A rocket is launched straight up with constant acceleration. Four seconds after liftoff, a bolt falls off the side of the rocket. The bolt hits the ground 6.0 s later. What was the rockets...
The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand a. From 8:00 to 8:20 A.M.? b. From 8:00 to 9:00 A.M.?
A pine cone falls straight down from a pine tree growing on a 20 slope. The pine cone hits the ground with a speed of 10 m/s. What is the component of the pine cones impact velocity (a) Parallel to...
For a projectile, which of the following quantities are constant during the flight: x, y, r, v x , v y , v, a x , a y ? Which of these quantities are zero throughout the flight?
You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground....
A rifle is aimed horizontally at a target 50 m away. The bullet hits the target 2.0 cm below the aim point. a. What was the bullets flight time? b. What was the bullets speed as it left the barrel?
Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the...
A bicycle wheel is rotating at 50 rpm when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of 0.50 rad / s2. a. What is the wheels angular velocity, in rpm, 10 s...
Starting from rest, a DVD steadily accelerates to 500 rpm in 1.0 s, rotates at this angular speed for 3.0 s, then steadily decelerates to a halt in 2.0 s. How many revolutions does it make?
A rubber ball is dropped onto a ramp that is tilted at 20°, as shown in FIGURE P4.59. A bouncing ball obeys the law of reflection, which says that the ball leaves the surface at the same angle it...
Evaluate the matrix [B] for the quadratic quadrilateral element shown in Figure 1015 on page 521 (Section 10.5). (a) (b) 3. (20, 15) (12, 15) (10, 10)- (20, 10) (20, 20) (12, 16) (10, 10) (20, 10)
In Fig. P5.68 m 1 = 20.0 kg and α = 53.1 o . The coefficient of kinetic friction between the block and the incline is μ k = 0.40. What must be the mass of the hanging...
Consider the system shown in Fig. P6.86. The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to...
A 350-kg roller coaster starts from rest at point A and slides down the frictionless loop-the-loop shown in Fig. P7.45. (a) How fast is this roller coaster moving at point B? (b) How hard does it...
The position of a squirrel running in a park is given by r = [(0.280 m/s)t + (0.0360 m/s 2 )t 2 ]i + (0.0190 m/s 3 )t 3 j. (a) What are and u x (t) and u y (t), the x- and y-components of the...
A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t = 0, the wheel turns through 8.20 revolutions in 12.0 s. At t = 12.0 s the kinetic...
Two uniform solid spheres, each with mass and radius R = 0.0800 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with...
The point of the needle of a sewing machine moves in SHM along the x-axis with a frequency of 2.5 Hz. At t = 0 its position and velocity components are +1.1 cm 15 cm/s. and respectively. (a) Find the...
A small block is attached to an ideal spring and is moving in SHM on a horizontal, friction less surface. When the block is at x = 0.280 m, the acceleration of the block is 5.30 m/s 2 . What is the...
A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 70.0 Hz, amplitude 5.00 mm, and...
A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat...
A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at a temperature of 20.0C. A 0.250-kg block of iron at 85.0C is dropped into the pot. Find the final temperature of the...
In a container of negligible mass, 0.200 kg of ice at an initial temperature of 40.0 o C is mixed with a mass m of water that has an initial temperature of 80.0 o C. No heat is lost to the...
Two rods, one made of brass and the other made of cop-per, are joined end to end. The length of the brass section is 0.200 m and the length of the copper section is 0.800 m. Each segment has...
Solve this ODE using a Symbolic software program: All initial conditions for y and its derivatives are zero. d'y dy + 16y 176 + 105y = 1 + 86y dt? dr dt di3 dt
Can a tank with the outflow rate fixed by a constant speed pump reach a steady state if the inlet flow rate undergoes a step change? Why, or why not? If the transfer function is G(s) = K/s, is it...
Consider the transfer function (a) What are the gain, time delay, time constants, poles, and zeros of G(s)? (b) Will the step response of this transfer function exhibit (i) inverse response or (ii)...
For the following statements, discuss whether they are always true, sometimes true, always false, or sometimes false. Cite evidence from this chapter. (a) Increasing the controller gain speeds up the...
