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Consider small-amplitude (linear) shallow-water waves in which the height of the bottom boundary varies, so the unperturbed waters depth is variable: h o = h o (x, y). (a) Using the theory of... Consider a thin disk with radius R at z = 0 in a Lorentz reference frame. The disk rotates rigidly with angular velocity . In the early years of special relativity there was much confusion over the... Another magnetic confinement device which brings out some important principles is the spheromak. Spheromaks can be made in the laboratory (Bellan, 2000) and have also been proposed as the basis of a... Consider the control system discussed in the last two long paragraphs of Box 22.2. It has GH = (1+ iz)[iz(1 iz)] 1 , with z = a dimensionless frequency and some time constant. (a) Show that there... In our discussion of recombination, we related the emission of Lyman photons to their absorption. This involves some important ideas in the theories of radiation and thermodynamics. (a) Consider a... The cosmic dawn that preceded the epoch of reionization can be probed by low frequency CMB observations using a special radio hyperfine line emitted and absorbed by hydrogen atoms. This line is... The Dinosaur Adventure Theme Park needs $200 million to build a monorail that will run through the park. The park's financial advisors believe that it will be able to borrow the the money by issuing... A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jets acceleration,... Determine the signs (positive, negative, or zero) of the position, velocity, and acceleration for the particle in FIGURE Q1.8. Figure Q1.8 FIGURE EX1.18 shows the motion diagram of a drag racer. The camera took one frame every 2 s. Figure EX 1.18 a. Measure the x-value of the racer at each dot. List your data in a table similar to Table... Convert the following to SI units: a. 8.0 in b. 66 ft/s c. 60 mph d. 14 in 2 Sam is recklessly driving 60 mph in a 30 mph speed zone when he suddenly sees the police. He steps on the brakes and slows to 30 mph in three seconds, looking nonchalant as he passes the officer. How... (a) Give an example of a vertical motion with a positive velocity and a negative acceleration. (b) Give an example of a vertical motion with a negative velocity and a negative acceleration? FIGURE EX2.9 shows the velocity graph of a particle. Draw the particles acceleration graph for the interval 0 s ¤ t ¤ 4 s. Figure Ex 2.9 (m/s) 4+ 2- t (s) 0+ 2 FIGURE EX2.7 showed the velocity graph of blood in the aorta. What is the bloods acceleration during each phase of the motion, speeding up and slowing down? Figure Ex 2.7 5 (m/s) 1.04 0.8- 0.6- 0.4-... A student standing on the ground throws a ball straight up. The ball leaves the students hand with a speed of 15 m/s when the hand is 2.0 m above the ground. How long is the ball in the air before it... As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon.... A skier is gliding along at 3.0 m/s on horizontal, friction less snow. He suddenly starts down a 10 o incline. His speed at the bottom is 15 m/s. What is the length of the incline? How long does it... A particle moving along the x-axis has its velocity described by the function v x = 2t 2 m/s, where t is in s. Its initial position is x 0 = 1 m at t 0 = 0 s. At t = 1 s what are the particles (a)... You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.50 s and that your car brakes with constant... Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not. A cannon tilted upward at 30 fires a cannonball with a speed of 100 m/s. What is the component of the cannonballs velocity parallel to the ground? On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed... A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 4.0 m above the ground. The ball lands 25 m... When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 50 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the... A kayaker needs to paddle north across a 100-m-wide harbor. The tide is going out, creating a tidal current that flows to the east at 2.0 m/s. The kayaker can paddle with a speed of 3.0 m/s. a. In... Susan, driving north at 60 mph, and Trent, driving east at 45 mph, are approaching an intersection. What is Trents speed relative to Susans reference frame? Vector A is in the direction 34.0 o clockwise from the y-axis. The x-component of A is A x = 16.0 m. (a) What is the of A? (b) What is the magnitude