DO NOT USE UNLOCKS

What is the maximum segment length of a 100Base-FX network,Thelast character('X', etc) refers to the line code method used. Line code is a pattern of voltage, current or photons used to represent the digital data transmitted on the transmission line.Fast Ethernetcable is sometimes referred to as100BaseXwhere X can be replaced by two variants i.e. FX and TX .In most of the Fast Ethernet applications, theindividual devicesare connected bytwisted-pair copper wiresi.e.100BaseTX(maximum segment length is only 100 meters) and thee optical fibers are used fortransmission over longer distances(as maximum segment length is 2000 meters of 100baseFX). So,100baseTX to 100Base FXconvertor is required flor sending the signal from the sender end over the optical fiber. Similarly, at the receiver end,100baseFX to 100Base TXis required. A combinational logic circuit takes a 4-bit unsigned binary integer number at its inputs labelled D3 , D2 , D1 and D0 , where D3 is the most significant bit. For decimal input 1, 2, 3, 5, 7, 11 and 13, the output S is to be at logic 1, and it is to be at logic 0 otherwise. (i) Write down the truth table for the required combinational logic function. (ii) Using a Karnaugh map, determine the simplified Boolean expression for the output S in terms of the inputs D3 to D0 in a minimum sum-of-products form. (iii) Describe what is meant by an essential term in a Karnaugh map. Write down the essential terms for the Karnaugh map in (ii). (iv) Using a Karnaugh map, this time determine the required simplified Boolean expression for the output S in a minimum product-of-sums form. [10 marks] (b) Provide a circuit diagram which implements the following Boolean function using only NAND gates F = (A + D).(B + C + D).(A + B + C) that has the don't care states: A.B.C.D, A.B.C.D, A.B.C.D and A.B.C.D [4 marks] ( (a) Show how two NOR gates may be connected to form an RS latch. Describe its operation and give a table relating its inputs to its outputs. How could you use this circuit to eliminate the effect of contact bounce in a single pole double throw switch supplying an input to a digital logic circuit? [6 marks] (b) The state sequence for a particular 4-bit binary up-counter is as follows: Show how four negative edge triggered T-type flip-flops (FFs) with outputs labelled QA , QB , QC and QD can be used to implement a ripple counter having the specified state sequence. Show any combinational logic necessary assuming that the FFs have asynchronous reset inputs available. [4 marks] (c) Using the principles of synchronous design, determine the next state combinational logic expressions required to implement a counter having the state sequence specified in part (b ). Assume that D-type FFs are to be used and that unused states do not occur. [4 marks] (d) Explain carefully what happens if the counter in (c ) starts in state 1 1 1 0 . In general, how can start-up problems be overcome in the design of synchronous state machines? [4 marks] (e) What are the advantages and disadvantages of the synchronous design in part (c ) compared with the alternative design in part (b )? [2 marks]

section B

A particle can move along only an $x$ axis, where conservative forces act on it (Fig. $8-66$ and the following table). The particle is released at $x=5.00 \mathrm{m}$ with a kinetic energy of $K=14.0 \mathrm{J}$ and a potential energy of $U=0 .$ If its motion is in the negative direction of the $x$ axis, what are its (a) $K$ and $(b) U$ at $x=2.00 \mathrm{m}$ and its (c) $K$ and (d) $U$ at $x=0 ?$ If its motion is in the positive direction of (h) $U$ at $x=12.0 \mathrm{m},$ and its (i) $K$ and $(\mathrm{j}) U$ at $x=13.0 \mathrm{m}$ ? (\textrm{k} ) ~ P l o t ~ $U(x)$ versus $x$ for the range $x=0$ to $x=13.0 \mathrm{m} .$ Next, the particle is released from rest at $x=0 .$ What are $(1)$ its kinetic energy at $x=5.0 \mathrm{m}$ and $(\mathrm{m})$ the maximum positive position $x_{\mathrm{max}}$ it reaches? $(\mathrm{n})$ What does the particle do after it reaches $x_{\max } ?$ Range0to 2.00m2.00mto3.00m3.00mto8.00m8.00mto11.0mForceF1=+(3.00N)i^F1=+(5.00N)i^F=0F3=(4.00N)i^Range Force0to 2.00mF1=+(3.00N)i^2.00mto3.00mF1=+(5.00N)i^3.00mto8.00mF=08.00mto11.0mF3=(4.00N)i^

A 1500 $\mathrm{kg}$ car begins sliding down a $5.0^{\circ}$ inclined road with a speed of 30 $\mathrm{km} / \mathrm{h}$ . The engine is turned off, and the only forces acting on the car are a net frictional force from the road and the gravitational force. After the car has traveled 50 $\mathrm{m}$ along the road, its speed is 40 $\mathrm{km} / \mathrm{h}$ (a) How much is the mechanical energy of the car reduced because of the net frictional force? (b) What is the magnitude of that net frictional force?