The following data were collected from a cell concentration sensor measuring absorbance in a biochemical stream. The input u is the flow rate deviation (in dimensionless units) and the sensor output...
An electronic PID temperature controller is at steady state with an output of 12 mA. The set point equals the nominal process temperature initially. At t = 0, the error signal is increased at the...
What differential equation model represents the parallel PID controller with a derivative filter? (a) Repeat for the series PID controller with a derivative filter. (b) Simulate the time response of...
The dynamic behavior of a temperature sensor / transmitter can be modeled as a first-order transfer function (in deviation variables) that relates the measured value T m to the actual temperature, T...
If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003C and the pressure is 92 atm?
(a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain K cu using a Bode plot. Using simulation, verify that values of K c > K cu cause...
Use arguments based on the phase angle in frequency response to determine if the following combinations of G = G v G p G m and G c become unstable for some value of K c . a. b. c. d. e. |G = G. = K....
(a) Sketch the I C - V CE characteristics in the forward-active region for an npn transistor with β F = 100 (measured at low V CE ), V A = 50 V, BV CBO = 120 V, and n = 4. Use Where M is...
What is the sheet resistance of a layer of 1 -cm material that is 5 mm thick?
Consider a satellite in orbit about a spherically symmetric planet. If the orbit is circular, the sub-satellite point travels uniformly along its circular track. If the orbit is not circular,...
Prove Equations (10.2) to (10.5). Equation 10.2 Equation 10.3 Equation 10.4 Equation 10.5 Av = 2GM RE R GM Av
For the system of capacitors shown in Fig. E24.21, a potential difference of 25 V is maintained across ab. (a) What is the equivalent capacitance of this system between a and b? (b) How much charge...
Two small stereo speakers A and B that are 1.40 m a part are sending out sound of wavelength 34 cm in all directions and all in phase. A person at point P starts out equidistant from both speakers...
The electron in a hydrogen atom can be considered to be in a circular orbit with a radius of 0.0529 nm and a kinetic energy of 13.6 eV. If the electron behaved classically, how much energy would it...
A process control engineer has decided to install an automated shower control system in a bathroom of her mansion. The design calls for a system that can deliver 3 gal/min of water at 110 F by...
Find the acute angle between the two vectors A = 2a x + a y + 3a z and B = a x 3a y + 2a z by using the definition of (a) The dot product; (b) The cross product.
Two point charges of 100C are located at (2, 1, 0) and (2, 1, 0). The surface x = 0 is a conducting plane. (a) Determine the surface charge density at the origin. (b) Determine S at P(0, h, 0).
Obtain the complex exponential Fourier series coefficients for the (a) pulse train, (b) half-rectified sinewave, (c) full-rectified sinewave, and (d) triangular waveform as given in Table 2.1. Table...
The positive portion of the envelope of the output of an AM modulator is shown in Figure 3.33. The message signal is a waveform having zero DC value. Determine the modulation index, the carrier...
An FM modulator has output where f d = 20 Hz/V. Assume that m(t) is the rectangular pulse m(t) = 4II [1/8(t - 4)] (a) Sketch the phase deviation in radians. (b) Sketch the frequency deviation in...
Prove that J n (β) can be expressed as and use this result to show that J -n (β) = (-1) n J n (β) cos(B sin x )dx J(B) =
An FM modulator with f d = 10 Hz/V. Plot the frequency deviation in Hz and the phase deviation in radians for the three message signals shown in Figure 4.37. Figure 4.37 (0) 4 3 1 3 4 () () 3 3 2 2.5...
Develop a computer program and use the program to verify the simulation results shown in Figures 4.24 and 4.25. Figure 4.24 Figure 4.25 80 Af = 40 Hz 60 ww Af = 45 Hz 20 Af = 35 Hz Af= 20 Hz -20 2 4 ...
Determine the average power absorbed by each resistor in Figure 10.30. Lossless, v= 2c/3 Z, = 50 2 0.5/0 A 25 2 100 2 2.6 2
Space scientists have a large test chamber from which all the air can be evacuated and in which they can create a horizontal uniform electric field. The electric field exerts a constant horizontal...
