In Fig. E6.7 assume that there is no friction force on the 20.0-N block that sits on the tabletop. The pulley is light and frictionless. (a) Calculate the tension T in the light string that connects...

Your cat Ms. (mass 7.00 kg) is trying to make it to the top of a frictionless ramp 2.00 m long and inclined upward 30.0 at above the horizontal. Since the poor cat cant get any traction on the ramp,...

Starting at t = 0, a horizontal net force F(0.280 N/s)ti + (0.450 N/s 2 )t 2 j is applied to a box that has an initial momentum p = ( 3.00 kg m/s)i + (4.00 kg m/s)j. What is the momentum of the box...

A thin, uniform rod has length L and mass M. Calculate the magnitude of the gravitational force the rod exerts on a particle with mass m that is at a point along the axis of the rod a distance x from...

If a pilot accelerates at more than 4g, he begins to gray out but doesnt completely lose consciousness. (a) Assuming constant acceleration, what is the shortest time that a jet pilot starting from...

Two cars, A and B, move along the x-axis. Figure E2.32 is a graph of the positions of A and B versus time. Figure E2.32 (a) In motion diagrams (like Figs. 2.13b and 2.14b), show the position,...

A metal bar is in the xy-plane with one end of the bar at the origin. A force F = (7.00 N)i + (3.00 N)j is applied to the bar at the point x = 3.00 m, y = 4.00 m. (a) In terms of unit vectors i and...

In a simplified version of the musculature action in leg raises, the abdominal muscles pull on the femur (thigh bone) to raise the leg by pivoting it about one end (Fig. P11.57). When you are lying...

You need to extend a 2.50-inch-diameter pipe, but you have only a 1.00-inch-diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 6.00 cm s in the...

Viscous blood is flowing through an artery partially clogged by cholesterol. A surgeon wants to remove enough of the cholesterol to double the flow rate of blood through this artery. If the original...

A square object of mass m is constructed of four identical uniform thin sticks, each of length L, attached together. This object is hung on a hook at its upper corner (Fig. P14.79). If it is rotated...

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. The hot water is to be used when needed. The drawbacks are that energy is wasted because the tank loses...

One suggested treatment for a person who has suffered a stroke is immersion in an ice-water bath at 0C to lower the body temperature, which prevents damage to the brain. In one set of tests, patients...

A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at 20.0 o C. The ice is in an insulated container of negligible mass and no heat is...

A steel rod 0.450 m long and an aluminum rod 0.250 m long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is...

Suppose that both ends of the rod in Fig. 17.23a are kept at a temperature of 0 o C, and that the initial temperature distribution along the rod is given by T = (100 o C) sin Ïx/L where x is...

For the three stirred-tank system of Exercise 3.20 (Part (b)1), use symbolic system software to find the exit con-centration of tank 3, c 3 (t), after a rectangular pulse in c i (t) occurs at t = 0....

A thermometer has first-order dynamics with a time constant of 1 sec and is placed in a temperature bath at 120 F. After the thermometer reaches steady state, it is suddenly placed in a bath at 140 ...

Three stirred-tanks in series are used in a reactor train (see Fig. E3.20). The flow rate into the system of some inert species is maintained constant while tracer tests are conducted. Assuming that...

onsider the model of the electrically heated stirred-tank system in Section 2.4.3. Subscript e refers to the heating element: (a) Derive transfer functions relating changes in outlet temperature T to...

Using the step responses of (1) an integrating element and (2) a first-order process to an input change of magnitude M. (a) Show that the step response for an input change M of a first-order process...

The output response data y shown in Table E7.9 were generated from a step change in input u from 1 to 5 at time t = 0. Develop a transfer function model of the form Y(s) Ke-0s (T,8 +1)(t,s + 1) U(s)...

Noisy data for the step response of a boiler temperature T to a decrease in air flow rate q from 1000 to 950 cfm are shown below. Develop a FOPTD model using a method from Chapter 7. Be sure to use...

A control system has G v = G m = 1 and a second-order process G p with K p = 2, 1 = 4 min, and 2 = 1 min, which is to be controlled by a PI controller with K c = 2 and I = 1 = 4 min (i.e., the...

If two electrons are each 1.50 x 10 -10 m from a proton, as shown in Fig. E 21.37, find the magnitude and direction of the net electric force they will exert on the proton. Figure E21.37 65.0

Figure E16.26 shows cascade temperature control of a polymerization reactor, which uses feed heat exchange to adjust the reactor temperature. Using the instrumentation diagram, explain how this...