of A? Vector A has magnitude 12.0 m and vector B has magnitude 16.0 m. The scalar product A B is 90.0 m 2 . What is the magnitude of the vector product between these two vectors? Vector A has magnitude 6.00 m and vector B has magnitude 3.00 m. The vector product between these two vectors has magnitude 12.0 m 2 . What are the two possible values for the scalar product of these... The Mars Polar Lander spacecraft was launched on January 3, 1999. On December 3, 1999, the day Mars Polar Lander touched down on the Martian surface, the positions of the earth and Mars were given by... An astronaut is inside a 2.25 10 6 kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound (331 m/s) as quickly as possible, but you also do... Two boxes connected by a light horizontal rope are on a horizontal surface, as shown in Fig. P5.35. The coefficient of kinetic friction between each box and the surface is μ k = 0.30.... Block A in Fig. P5.73 weighs 2.40 N and block B weighs 3.60 N. The coefficient of kinetic friction between all surfaces is 0.300. Find the magnitude of the horizontal force necessary to drag block B... You push your physics book 1.50 m along a horizontal tabletop with a horizontal push of 2.40 N while the opposing force of friction is 0.600 N. How much work does each of the following forces do on... Adult cheetahs, the fastest of the great cats, have a mass of about 70 kg and have been clocked running at up to 72 mph (32 m/s). (a) How many joules of kinetic energy does such a swift cheetah have?... A 30.0-kg crate is initially moving with a velocity that has magnitude 3.90 m s in a direction 37.0 o west of north. How much work must be done on the crate to change its velocity to 5.62 m s in a... A 6.0-kg box moving 3.0 m/s at on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the workenergy theorem to find the maximum compression of the spring? A force in the +x-direction with magnitude F(x) = 18.0 N (0.530 N/m)x is applied to a 6.00-kg box that is sitting on the horizontal, frictionless surface of a frozen lake. F(x) is the only... A net force along the x-axis that has x-component F x = 12.0 N + (0.300 N/m 2 )x 2 is applied to a 5.00-kg object that is initially at the origin and moving in the x-direction with a speed of 6.00 m... The maximum height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72-kg person in such a jump? Where does this... For its size, the common flea is one of the most accomplished jumpers in the animal world. A 2.0-mm-long, 0.50-mg critter can reach a height of 20 cm in a single leap. (a) Neglecting air drag, what... While a roofer is working on a roof that slants at 36 above the horizontal, he accidentally nudges his 85.0-N toolbox, causing it to start sliding downward, starting from rest. If it starts 4.25 m... A ball is thrown upward with an initial velocity of 15 m/s at an angle of 60.0 above the horizontal. Use energy conservation to find the balls greatest height above the ground? A small block with mass 0.0500 kg slides in a vertical circle of radius R = 0.800 on the inside of a circular track. There is no friction between the track and the block. At the bottom of the blocks... A small block with mass 0.0400 kg slides in a vertical circle of radius R = 0.500 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of... Two stars, with masses M 1 and M 2 , are in circular orbits around their center of mass. The star with mass has M 1 an orbit of radius R 1 ; the star with mass M 2 has an orbit of radius R 2 . (a)... A bird is flying due east. Its distance from a tall building is given by x(t) = 28.0 m + (12.4 m/s)t (0.0450 m/s 3 )t 3 . What is the instantaneous velocity of the bird when t = 8.00 s? A race car starts from rest and travels east along a straight and level track. For the first 5.0 s of the cars motion, the eastward component of the cars velocity is given by U x (t) = (0.860 m/s 2... A jet fighter pilot wishes to accelerate from rest at a constant acceleration of 5g to reach Mach 3 (three times the speed of sound) as quickly as possible. Experimental tests reveal that he will... The Champion Jumper of the Insect World. The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0 above the horizontal, some of the tiny critters... A small toy airplane is flying in the xy-plane parallel to the ground. In the time interval to t = 0 to t = 1.00 s, its velocity as a function of time is given by v = (1.20 m/s 2 )ti + [12.0 m/s ... Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (a) Find the x- and y-components of each... Two crates, one with mass 4.00 kg and the other with mass 6.00 kg, sit on the friction less surface of a frozen pond, connected by a light rope (Fig. P4.43). A woman wearing golf shoes (so she can... A typical male sprinter can maintain his maximum acceleration for 2.0 s and his maximum speed is 10 m/s. After reaching this maximum speed, his acceleration becomes zero and then he runs at constant... A lunar lander is descending toward the moons surface. Until the lander reaches the surface, its height above the surface of the moon is given by y(t) = b ct + dt 2 , where b = 800 m is the initial... Flying Leap of the Flea. High-speed motion pictures (3500 frames/second) of a jumping, 210-μg flea yielded the data used to plot the graph given in Fig. E2.54. (See The Flying Leap of... A frictionless pulley has the shape of a uniform solid disk of mass 2.50 kg and radius 20.0 cm. A 1.50-kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Fig.... A thin, light wire is wrapped around the rim of a wheel, as shown in Fig. E9.49. The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The... A thin, light wire is wrapped around the rim of a wheel, as shown in Fig. E9.49. The wheel rotates about a stationary horizontal axle that passes through the center of the wheel. The wheel has radius... A thin uniform rod has a length of 0.500 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod... Starting from rest, a constant force F = 100 N is applied to the free end of a 50-m cable wrapped around the outer rim of a uniform solid cylinder, similar to the situation shown in Fig. 10.9(a). The... A therapist tells a 74-kg patient with a broken leg that he must have his leg in a cast suspended horizontally. For minimum discomfort, the leg should be supported by a vertical strap attached at the... As part of an exercise program, a 75-kg person does toe raises in which he raises his entire body weight on the ball of one foot (Fig. P11.63). The Achilles tendon pulls straight upward on the heel... You decide to visit Santa Claus at the north pole to put in a good word about your splendid behavior throughout the year. While there, you notice that the elf Sneezy, when hanging from a rope,... On December 25, 2004, the Huygens probe separated from the Cassini spacecraft orbiting Saturn and began a 22-day journey to Saturns giant moon Titan, on whose surface it landed. Besides the data in... The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular,... Sound is detected when a sound wave causes the tympanic membrane (the eardrum) to vibrate. Typically, the diameter of this membrane is about 8.4 mm in humans. (a) How much energy is delivered to the... Example 2.1 plots responses for changes in input flows for the stirred tank blending system. Repeat part (b) and plot it. Next, relax the assumption that V is constant, and plot the response of x(t)... Use Laplace transforms to find the solution to the following set of equations for x = e t and zero initial conditions. dy + 2 %3D dt dy2 + , 3 2, dt 2y1 Sketch the level response for a bathtub with cross-sectional area of 8ft 2 as a function of time for the following sequence of events; assume an initial level of 0.5 ft with the drain open. The... Consider a transfer function: Y(s)/U(s) = d/bs + c (a) What is the steady-state gain? (b) For a step change of magnitude Min the input, will the output response be bounded for all values of constants... Consider the transfer function model in Exercise 4.2. For an initial condition of y(0) = 4 and a step change in u of magnitude 2 (at t = 0), calculate the response, y(t). A continuous, stirred-tank reactor is initially full of water with the inlet and exit volumetric flow rates of water having the same numerical value. At a particular time, an operator shuts off the... A horizontal cylindrical tank shown in Fig. E4.13a is used to slow the propagation of liquid flow surges in a processing line. Figure E4.13b illustrates an end view of the tank and w t is the width... An operator tests the dynamic behavior of a furnace in order to identify the transfer function relating the furnace temperature (output) to the heat input. The operator performs a series of step... An operator introduces a step change in the flow rate q i to a particular process at 3:05 A.M., changing the flow from 500 to 520 gal/min. The first change in the process