A 3-m-high, 6-m-wide rectangular gate is hinged at the top edge at A and is restrained by a fixed ridge at B. Determine the hydrostatic force exerted on the gate by the 5-m-high water and the...

A small object with mass m = 0.0900 kg moves along the +x-axis. The only force on the object is a conservative force that has the potential-energy function U(x) = -x 2 + x 3 , where = 2.00 J/m 2 and...

A thin layer of liquid, draining from an inclined plane, has a velocity profile v x v 0 (2y/h - y 2 /h 2 ), where v 0 is the surface velocity. If the plane has width 10 cm into the paper, determine...

Determine the capillary rise for a water-air-glass interface at 40C in a clean glass tube having a radius of 1 mm.

The tank is accelerated upward at a uniform rate. Does the manometer level go up or down? P = 2 psig

Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool. A simplified picture of the situation is provided in the figure below....

In a biofuels plant distillation tower, a single-pass shell- and-tube heat exchanger is used to condense saturated ethanol vapor to saturated ethanol liquid using water as the tube-side cooling...

Determine the required heat-transfer surface area for a heat exchanger constructed from 10-cm OD tubes. A 95% ethanol solution (c p = 3.8l0kJ/kg K), flowing at 6.93 kg/s is cooled from 340 to 312 K...

The spherical gel capsule shown in the figure at the top of the next column is used for long-term, sustained drug release. A saturated liquid solution containing the dissolved drug (solute A) is...

Consider a single, porous, spherical, inert mineral particle. The pores inside the particle are filled with liquid water (species B). We are interested in analyzing the molecular diffusion of the...

A wetted wall tower is used to aerate water using air at 2.0 atm total system pressure and 20C. The molar composition of air is 21% O 2 , 78% N 2 , and 1% other gases. Let solute A = O 2 . At 20C,...

Consider the physical system shown in the figure on page 532. which represents a simplified scenario for the treatment of tumor (cancer) tissue. In this experiment, a slab of living tissue is in...

When a nerve cell fires, charge is transferred across the cell membrane to change the cells potential from negative to positive. For a typical nerve cell, 9.0 pC of charge flows in a time of 0.50 ms....

What is the current through the 10 resistor in FIGURE P28.63?Is the current from left to right or right to left? ww 50 12 V ww 10 N 3 V ww 50 9 V FIGURE P28.63

FIGURE EX30.14 shows a 10-cm-diameter loop in three different magnetic fields. The loop??s resistance is 0.20 . For each, what are the size and direction of the induced current? a. b. c. X X

The intensity at the central maximum of a double-slit interference pattern is 4I 1 . The intensity at the first minimum is zero. At what fraction of the distance from the central maximum to the first...

Pure liquid benzene (C 6 H 6 ) at 290 K flows as a thin film down the outside of a vertical, 0.08-m-diameter cylinder at a flow rate of 4.0 kg/hr. Dry air at 290 K and 1.0 atm flows perpendicular to...

Chilled water enters a thin-shelled 5-cm-diameter, 150-m-long pipe at 7C at a rate of 0.98 kg/s and leaves at 8C. The pipe is exposed to ambient air at 30C with a heat transfer coefficient of 9 W/m 2...

Two concentric spheres with diameters of 5 cm and 10 cm are having the surface temperatures maintained at 100°C and 200°C, respectively. The enclosure between the two concentric spherical...

At Super KEKB it is planned to collide 4 GeV positrons with 7 GeV electrons to form (4S) particles. If the latter decay to B particles with equal energies, how far will they travel on average before...

The reaction (10.6b) is forbidden to occur via lowest-order weak interactions like Figure 10.5(b). However, it can proceed by higher order diagrams involving the exchange of two or more bosons. Draw...

In our discussion of the reaction e + + e μ + + μ , we completely neglected the Higgs exchange diagram of Figure 10.30, compared with the dominant diagrams of Figures...

The mechanisms of muon decay (9.4) and the semileptonic decay of the charmed quark (9.21a) are essentially the same. Use this to estimate the rate for the charmed quark decay, assuming that its mass...

Use the method of dimensions to show that if W-exchange is approximated by a zero-range interaction and the masses of all final-state particles are neglected. If quark mass corrections are taken into...

The US total electrical power consumption in 2010 was 3.9 TkWh. Utilities try to maintain a capacity that is twice the average power consumption to allow for high demand on hot summer days. What...

Estimate Earths kinetic energy of rotation (the moment of inertia of a uniform sphere is 2/5 MR 2 ).