(a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO 2 atmosphere), Venus (with an average temperature of...

An average sleeping person metabolizes at a rate of about 80 W by digesting food or burning fat. Typically, 20% of this energy goes into bodily functions, such as cell repair, pumping blood, and...

The process abc shown in the pV-diagram in Fig. E19.11 involves 0.0175 mole of an ideal gas. (a) What was the lowest temperature the gas reached in this process? Where did it occur? (b) How much work...

The batteries shown in the circuit in Fig. E26.24 have negligibly small internal resistances. Find the current through (a) The 30.0- resistor; (b) The 20.0- resistor; (c) The 10.0-V Figure E26.24...

A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0...

Scientists are working on a new technique to kill cancer cells by zapping them with ultrahigh-energy (in the range of 10 12 W) pulses of light that last for an extremely short time (a few...

The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 380 nm (violet) to 750 nm (red), as...

Very short pulses of high-intensity laser beams are used to repair detached portions of the retina of the eye. The brief pulses of energy absorbed by the retina weld the detached portions back into...

A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of ...

Light of original intensity l 0 passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.32. You want to adjust the angle Ï so that the intensity at...

A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 10 -3 Wb. What must be the magnitude of the rate of...

Two insulated wires perpendicular to each other in the same plane carry currents as shown in Fig. E28.29. Find the magnitude of the net magnetic field these wires produce at points P and Q if the...

A parallel-plate capacitor is made from two plates 12.0 cm on each side and 4.50 mm apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas ®...

A uniform line charge of 16 nC/m is located along the line defined by y = 2, z = 5. If = 0: (a) Find E at P(1, 2, 3). (b) Find E at that point in the z = 0 plane where the direction of E is given by...

Given the surface charge density, s = 2C/m 2 , existing in the region < 0.2 m, z = 0, find E at (a) P A ( = 0, z = 0.5); (b) P B ( = 0, z = 0.5). Show that (c) The field along the z axis reduces...

Surface charge of uniform density Ï s lies on a spherical shell of radius b, centered at the origin in free space. (a) Find the absolute potential everywhere, with zero reference at infinity....

A spherically symmetric charge distribution in free space (with 0 < r < ) is known to have a potential function V(r ) = V 0 a 2 /r 2 , where V 0 and a are constants. (a) Find the electric field...

(a) Using data tabulated in Appendix C, calculate the required diameter for a 2-m-long nichrome wire that will dissipate an average power of 450 W when 120 V rms at 60 Hz is applied to it. (b)...

Let the cylindrical surfaces = 4 cm and = 9 cmenclose two wedges of perfect dielectrics, r1 = 2 for 0 < < /2 and r2 = 5 for /2 < < 2. If E1 = (2000/)a V/m, find (a) E 2 ; (b) The total...

Using the uniqueness property of the Fourier series, find exponential Fourier series for the following signals (f 0 is an arbitrary frequency): (a) x 1 (t) = sin 2 (2f 0 t) (b) x 2 (t) = cos(2f 0 t)...

Rework Problem 3.8 for the message signal m(t) = 9 cos(20t) + 8 cos(60t) Data from Problem 3.8 (a) Write the equation for m n (t), the normalized signal with a minimum value of -1. (b) Determine {m 2...

An AM modulator operates with the message signal m(t) = 9 cos (20t) - 8 cos (60t) The unmodulated carrier is given by 110 cos(200t) and the system operates with an index of 0.8. (a) Write the...

Assume that a DSB signal x c (t) = A c m(t) cos (2f c t + 0 ) is demodulated using the demodulation carrier 2 cos [2f c t + (t)]. Determine, in general, the demodulated output y D (t). Let A c = 1...

A sinusoidal message signal has a frequency of 250 Hz. This signal is the input to an FM modulator with an index of 8. Determine the bandwidth of the modulator output if a power ratio, P r , of 0.8...

In a certain digital data transmission system the probability of a bit error as a function of timing jitter is given by where z is the signal-to-noise ratio, |ÎT|, is the timing jitter, and T...

A simple model for a multi path communications channel is shown in Figure 5.20(a). Figure 5.20 (a) (a) Find H c (f) = Y(f) / X (f) for this channel and plot |H c (f)| for β = 1 and 0.5....

The random variable has pdf where u(x) is the unit step. Determine the mean and the variance of the random variable thus defined. fx(x) = ;5(x 5) + lu(x 4) u(x 8)]

A circle is divided into 21 equal parts. A pointer is spun until it stops on one of the parts, which are numbered from 1 through 21. Describe the sample space and, assuming equally likely outcomes,...

