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A bicycle wheel of radius 0.30 m is spinning at a rate of 60 revolutions per minute. (a) What is the centripetal acceleration of a point on the edge of the wheel? (b) What is the period of the wheels... A car of mass 1700 kg is traveling without slipping on a flat, curved road with a radius of curvature of 35 m. If the cars speed is 12 m/s, what is the frictional force between the road and the tires? If the masses of the objects in Problem 35 are both increased by a factor of 5, by what factor does the gravitational force change? Do not use a calculator to solve this problem! Data From Problem 35... A roller-coaster track is designed so that the car travels upside down on a certain portion of the track as shown in Figure P5.20. What is the minimum speed the roller coaster can have without... Find the ratio of your weight on the Earth to your weight on the surface of the Sun. WEarth W Sun Using Fig. 7.85 , design a problem to help other students better understand source-free RC circuits. For the circuit shown in Fig. 7.85 , find i(t), t > 0. t= 0 R, R2 R3 +1 For the circuit in Fig. 7.91 , find i o for t > 0. t= 0 4 H 24 V(+ 4 8 Determine v(t) for t > 0 in the circuit of Fig. 8.87 . 250 mH 3 20u(t) V (+ 4 20u(t) A v(t) 500 mF A series RLC circuit has R = 80 , L = 240 mH, and C = 5 mF. If the input voltage is v(t) = 115 cos 2t, find the current flowing through the circuit. Using Fig. 9.40 , design a problem to help other students better understand phasor relationships for circuit elements. Two elements are connected in series as shown in Fig. 9.40 . If i = 12 cos (2t -... Determine the admittance Y for the circuit in Fig. 9.44 . 10 J30 WW 10 -10 J10 rell Using Fig. 9.45 , design a problem to help other students better understand admittance. Find i(t) and v(t) in each of the circuits of Fig. 9.45. a. b. (t) R2 R1 Vs(t) (+ all Find current I o in the circuit shown in Fig. 9.50 . 40 2 5/0 A -j40 2 20 2 j40 Q relll Find Z T and V o in the circuit in Fig. 9.71 . Let the value of the inductance equal j20 Ω. Z7 V. 10 -j20 2 5/30 A 20 2 elle A coin of diameter D C is 300 cm in front of a parallel wall on which is hung a circular flat mirror of diameter D M . A person stands 900 cm from the wall. Show that D M = 3/4 D C is the... Consider the case of two positive thin lenses, L 1 and L 2 , separated by 5 cm. Their diameters are 6 and 4 cm, respectively, and their focal lengths are 1 = 9 cm and 2 = 3 cm. If a diaphragm with... A classic 35-mm film camera has a single thin lens having a 50.0-mm focal length. A woman 1.7 m tall stands 10.0 m in front of the camera. (a) Show that the lens-film distance must be 50.3 mm. (b)... Find the gravitational force of the Sun on the Earth. A rock of mass m is tied to a string of length L and swung in a horizontal circle of radius r. The string can withstand a maximum tension T max before it breaks. (a) What is the maximum speed v max... A positive meniscus lens with an index of refraction of 2.4 is immersed in a medium of index 1.9. The lens has an axial thickness of 9.6 mm and radii of curvature of 50.0 mm and 100 mm. Compute the... Write out the truth table for the following equation: F = (A B) + A' (B' C) (a) Find all the static hazards in the following circuit. For each hazard, specify the values of the input variables and which variable is changing when the hazard occurs. For one of the hazards,... In the following Verilog code, A, B, C, and D are 0 at time 10 ns. If D changes to 1 at 20 ns, specify the times at which A, B, and C will change and the values they will take. (a) always @(D) begin... A sequential circuit has one input (X) and two outputs (D and B). X represents a 4-bit binary number N, which is input least significant bit first. D represents a 4-bit binary number equal to N 2,... Develop a Verilog model for a 16-bit carry look-ahead adder utilizing the 4-bit adder from Figure 4-10 as a module. (a) If gate delays are 5ns, what is the delay of the fastest 4-bit ripple carry adder? (b) If gate delays are 5ns, what is the delay of the fastest 4-bit adder? What kind of adder will it be? In the following circuit, the XOR gate has a delay in the range of 2 to 16 ns. The D flip-flop has a propagation delay from clock to Q in the range 12 to 24 ns. The setup time is 8 ns, and the