Consider two resistors placed in series, one after the other, in an electric circuit connected to a battery with voltage V. Show that the effective resistance of the pair is R 1 +R 2 by using the...

Derive eq.? ?by taking the time derivative of eq.? ?and using Maxwell?s equations. (, 1) +V. S(x,1) %3 -j(,1) (x, 1) at

A low-flow shower head averages 4.8 L/min. Taking other data from Example 5.3, estimate the energy savings (in J/y) if all the people in your country switched from US code to low-flow shower heads.

Suppose a small stoneware kiln with surface area 5m 2 sits in a room that is kept at 25 C by ventilation. The 15 cm thick walls of the kiln are made of special ceramic insulation, which has k =...

When an object is in radiative equilibrium with its environment at temperature T, the rates at which it emits and absorbs radiant energy must be equal. Each is given by dQ 0 /dt = T 4 A. If the...

In one dimension, compare the plane wave solutions to the heat equation ?T/?t = a? 2 T/?x 2 with plane wave solutions to the free Schr?dinger equation Show that the heat equation has real solutions...

Check that the s vap and h vap quoted in Table 12.1 are consistent with h = u + pv and s = h/T. Table 12.1 p(Tsat) 1x 10 Pa (99.61C) 1.2 x 10 Pa (104.78 C) h Temp [C] [m*kg] [m*/kg] [kJ/kg] [kJ/kg]...

When we designed the Rankine steam cycle in 13.3.5 we ignored the circulating waters kinetic and potential energy, having claimed earlier that they are negligible. Using the work per unit mass done...

Check that 3 He is less tightly bound than 3 H. Explain why 3 H decays to 3 He, and not vice versa.

Verify the expressions for the Q-value in ? ? -decay and electron capture, eq. (17.34)? Q(B) = A(Z, A) A(Z + 1, A), Q(B+) = A(Z, A) A(Z 1, A) 2Ae Q(EC) = A(Z, A) - A(Z 1, A),

When 235 U fissions by absorbing a slow neutron, 93 Zr is one of the most common fission fragments. Suppose three neutrons are given off in the fission. What is the other nucleus produced in this...

Verify the classical energy loss formula (18.4) For an elastic two-body collision. Use the notation in the Figure 18.8 Use the fact that the relationship between a velocity vector V in the target...

The energy released per nucleon for (a) fission of 235 U; (b) dt fusion.

Suppose a pressurized water reactor is loaded with 200 tons of 3% enriched uranium. The reactor has been designed to run with an average thermal-neutron flux of ?? n ??= 1.5?10 13 cm ?2 s ?1 for a...

Look up the standard enthalpies of formation of glucose and ethanol (Table 9.8), and verify that eq. (26.4) is exothermic. Then verify that the gravimetric energy density (relative to combustion) of...

What is the maximum power that could be extracted by a mechanical device of cross-sectional area 10 m 2 in a steady wind at 10 m/s?

The maximum takeoff mass for a Boeing 777-300ER passenger jet is 3.5 10 5 kg. The planes wing area is about 440 m 2 . Compute the average air pressure on the planes wings required to overcome the...

An upward force of 18 N is applied via a string to lift a ball with a mass of 1.5 kg. a. What is the net force acting upon the ball? b. What is the acceleration of the ball?

Suppose that a 200-g mass (0.20 kg) is oscillating at the end of a spring upon a horizontal surface that is essentially friction-free. The spring can be both stretched and compressed and has a spring...

Given the following approximations for planetary albedos and given approximate radii of their orbits, estimate the average effective temperature of the planets Mars and Neptune. (The effective...

In the T2K experiment the proton beam accelerated by the J-PARC high-intensity proton synchrotron is driven on a target. The emerging pions are focussed in the forward direction and then drift in a...

How can the neutron be unstable in free space, but stable when inside a nucleus?

A spherical time-release capsule was developed to release pesticide to surrounding soil, as shown in the figure below. The capsule is 1.0 cm in diameter, and is made of a polymer containing a uniform...

As part of a process to fabricate materials with ordered pore arrays, the diffusion-limited solvent etching process shown in the figure (next column) is used to remove a contaminant (solid solute A,...

Helpers of the Homeless plans to lease some new equipment. The lease calls for payments of $750 per year and is based on 10 annual payments and a 6 percent interest rate. As an accommodation to the...

Your roommate drops a tennis ball from a third-story balcony. It hits the sidewalk and bounces as high as the second story. Draw a complete motion diagram of the tennis ball from the time it is...

