force, and moment in the beam at sections passing through points $D$ and $E .$ Point $D$ is located just to the left of the 5 -kip load.

Internal Forces

05:33

Engineering Mechanics: Statics and Dynamics

Determine the distance $a$ between the bearings in terms of the shaft's length $L$ so that the moment in the symmetric shaft is zero at its center.

Internal Forces

Stress, Strain, and Elastic Moduli

31 Practice Problems

06:17

Physics for Scientists and Engineers

Find the mass $m$ of the counterweight needed to balance the $1500-\mathrm{kg}$ truck on the incline shown in Figure $\mathrm{P} 12.9$ Assume all pulleys are friction-less and mass-less. (FIGURE CAN'T COPY)

Static Equilibrium and Elasticity

01:32

Physics

An anchor, made of cast iron of bulk modulus $60.0 \times 10^{9} \mathrm{Pa}$ and of volume $0.230 \mathrm{m}^{3},$ is lowered over the side of the ship to the bottom of the harbor where the pressure is greater than sea level pressure by $1.75 \times 10^{6} \mathrm{Pa} .$ Find the change in the volume of the anchor.

Elasticity and Oscillations

04:47

Physics

A sphere of copper is subjected to 100 MPa of pressure. The copper has a bulk modulus of 130 GPa. By what fraction does the volume of the sphere change? By what fraction does the radius of the sphere change?

Elasticity and Oscillations

Elasticity and Plasticity

11 Practice Problems

02:10

Physics for Scientists and Engineers with Modern Physics

(III) A metal cylinder has an original diameter of 1.00 $\mathrm{cm}$
and a length of 5.00 $\mathrm{cm} .$ A tension test was performed on
the specimen and the data are listed in the Table. (a) Graph the stress on the specimen vs. the strain. (b) Considering
only the elastic region, find the slope of the best-fit straight
line and determine the elastic modulus of the metal.

Static Equilibrium; Elasticity and Fracture

09:01

Physics for Scientists and Engineers with Modern Physics

A cube of side $\ell$ rests on a rough floor. It is subjected to a
steady horizontal pull $F,$ F, exerted a distance $h$ above the
floor as shown in Fig. $84 .$ As $F$ is increased, the block will
either begin to slide, or begin to tip over. Determine the coefficient of static friction $\mu_{\mathrm{s}}$ so that $(a)$ the block begins to
slide rather than tip; $(b)$ the block begins to tip. [Hint. Where will the
normal force on the block act if it tips?

Static Equilibrium; Elasticity and Fracture

03:15

College Physics

$\bullet$ $\bullet$ A steel cable with cross-sectional area of 3.00 $\mathrm{cm}^{2}$ has an elastic limit of $2.40 \times 10^{8}$ Pa. Find the maximum upward acceleration that can be given to a 1200 kg elevator supported by the cable if the stress is not to exceed one-third of the elastic limit.

Elasticity and Periodic Motion

Rigid Object Under a Net Torque

27 Practice Problems

07:41

University Physics Volume 1

What three factors affect the torque created by a force relative to a specific pivot point?

Static Equilibrium and Elasticity

06:24

College Physics

Calculate the net torque (magnitude and direction) on the beam in Figure P 8.5 about (a) an axis through $O$ perpendicular to the page and (b) an axis through $C$ perpendicular to the page.

Rotational Equilibrium and Dynamics

00:42

College Physics

The fishing pole in Figure P8.3 makes an angle of 20.0° with the horizontal. What is the magnitude of the torque exerted by the fish about an axis perpendicular to the page and passing through the angler’s hand if the fish pulls on the fishing line with a force $\overrightarrow{\mathbf{F}}=1.00 \times 10^{2} \mathrm{N}$ at an angle $37.0^{\circ}$ below the horizontal? The force is applied at a point 2.00 $\mathrm{m}$ from the angler's bands.

Rotational Equilibrium and Dynamics