hold... Calculate the Laplace transform of the infinite train of unit impulses in Fig. 15.31 . f(t) A 8 t 4 (a) Construct an SM chart equivalent to the following state table. Test only one variable in each decision box. Try to minimize the number of decision boxes. (b) Write a Verilog description of the... (a) In which applications should a designer use a CPLD rather than an FPGA? (b) In which applications should a designer use an MPGA rather than an FPGA? (c) In which applications should a designer... The block diagram for an elevator controller for a building with two floors is shown in the following diagram. The inputs FB 1 and FB 2 are floor buttons in the elevator. The inputs CALL 1 and CALL 2... Two coils are mutually coupled, with L 1 = 50 mH, L 2 = 120 mH, and k = 0.5. Calculate the maximum possible equivalent inductance if: (a) The two coils are connected in series. (b) The coils are... Two coils connected in series-aiding fashion have a total inductance of 500 mH. When connected in a series-opposing configuration, the coils have a total inductance of 300 mH. If the inductance of... Using the superposition principle, find i x in the circuit of Fig. 10.88 . +) 20 cos(2t 60) V 10 cos(2t + 10)A( 4 H -|00 all Find v o for the circuit in Fig. 10.86 , assuming that i s (t) = 2 sin (2t) + 3 cos (4t) A. i,(t) 10 5 HE Vo rell A rectangular channel must carry 2.0 m 3 /s of water from a water-cooled refrigeration condenser to a cooling pond. The available slope is 75 mm over a distance of 50 m. The maximum depth of flow is... A drainage structure for an industrial park has a trapezoidal cross-section similar to that shown in Fig. 14.2 (c). The bottom width is 3.50 ft and the sides are inclined at an angle of 60 from the... A rectangular channel has a bottom width of 2.75 m. Compute the hydraulic radius when the fluid depth is 0.50 m. Compute the hydraulic radius for a circular drain pipe running half full if its inside diameter is 300 mm. For the circuit in Fig. 16.73 , find v(t) for t > 0. Assume that i(0) = 2 A. i(t) 10 HE v(t) 2 H 2i(t) Find the output voltage v o (t) in the circuit of Fig. 16.64 . t= 0 10 1H3 10 mF 1.5 A () 52 Vo The switch in the circuit of Fig. 16.61 is moved from position a to b (a make before break switch) at t = 0. Determine i(t) for t > 0. 0.02 F 14 +) 15 V bo i(t) 2 2 H ell t = 0 5 A (+1 Determine v for t > 0 in the circuit in Fig. 16.60 . 250 mH ele 20u(t) A 4 20u(t) V 500 mF +1 Every year, there is a foot race to the top of the Empire State Building. The vertical distance traveled (using the stairs!) is about 440 m. The current record for this race is about 9 min 30 s. If... A skier of mass 100 kg starts from rest at the top of the ski slope of height 100 m shown in Figure P6.71. If the total work done by friction is -3.0 ?? 10 4 J, what is the skier???s speed when he... A mass and spring are arranged on a horizontal, friction less table as shown in Figure P6.58. The spring constant is k = 500 N/m, and the mass is 4.5 kg. The block is pushed against the spring so... Consider again the roller coaster in Figure P6.32, but now assume the roller coaster starts with a speed of 12 m/s at point A. Find the speed of the roller coaster when it reaches locations B and C.... You use an elevator to travel from the first floor (h = 0) to the fourth floor of a building (h = 12 m). If you start from rest and you end up at rest on the fourth floor, what is the work done by... An archer is able to fire an arrow (mass 0.020 kg) at a speed of 250 m/s. If a baseball (mass 0.14 kg) is given the same kinetic energy, what is its speed? A tomato of mass 0.22 kg is dropped from a tall bridge. If the tomato has a speed of 12 m/s just before it hits the ground, what is the kinetic energy of the tomato? A sphere of mass 35 kg is attached to one end of a rope as shown in Figure P6.1. It is found that the rope does an amount of work W = 550 J in pulling the sphere upward through a distance 1.5 m. Find... Figure 16.23 is a sketch of a turbine in which the incoming stream of water at 15°C has a diameter of 7.50 mm and is moving with a velocity of 25 m/s. Compute the force on one blade of the... A bend in a tube causes the flow to turn through an angle of 135. The pressure ahead of the bend is 275 kPa. If the standard hydraulic copper tube, 100 mm OD 3.5 mm wall, carries 