I was driving along at 20 m/s, trying to change a CD and not watching where I was going. When I looked up, I found myself 45 m from a railroad crossing. And wouldnt you know it, a train moving at 30...

A boat takes 3.0 hours to travel 30 km down a river, then 5.0 hours to return. How fast is the river flowing?

A narrow, U-shaped glass tube with open ends is filled with 25.0 cm of oil (of specific gravity 0.80) and 25.0 cm of water on opposite sides, with a barrier separating the liquids (Fig. P12.58)....

Calculate the ratio of the spectral radiances of black bodies at 300 K and 6000 K at (i) A wavelength of 0.1 m, (ii) A wavelength of 1 m, (iii) A frequency of 1000 GHz, (iv) A frequency of 1 GHz.

Use the data of Table 4.3 to estimate the effective raindrop radius, number density and sedimentation rate for rain rates of 1 and 100 mm/hr, assuming that all the drops are spherical and have the...

Sea water has an electrical conductivity of typically about 4 S m-1. The real part of its dielectric constant at radio frequencies of 100 MHz and below is 88.2. By assuming that the imaginary part...

Show that Equation (2.31) can be approximated by Equation (2.33) at sufficiently low frequencies. exp(x) 1 + x when |x| < < 1.

Estimate the illuminance at the Earths surface due to solar illumination when the Sun is 45 0 above the horizon. Use Equation (5.1), but approximate the function V(λ) shown in Figure 5.1...

Derive the characteristic equation for a control system with the following transfer functions: G c = K c , Is the system stable for (a) K c = 9, (b) K c = 11, (c) K c = 13? Gm 0.5 |G,G, : s+3* (s +...

A process, including the sensor and control valve, can be modeled by the transfer function: (a) If a proportional-only controller is used, what is the maximum value of controller gain K c that will...

Repeat Problem 1.5 for a doping density of 10 15 atoms/cm3 and F = 400. Data from Problem 1.5: If the collector doping density in a transistor is 6 10 15 atoms/cm 3 , and is much less than the base...

The satellite Jason is in a circular orbit with a semimajor axis of 7714 km and an inclination of 66. (i) Show that this orbit is suitable for altimetry. (ii) Comment on the suitability of the orbit...

An integrated-circuit npn transistor has the following measured characteristics: r b = 100, r c = 100, 0 = 100, r o = 50 k at I C =1 mA, f T = 600 MHz with I C = 1 mA and V CB = 10 V, f T = 1 GHz...

Explain how it is possible for the horizontal resolution of a radar altimeter to exceed the limit set by diffraction at the antenna, provided that the pulse duration t p is short enough, and derive...

An airborne scanning laser profiler transmits pulses at a frequency f 0 . Its field of view is scanned in a direction perpendicular to the aircrafts velocity through an angle ±Î¸...

If E = 20e 5y (cos 5xa x sin 5xa y ), find (a) |E| at P(/6, 0.1, 2); (b) A unit vector in the direction of E at P; (c) The equation of the direction line passing through P.

Given the current density J = 10 4 [sin(2x)e 2y a x + cos(2x)e 2y a y ] kA/m 2 (a) Find the total current crossing the plane y = 1 in the a y direction in the region 0 < x < 1, 0 < z < 2. (b) Find...

A semiconductor sample has a rectangular cross section 1.5 by 2.0 mm, and a length of 11.0 mm. The material has electron and hole densities of 1.8 10 18 and 3.0 10 15 m 3 , respectively. If e =...

Figure 3.36 shows the spectrum of a VSB signal. The amplitude and phase characteristics are the same as described in Example 3.3. Show that upon coherent demodulation, the output of the demodulator...

An AM modulator has output x c (t) = 40 cos [20(200)t] + 5 cos[2(180)t] + 5 cos[2(220)t] Determine the modulation index and the efficiency.

Two Gaussian random variables X and Y, with zero means and variances Ï 2 , between which there is a correlation coefficient p, have a joint probability-density function given by The marginal pdf...

A 30 g ball rolls around a 40-cm-diameter L-shaped track, shown in FIGURE P8.53, at 60 rpm. What is the magnitude of the net force that the track exerts on the ball? Rolling friction can be...

In Figure 12.1, let region 2 be free space, while μ r1 = 1, " r1 = 0, and ' r1 is unknown. Find ' r1 if (a) The amplitude of E 1 is one-half that of E + 1 ; (b) (S 1 ) is one-half of (S...