Using only the Fourier transform of the unit impulse function and the differentiation theorem, find the Fourier transforms of the signals shown in Figure 2.36.

The surface x = 0 separates two perfect dielectrics. For x > 0, let r = r 1 = 3, while r 2 = 5 where x < 0. If E 1 = 80a x 60a y 30a z V/m, find (a) EN 1 ; (b) ET 1 ; (c) E 1 ; (d) The angle 1...

Two random variables X and Y have means and variances given below: m x = 1 2 x = 4 m y = 3 2 y = 7 A new random variable Z is defined as Z = 3X - 4Y Determine the mean and variance of Z for each of...

A load, Z L = 25+ j75 , is located at z = 0 on a lossless two-wire line for which Z 0 = 50 and v = c. (a) If f = 300 MHz, find the shortest distance d (z = d) at which the input admittance has a...

With the aid of the Smith chart, plot a curve of |Z in | versus l for the transmission line shown in Figure 10.33. Cover the range 0 < l/λ < 0.25. 20 Lossless Lossless 20 Zo = 50 2 Zo...

Referring to Problem 7.1, what are the following probabilities for each case? (a)F X (X ¤ 2A,t = 4) (b)F X (X ¤ 0,t = 4) (c)F X (X ¤ 2A,t = 2) Data From Problem 7.1 A fair die is...

The normalized load on a lossless transmission line is 2 + j 1. Let = 20 m and make use of the Smith chart to find (a) The shortest distance from the load to a point at which z in = r in + j0, where...

A lossless transmission line having characteristic impedance Z 0 = 50 is driven by a source at the input end that consists of the series combination of a 10-V sinusoidal generator and a 50-resistor....

Given two independent, wide-sense stationary random processes X(t) and Y(t) with auto correlation functions R x () and R Y (), respectively. (a) Show that the auto correlation function R Z () of...

Consider the region defined by |x|, |y|, and |z| < 1. Let r = 5, r = 4, and = 0. If J d = 20 cos(1.5 10 8 t bx)a y A/m 2 (a) Find D and E; (b) Use the point form of Faradays law and an...

The parallel-plate transmission line shown in Figure 9.7 has dimensions b = 4 cm and d = 8 mm, while the medium between the plates is characterized by μ r = 1, r = 20, and Ï = 0....

The cones θ = 21¦ and θ = 159¦ are conducting surfaces and carry total currents of 40 A, as shown in Figure 8.17. The currents return on a spherical conducting...

A small bead slides around a horizontal circle at height y inside the cone shown in FIGURE CP8.69. Find an expression for the beads speed in terms of a, h, y, and g. a FIGURE CP8.69

A student has 65-cm-long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any? The distance from the handle to the bottom of...

A 500 g model rocket is on a cart that is rolling to the right at a speed of 3.0 m/s. The rocket engine, when it is fired, exerts an 8.0 N vertical thrust on the rocket. Your goal is to have the...

A hollow tubular conductor is constructed from a type of brass having a conductivity of 1.2 10 7 S/m. The inner and outer radii are 9 and 10 mm, respectively. Calculate the resistance per meter...

A uniform plane wave in free space has electric field vector given by E s = 10e jx a z + 15e jx a y V/m. (a) Describe the wave polarization. (b) Find H s . (c) Determine the average power density in...

A right-circularly polarized plane wave is normally incident from air onto a semi-infinite slab of plexiglas (' r = 3.45, " r = 0). Calculate the fractions of the incident power that are reflected...

An air-filled rectangular waveguide is to be constructed for single-mode operation at 15 GHz. Specify the guide dimensions, a and b, such that the design frequency is 10 percent higher than the...

Consider a sphere of radius r = 4 centered at (0, 0, 3). Let S 1 be that portion of the spherical surface that lies above the xy plane. Find S1 ( H) dS if H = 3 a in cylindrical coordinates.

A coaxial cable has conductor dimensions of a = 1.0 mm and b = 2.7 mm. The inner conductor is supported by dielectric spacers ( r = 5) in the form of washers with a hole radius of 1 mm and an outer...

The inner conductor of the transmission line shown in Figure 6.13 has a square cross section 2a ? 2a, whereas the outer square is 4a ? 5a. The axes are displaced as shown. (a) Construct a good-sized...

In free space, let = 2000/r 2.4 . (a) Use Poissons equation to find V(r) if it is assumed that r 2 E r 0 when r 0, and also that V 0 as r . (b) Now find V(r) by using Gausss law and a line...