0.12 m 3 /s of... A sharp-edged orifice is placed in a 10-in-diameter pipe carrying ammonia. If the volume flow rate is 25 gal/min, calculate the deflection of a water manometer (a) If the orifice diameter is 1.0 in... Find the center of mass of the four particles in Figure P7.42. Their masses are m 1 = 12 kg, m 2? = 18 kg, m 3 = 7.9 kg, and m 4 = 23 kg. Figure P7.42 ? y (m). -10 -5. (m) 10- -5. m2 A rubber ball is dropped and bounces vertically from a horizontal concrete floor. If the ball has a speed of 3.0 m/s just before striking the floor and a speed of 2.5 m/s just after bouncing, what is... An egg and a tomato of equal mass are dropped from the roof of a three-story building onto the sidewalk below. The sidewalk imparts an impulse to both as they splatter. (a) Is the impulse imparted to... Suppose we place a chamber 10.0 cm long with flat parallel windows in one arm of a Michelson Interferometer that is being illuminated by 600-nm light. If the refractive index of air is 1.000 29 and... Imagine a Fresnel double mirror (in air) illuminated by monochromatic light at 600.0 nm. The source slit is parallel to and 1.000 m from the line of intersection of the mirrors. If the bright fringes... Two pinholes in a thin sheet of aluminum are 1.00 mm apart and immersed in a large tank of water (n = 1.33). The holes are illuminated by 0 = 589.3 nm plane waves, and the resulting fringe system is... Two incoherent lightbeams represented by (1, 1, 0, 0) and (3, 0, 0, 3) are superimposed. (a) Describe in detail the polarization states of each of these. (b) Determine the resulting Stokes parameters... Figure P.8.67 shows two Polaroid linear polarizers and between them a microscope slide to which is attached a piece of cellophane tape. Explain what you see. Figure P.8.67 An L-state traverses an eighth-wave plate having a horizontal fast axis. What is its polarization state on emerging? Right-circular light passes through a quarter-wave plate with a horizontal fast axis. Explain why you can expect the light to emerge linearly polarized at 45 in the first and third quadrants. Suppose you were given a linear polarizer and a quarter-wave plate. How could you determine which was which, assuming you also had a source of natural light? A narrow beam of natural light is incident at 56.0 on a glass plate (n = 1.50) in air. The reflected light is partially polarized. Determine the degree of polarization. Light reflected from a glass (n g = 1.65) plate immersed in ethyl alcohol (n e = 1.36) is found to be completely linearly polarized. At what angle will the partially polarized beam be transmitted... What is Brewsters angle for reflection of light from the surface of a piece of glass (n g = 1.65) immersed in water (n w = 1.33)? At what angle will the reflection of the sky coming off the surface of a pond (n = 1.33) completely vanish when seen through a Polaroid filter? A beam of light enters a calcite prism from the left, as shown in Fig. P.8.36. There are three possible orientations of the optic axis of particular interest, and these correspond to the x-, y-, and... A thin film of ethyl alcohol (n = 1.36) spread on a flat glass plate and illuminated with white light shows a color pattern in reflection. If a region of the film reflects only green light (500 nm)... Discuss in detail what you see in Fig. P.8.33. The crystal in the photograph is calcite, and it has a blunt corner at the upper left. The two Polaroids have their transmission axes parallel to their... Given that 300 W/m 2 of light from an ordinary tungsten bulb arrives at an ideal linear polarizer, what is its radiant flux density on emerging? Write an expression for a P-state lightwave of angular frequency and amplitude E 0 propagating along a line in the xyplane at 45 to the x-axis and having its plane-of-vibration corresponding to the... Analytically, show that the superposition of an R- and an L-state having different amplitudes will yield an E-state, as shown in Fig. 8.11. What must ε be to duplicate that figure? Fig.... Consider the disturbance given by the expression vector E(z, t) = [i cos t + j cos (t - /2)]E 0 sin kz. What kind of wave is it? Draw a rough sketch showing its main features. Describe completely the state of polarization of each of the following waves: (a) = Eo cos (kz wt) jE, cos (kz wt) |(b) E = Eo