Consider a base band antipodal PAM system with channel bandwidth of 5 kHz and a desired data rate of 20 kbps. (a) What is the required value for M? (b) What value of E d / N 0 in dB will give a bit...

Determine the dc collector currents in Q 1 and Q 2 , and then the input resistance and voltage gain for the Darlington emitter follower of Fig. 3.74. Neglect r μ , r b , and r o ....

Determine the input resistance, transconductance, output resistance, and maximum open-circuit voltage gain for the CS-CG circuit of Fig.3.38 if I D1 = I D2 = 250 A. Assume W/L=100, =0.1 V 1 , and =...

Repeat Problem 7.21 if the input signal is a current source of value i i applied at the base of Q 1 . (That is, i i replaces the voltage source Ï i and resistance R S .) The transfer function is...

You hold a hose at waist height and spray water horizontally with it. The hose nozzle has a diameter of 1.80 cm, and the water splashes on the ground a distance of 0.950 m horizontally from the...

A large, 40.0-kg cubical block of wood with uniform density is floating in a freshwater lake with 20.0% of its volume above the surface of the water. You want to load bricks onto the floating block...

Consider a simple ideal Rankine cycle with fixed turbine inlet conditions. What is the effect of lowering the condenser pressure on Pump work input: (a) increases, (b) decreases, (c) remains the same...

As a test of orienteering skills, your physics class holds a contest in a large, open field. Each contestant is told to travel 20.8 m due north from the starting point, then 38.0 m due east, and...

A stone is thrown into the air at an angle above the horizontal and feels negligible air resistance. Which graph in Fig. Q3.16 best depicts the stones speed v as a function of time t while it is in...

You have a bucket containing an unknown liquid. You also have a cube-shaped wooden block that you measure to be 8.0 cm on a side, but you dont know the mass or density of the block. To find the...

The electric field is measured for points at distances r from the center of a uniformly charged insulating sphere that has volume charge density Ï and radius R, where r < R (Fig. P22.60)....

Using the geometric relations given below and the chain rule for differentiation, show that and when r 2 = x 2 + y 2 and tanθ = y/x. sin 0 + cos 0. r r 0 cos 0 a r 0 + sin 0 r ||

Transform the operator to cylindrical coordinates (r, θ, z), using the results of Problems 1.7 and 1.9. Data From Problem 1.7 Show that the unit vectors e r and e θ in a...

In a boundary layer where the velocity profile is given by where δ is the velocity boundary-layer thickness, plot the dimensionless dissipation function, Φδ 2...

A 2.5-cm thick sheet of plastic (k = 2.42 W/m K) is to be bonded to a 5-cm thick aluminum plate. The glue that will accomplish the bonding is to be held at a temperature of 325 K to achieve the best...

A thick plate made of stainless steel is initially at a uniform temperature of 300C. The surface is suddenly exposed to a coolant at 20C with a convective surface coefficient of 110 W/m 2 K....

Using the appropriate integral formulas for flow parallel to a flat surface with a constant free-stream velocity, develop expressions for the local Nusselt number in terms of Re x and Pr for velocity...

Water, at 60F, enters a 1-in.-ID tube that is used to cool a nuclear reactor. The water flow rate is 30 gal/min. Determine the total heat transfer and the exiting water temperature for a 15-ft-long...

Engine oil with properties given below flows at a rate of 136 kg per hour through a 7.5-cm-ID pipe whose inside surface is maintained at 100°C. If the oil enters at 160°C, what will its...

A room measuring 12 ft by 20 ft by 8 ft high has its floor and ceiling temperatures maintained at 85F and 65F, respectively. Assuming the walls to be re-radiating and all surfaces to have an...

A gray, diffuse circular heater with a diameter of 15 cm is placed parallel to a second gray, diffuse receiver with a spacing of 7.5 between them. The backs of both surfaces are insulated and...

Starting with the Ficks rate equation for the diffusion of A through a binary mixture of components A and B, given by Show that and state all assumptions needed to arrive at this result. NA =...

The general form of the StefanMaxwell equation for mass transfer of species i in an n-component ideal gas mixture along the z-direction for flux is given by Show that for a gas-phase binary mixture...

Derive Equation 26.33 for the induced surface charge density on the dielectric in a capacitor. Equation 26.33 nol 1 Ninduced

Microvia are microscopic passages between two thin films on a microelectronic device. Often, microvia are filled with a conductive metal to make a microscopic conductor for the flow of electrons...