The characteristic impedance of a certain lossless transmission line is 72. If L = 0.5H/m, find (a) C; (b) p; (c) if f = 80 MHz. (d) The line is terminated with a load of 60 . Find and s.
Determine the input resistance, transconduc-tance, output resistance, and maximum open-circuit voltage gain for the CE-CB circuit of Fig. 3.36 if I C1 = I C2 = 250 µA. Fig. 3.36: R. Q2 VBIAS...
Determine the output current and output resistance of the circuit shown in Fig. 4.61. Fig. 4.61: + 15 V 13.7 k2 |'OUT Q2 700 2
For the common-drain amplifier of Fig. 3.73, assume W/L = 10 and λ = 0. Use Table 2.2 for other parameters. Find the dc output voltage V O and the small-signal gain ν o...
For the circuit of Fig. 6.53, determine the output current as a function of the input voltage. Assume that the transistor operates in the active region. Figure 6.53 lout Ideal Vin
Find the short-circuit transconductance of the super-source follower shown in Fig. 3.43. Assume I 1 = 200 A, I 2 = 100 A, W 1 = 30 m, and W 2 = 10 m. Also, assume that both transistors operate in the...
Plot I D versus V GS for an n-channel MOSFET with W = 1 µm, L = 1 µm, k = 54 µA/V 2 , λ = 0, V DS = 5 V, V SB = 0, V t0 = 0.7 V, and ° c = 1.5 à 10 6 V/m....
Consider a hypothetical layer of silicon that has an n-type impurity concentration of 10 17 cm 3 at the top surface, and in which the impurity concentration decreases exponentially with distance into...
Determine the unloaded voltage gain ν o /ν i and output resistance for the circuit of Fig. 4.58. Check with SPICE and also use SPICE to plot out the large-signal V O -V I...
A channel of bandwidth 100 kHz is available. Using null-to-null RF bandwidths, what data rates may be supported by: (a) BPSK; (b) coherent FSK (tone spacing = 1 2T); (c) DPSK; (d) non-coherent FSK...
Even though steel is about 7 to 8 times denser than water, a steel paper clip or razor blade can be made to float on water! Explain and discuss. Predict what would happen if you mix some soap with...
A river flowing steadily at a rate of 175 m 3 /s is considered for hydroelectric power generation. It is determined that a dam can be built to collect water and release it from an elevation...
The differential instrumentation amplifier shown in Fig. 6.56 must have a voltage gain of 10 3 with an accuracy of 0.1 percent. What is the minimum required open-loop gain of the op amp? Assume the...
Suppose an op amp with PSRR + = 10 is con-nected in the voltage-follower configuration shown in Fig. 6.3c. The input V S is set to zero, but a low- fre-quency ac signal with peak magnitude V sup =20...
A 50-cm-thick layer of oil floats on a 120-cm-thick layer of water. What is the pressure at the bottom of the water layer?
The air velocity in the duct of a heating system is to be measured by a Pitot-static probe inserted into the duct parallel to the flow. If the differential height between the water columns connected...
The U.S. National Institute of Standards and Technology (NIST) maintains several accurate copies of the international standard kilogram. Even after careful cleaning, these national standard kilograms...
A CMOS amplifier stage is shown in Fig. 7.49. Select W/L for M 1 and M 5 to give V i = V O = 2.5V dc and |I D | = 100 µA bias in all devices. The minimum value of L and W is 2 µm....
An amplifier has a low-frequency forward gain of 5000 and its transfer function has three negative real poles with magnitudes 300 kHz, 2 MHz, and 25 MHz. (a) Calculate the dominant-pole magnitude...
The amplifier of Problem 9.5 is to be compensated by reducing the magnitude of the most dominant pole. (a) Calculate the dominant-pole magnitude required for unity-gain compensation with 45 phase...
Repeat Problem 9.9 if the circuit is compensated by using shunt capacitance to ground at the input of the second stage. Assume that this affects only the most dominant pole. Data from Prob. 9.9: An...
A conservative force F(vector) is in the +x-direction and has magnitude F(x) = /(x + x 0 ) 2 , where = 0.800 N m 2 and x 0 = 0.200 m. (a) What is the potential-energy function U(x) for this force?...