sin 2#(z/A vt) jEo sin 27(z/A vt) (c) = Eo sin (wt kz) + jEo... Consider the following two waves expressed in SI units: E x = 8 sin (ky - t + /2) and E z = 8 sin (ky - t). Which wave leads, and by how much? Describe the resultant wave. What is the value of its... Two waves E z = 4 sin (ky - t) and E x = 3 in (ky - t), both in SI units, overlap in space. Describe completely the state of polarization of the resultant. Write a behavioral Verilog code for a floating-point multiplier using the IEEE single precision floating-point format. Use an overloaded multiplication operator instead of using an add-shift... Realize the following next-state equation using a minimum number of Figure 6-1(a) logic blocks. Draw a diagram that shows the connections to the logic blocks and give the functions X and Y for each... Implement a 2-bit binary counter using one logic block as shown in Figure 6-1(a). A 0 is the least significant bit, and A 1 is the most significant bit of the counter. The counter has a synchronous... An 8-bit right-shift register with parallel load is to be implemented using an FPGA with logic blocks as shown in Figure 6-1(a). The flip-flops are labeled X 7 X 6 X 5 X 4 X 3 X 2 X 1 X 0 . The... Two long slits 0.10 mm wide, separated by 0.20 mm, in an opaque screen are illuminated by light with a wavelength of 500 nm. If the plane of observation is 2.5 m away, will the pattern correspond to... (a) Figure 9-8 presents a model for a subset of MIPS instructions. Enhance the model by adding modules to interface the model to input switches and LEDs/ displays on an FPGA prototyping board. Your... An old-fashioned (vinyl) record rotates at a constant rate of 33 rpm. (a) What is its angular speed in rad/s? (b) If the record has a radius of 18 cm, what is the linear speed of a point on its edge? A diver stands at rest at the end of a massless diving board as shown in Figure P8.16.? (a) If the mass of the diver is 120 kg and the board is 4.0 m long, what is the torque due to gravity on the... Two particles of mass m 1 = 15 kg and m 2 = 25 kg are connected by a massless rod of length 1.2 m. Find the moment of inertia of this system for rotations about the following pivot points: (a) the... If the mass of a wheel is increased by a factor of 2 and the radius is increased by a factor of 1.5, by what factor is the moment of inertia increased? Model the wheel as a solid disc. A ceiling fan of radius 45 cm runs at 90 rev/min. How far does the tip of the fan blade travel in 1 hour? A Ferris wheel is moving at an initial angular velocity of 1.0 rev/30 s. If the operator then brings it to a stop in 3.0 min, what is the angular acceleration of the Ferris wheel? Express your answer... A person carries a long pole of mass 12 kg and length 4.5 m as shown in Figure P8.20. Find the magnitude of the torque on the pole due to gravity. Figure P8.20 ? 60 Consider the flagpole in Figure P8.29. If the flagpole has a mass of 20 kg and length 10 m and the angle the cable makes with the pole is ?? = 25, what are the magnitude and direction of the force... Prove that the equation when applied to a transmission grating, is independent of the refractive index. a(sin 0)m sin ;) ^ [10.61] In a neutron star, all the mass has collapsed into a relatively small volume. (a) If a particular neutron star has a radius of 1000 m and a mass of 2.0 10 28 kg, what is its density? (b) Compare... Consider a box with a lid 1.5 m wide and 0.70 m long. If the inside of the box is evacuated (i.e., its pressure is zero), how much force is required to open the lid? Could you open the lid? Figure 10.12 shows a device that can be used to measure atmospheric pressure. If h = 6.5 m, what is the density of the liquid? Figure 10.12 ? Ptop = 0 (vacuum) h Patm A swimming pool of depth 2.5 m is filled with ordinary (pure) water ( = 1000 kg/m 3 ). (a) What is the pressure at the bottom of the pool? (b) When the pool is filled with very salty water, the... An object has a weight of 20 N in air and an apparent weight of 5.0 N when submerged in water. What is its density? Will it float? Consider an airplane wing of area 20 m 2 . If the airflow speed over the top of the wing is 200 m/s, while the speed across the bottom is 150 m/s, what is the lift force on the wing at sea level at...
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