A current sheet K = 8a x A/m flows in the region 2 < y < 2 in the plane z = 0. Calculate H at P(0, 0, 3).

A rectangular loop of wire in free space joins point A(1, 0, 1) to point B(3, 0, 1) to point C(3, 0, 4) to point D(1, 0, 4) to point A. The wire carries a current of 6 mA, flowing in the a z...

Show that (9.162) is the average energy in terms of Î for binary antipodal ASK. (9.162) Hc(f) = 1, |f| < %3D

Determine the output current in the circuit of Fig. 4.60. Fig. 4.60: Vcc= 15 V 20 k 1 Q1 Q2 10 k

Determine the output voltage as a function of the input voltage for the circuit of Fig. 6.54. Assume the op amp is ideal. Figure 6.54 1 k2 1 Vout +0 Vin

Determine the overall input resistance, voltage gain, and output resistance of the CC-CB connection of Fig. 3.79. Neglect r o , r μ , and r b . Note that the addition of a...

Derive and sketch the complete small-signal equivalent circuit for the device of Problem 1.15 with V GS = 1 V, V DS = 2 V, and V SB = 1 V. Use 0 = 0.7 V, C sb0 = C db0 = 20 fF, and C gb = 5 fF....

Use the device data of Problems 1.15 and 1.16 to calculate the frequency of unity current gain of this transistor with V DS = 3V, V SB = 0 V, V GS = 1 V, 1.5 V, and 2 V. Data from Prob. 1.16: Derive...

Calculate the threshold voltage of the pchannel transistors for the process given in Table 2.1. Table 2.1. First do the calculation for the unimplanted transistor, then for the case in which the...

Calculate the small-signal model parameters g m , r o , C gs , and C gd for a NMOS transistor. Assume the transistor operates in the active region with I D = 100 μA, V DS = 1V, V BS = 0...

Draw the block diagram of an M -power law circuit for synchronizing a local carrier for 8-PSK. Assume that f c = 10 MHz and T s = 0.1 ms. Care fully label all blocks, and give critical frequencies...

Use half-circuit analysis to determine A dm , A cm , A cmdm , and A dmcm for a resistively loaded differential pair with mismatched resistive loads, R 1 and R 2 . Assume that R 1 = 10.1 k and R 2 =...

Calculate an analytical expression for the small-signal output resistance R o of the bipolar cascode current mirror of Fig. 4.8. Assume that the input current source is not ideal and that the...

Calculate the output resistance of the Wilson current mirror shown in Fig. 4.57. What is the percentage change in I OUT for a 5-V change in VOUT? Compare your answer with a SPICE simulation using a...

Assume that you have a standard deck of 52 cards (jokers have been removed). (a) What is the information associated with the drawing of a single card from the deck? (b) What is the information...

Although G m [cm] of a differential pair with a current-mirror load can be calculated exactly from a small-signal diagram where mismatch is allowed, the calculation is complicated because the...

Using (8.146), derive an expression for the ratio of the noise power in y D (t) with de-emphasis to the noise power in y D (t) without de-emphasis. Plot this ratio as a function of W/f 3 . Evaluate...

One of the most amusing things a person can experience is that in certain parts of the world a still car on neutral going uphill when its brakes are released. Such occurrences are even broadcast on...

For the circuit of Fig. 5.10, assume that V CC = 12 V, R L = 1 kΩ, and V CE(sat) = 0.2 V. Assume that there is sufficient sinusoidal input voltage available at V i to drive V o to its...

For the circuit of Problem 5.10, calculate and sketch the waveforms of I c1 , V ce1 , and P c1 for device Q 1 over one cycle. Do this for output voltage amplitudes (zero to peak) of 11.5 V, 6 V, and...

At 45 latitude, the gravitational acceleration as a function of elevation z above sea level is given by g = a - bz, where a = 9.807 m/s 2 and b = 3.32 10 -6 s -2 . Determine the height above sea...

A 3kg rock is thrown upward with a force of 200 N at a location where the local gravitational acceleration is 9.79 m/s 2 . Determine the acceleration of the rock, in m/s 2 .

For the circuit of Fig. 5.25, assume that V CC = 15V, F (pnp) = 30, F (npn) = 150, I S (npn) = 10 14 A, I S (pnp) = 10 15 A, and for all devices V BE(on) = 0.7 V, V CE(sat) = 0.2 V. Assume that Q 5...