temperature T (initially at... A process has the transfer function, G(s) = 2e 2s / (s + 1). Compare the PI controller settings for the following design approaches: (a) IMC method ( c = 0.2) (b) IMC method ( c = 1.0) (c) ITAE... A data acquisition system for environmental monitoring is used to record the temperature of an air stream as measured by a thermocouple. It shows an essentially sinusoidal variation after about 15s.... Unit step response data are given in Table E7.15 for a process with gain K = 2. Fit the data to a first order model with no time delay. Next use linear regression to fit a first-order discrete-time... Two engineers are analyzing step-test data from a bioreactor. Engineer A says that the data indicate a second-order over damped process, with time constants of 2 and 6 min but no time delay. Engineer... For the control system based on the standard feedback control configuration in Fig. 11.8 determine whether the value of a affects the stability of the closed-loop system. Assume K c > 0. You do not... Consider the block diagram of a feedback control system in Fig. 11.8, where K m = 1, G p = 1 / s + 1, G d = 0, G v = K v e s , G c = 1, and G m = 1. A control engineer claims that the process will... As discussed in Section 22.5, human nerve cells have a net negative charge and the material in the interior of the cell is a good conductor. If a cell has a net charge of -8.65 pC, what are the... Determine if the following processes can be made unstable by increasing the gain of a proportional controller K c to a sufficiently large value using frequency response arguments: a. b. c. d. G,G,Gm... An electron is released from rest at a distance of 0.300 m from a large insulating sheet of charge that has uniform sur-face charge density . (a) How much work is done on the electron by the electric... Design a feedforwardfeedback control system for the blending system in Example 15.5, for a situation in which an improved sensor is available that has a smaller time delay of 0.1 min. Repeat parts... An uncharged metal sphere hangs from a nylon thread. When a positively charged glass rod is brought close to the metal sphere, the sphere is drawn toward the rod. But if the sphere touches the rod,... Neuronsare components of the nervous system of the body that transmit signals as electrical impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out... Measurement devices and their dynamics inï¬uence the design of feedback controllers. Brieï¬y indicate which of the two systems below would have its closed-loop performance enhanced... (a) One-third of a mole of He gas is taken along the path a b c shown as the solid line in Fig. P19.49. Assume that the gas may be treated as ideal. How much heat is transferred into or out of the... The pV-diagram in Fig. 20.5 shows a cycle of a heat engine that uses 0.250 mole of an ideal gas having y = 1.40. The curved part a of the cycle is adiabatic. (a) Find the pressure of the gas at point... The two charges q 1 and q 2 shown in Fig. E 21.44 have equal magnitudes. What is the direction of the net electric field due to these two charges at points A(midway between the charges), B, and C if... A small 12.3-g plastic ball is tied to a very light 28.6-cm string that is attached to the vertical wall of a room (Fig. P21.73). A uni-form horizontal electric field exists in this room. When the... Figure E19.8 shows ap V-diagram for an ideal gas in which its absolute temperature at bis one-fourth of its absolute temperature at a. (a) What volume does this gas occupy at point b? (b) How many... For the substrate pnp structure shown in Fig. 2.36 a, calculate IS, C je , C μ , and Ï F .Assume the doping profiles are as shown in Fig. 2.17. Figure 2.36 (a) Figure 2.17... A base-emitter voltage of 480 mV is measured on a super- test transistor with a 100 m 100 m emitter area at a collector current of 10 A. Calculate the Q B and the sheet resistance of the base... An n-channel implanted transistor from the process described in Table 2.1 displays a measured output resistance of 5 MΩ at a drain current of 10 μA, biased in the active... What is the total kinetic energy of the decay products when an upsilon particle at rest decays to + + ? An x ray with a wavelength of 0.100 nm collides with an electron that is initially at rest. The x rays final wavelength is 0.110 nm. What is the final kinetic energy of the electron?
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