A differential input stage is shown in Fig. 11.54. (a) Neglecting flicker noise, calculate expressions for the equivalent input noise voltage and current generators at the base of Q 1 . Use SPICE to...
A rope tied to a body is pulled, causing the body to accelerate. But according to Newtons third law, the body pulls back on the rope with a force of equal magnitude and opposite direction. Is the...
A ball is thrown from the edge of a high cliff. Regardless of the angle at which it is thrown, due to air resistance, the ball will eventually end up moving vertically downward. Justify this...
For the circuit of Fig. 9.41, parameter values are R F = 5 kΩ, R E = 50 Ω, and C F = 1.5 pF. The basic amplifier of the circuit is shown in Fig. 9.42 and has two negative real...
A technique that allows the return ratio to be simulated using SPICE without disrupting the dc operating point is shown in Fig. 8.60 and explained in Problem 8.33. (a) Use that technique to simulate...
(a) Find a set of orthonormal basis functions for the signals given below which are defined on the interval -1 t 1: x 1 (t) = t x 2 (t) = t 2 x 3 (t) = t 3 x 4 (t) = t 4 (b) Attempt to provide a...
(a) Find the optimum (matched) filter impulse response h 0 (t), as given by (9.45) for s 1 (t) and s 2 (t), shown in Figure 9.35. (b) Find ζ 2 as given (9.56). Plot ζ 2 versus...
Consider antipodal signaling with amplitude imbalance. That is, a logic 1 is transmitted as a rectangular pulse of amplitude A 1 and duration T, and a logic 0 is transmitted as a rectangular pulse of...
In regions far from the entrance, fluid flow through a circular pipe is one dimensional, and the velocity profile for laminar flow is given by u(r) = u max (1 - r 2 /R 2 ), where R is the radius of...
An object consists of a ball of weight W glued to the end of a uniform bar also of weight W. If you release it from rest, with the bar horizontal, what will its behavior be as it falls if air...
Air flows through a pipe at a rate of 120 L/s. The pipe consists of two sections of diameters 22 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the...
A 15.0-kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table (Fig. E8.44). Suddenly it is struck by a 3.00-kg stone...
In-compressible steady flow in the inlet between parallel plates is uniform, V 0 = 8 cm/s, while downstream, the flow develops into the parabolic profile v x = az(z 0 - z), where a is a constant....
The boom shown in Fig. E11.15 weighs 2600 N and is attached to a frictionless pivot at its lower end. It is not uniform; the distance of its center of gravity from the pivot is 35% of its length....
What is the thinnest film of MgF 2 (n = 1.39) on glass that produces a strong reflection for orange light with a wavelength of 600 nm?
FIGURE EX17.5 shows a standing wave oscillating at 100 Hz on a string. What is the wave speed? 50 cm FIGURE EX17.5
Bacteria vary in size, but a diameter of 2.0 m is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size?
How much work is done on the gas in the process shown in Figure EX19.1? p (kPa) 400- 200- V (cm') 0+ 100 200 300 FIGURE EX19.1
500 J of work must be done to compress a gas to half its initial volume at constant temperature. How much work must be done to compress the gas by a factor of 10, starting from its initial volume?
You throw a baseball straight up in the air so that it rises to a maximum height much greater than your height. Is the magnitude of the balls acceleration greater while it is being thrown or after it...
a. 100 J of heat energy are transferred to 20 g of mercury. By how much does the temperature increase? b. How much heat is needed to raise the temperature of 20 g of water by the same amount?
A 65 cm 3 block of iron is removed from an 800C furnace and immediately dropped into 200 mL of 20C water. What fraction of the water boils away?
A container holds 1.0 g of argon at a pressure of 8.0 atm. a. How much heat is required to increase the temperature by 100C at constant volume? b. How much will the temperature increase if this...
The volume of a gas is halved during an adiabatic compression that increases the pressure by a factor of 2.5. a. What is the specific heat ratio g? b. By what factor does the temperature increase?
A dripping water faucet steadily releases drops 1.0 s apart. As these drops fall, does the distance between them increase, decrease, or remain the same? Prove your answer.