We move a particle along an $x$ axis, first outward from $x=1.0 \mathrm{m}$ to $x=4.0 \mathrm{m}$ and then back to $x=1.0 \mathrm{m}$ , while an external force acts on it. That force is directed along the $x$ axis and its $x$ component can have different values for the outward trip and for the return trip. Here are the values (in newtons) for four situations, where $x$ is in meters: Outward(a)+3.0(b)+5.0(c)+2.0x(d)+3.0x2Inward3.0+5.02.0x+3.0x2OutwardInward(a)+3.03.0(b)+5.0+5.0(c)+2.0x2.0x(d)+3.0x2+3.0x2 Find the net work done on the particle by the external force for the round trip for each of the four situations. (e) For which, if any, is the external force conservative?

A spring with spring constant $k=200 \mathrm{N} / \mathrm{m}$ is suspended vertically with its upper end fixed to the ceiling and its lower end at position $y=0 . \mathrm{A}$ block of weight 20 $\mathrm{N}$ is attached to the lower end, held still for a moment, and then released. What are (a) the kinetic energy $K,$ (b) the change (from the initial value) in the gravitational potential energy $\Delta U_{g}$ and $(\mathrm{c})$ the change in the elastic potential energy $\Delta U_{e}$ of the spring-block system when the block is at $y=-5.0 \mathrm{cm} ?$ What are (d) $K,$ (e) $\Delta U_{g},$ and $(\mathrm{f}) \Delta U_{e}$ when $y=-10 \mathrm{cm},(g) K,(h) \Delta U_{g},$ and $(i) \Delta U_{c}$ when $y=-15 \mathrm{cm}$ and $(j) K,(k) \Delta U_{g},$ and $(1) \Delta U_{c}$ when $y=-20 \mathrm{cm} ?$

The maximum force you can exert on an object with one of your back teeth is about 750 $\mathrm{N}$ . Suppose that as you gradually bite on a clump of licorice, the licorice resists compression by one of your teeth by acting like a spring for which $k=2.5 \times 10^{5} \mathrm{N} / \mathrm{m} .$ Find

(a) the distance the licorice is compressed by your tooth and

(b) the work the tooth does on the licorice during the compression.

(c) Plot the magnitude of your force versus the compression distance. (d) If there is a potential energy associated with this compression, plot it versus compression distance. In the 1990 s the pelvis of a particular Triceratops dinosaur was found to have deep bite marks. The shape of the marks suggested that they were made by a Tyrannosaurus rex dinosaur. To test the idea, researchers made a replica of a $T$ rex tooth from bronze and aluminum and then used a hydraulic press to gradually drive the replica into cow bone to the depth seen in the Triceratops bone. A graph of the force required versus depth of penetration is given in Fig. $8-71$ for one trial; the required force increased with depth because, as the nearly conical tooth penetrated the bone, more of the tooth came in contact with the bone. (e) How much work was done by the hydraulic press $-$ and thus presumably by the $T .$ rex $-$ in such a penetration? (f) Is there a potential energy associated with this penetration? (The large biting force and energy expenditure attributed to the $T$ rex by this research suggest that the animal was a predator and not a scavenger.)

A skier weighing 600 $\mathrm{N}$ goes over a frictionless circular hill of radius $R=20 \mathrm{m}(\mathrm{Fig} .8-62) .$ Assume that the effects of air resistance on the skier are negligible. As she comes up the hill, her speed is 8.0 $\mathrm{m} / \mathrm{s}$ at point $B,$ at angle $\theta=20^{\circ} .(\mathrm{a})$ What is her speed at the hilltop (point $A$ ) if she coasts without using her poles? (b) What minimum speed can she have at $B$ and still coast to the hilltop? (c) Do the answers to these two questions increase, decrease, or remain the same if the skier weighs 700 N instead of 600 $\mathrm{N} ?$

When a click beetle is upside down on its back, it jumps upward by suddenly arching its back, transferring energy stored in a muscle to mechanical energy.This launching mechanism produces an audible click, giving the beetle its name. Videotape of a certain click-beetle jump shows that a beetle of mass $m=4.0 \times 10^{-6}$ kg moved directly upward by 0.77 $\mathrm{mm}$ during the launch and then to a maximum height of $h=0.30 \mathrm{m} .$ During the launch, what are the average magnitudes of (a) the external force on the beetle's back from the floor and (b) the acceleration of the beetle in terms of $g$

A single conservative force $F(x)$ acts on a 1.0 $\mathrm{kg}$ particle that moves along an $x$ axis. The potential energy $U(x)$ associated with $F(x)$ is given by U(x)=4xex/4JU(x)=4xex/4J where $x$ is in meters. At $x=5.0 \mathrm{m}$ the particle has a kinetic energy of 2.0 $\mathrm{J} .(\mathrm{a})$ What is the mechanical energy of the system? (b) Make a plot of $U(x)$ as a function of $x$ for $0 \leq x \leq 10 \mathrm{m},$ and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine (c) the least value of $x$ the particle can reach and (d) the greatest value of $x$ the particle can reach. Use part (b) to determine (e) the maximum kinetic energy of the particle and (f) the value of $x$ at which it occurs. (g) Determine an expression in newtons and meters for $F(x)$ as a function of $x$ . (h) For what (finite) value of $x$ does $F(x)=0 ?$

The potential energy of a diatomic molecule (a two-atom system like $\mathrm{H}_{2}$ or $\mathrm{O}_{2}$ ) is given by U=Ar12Br6U=Ar12Br6 where $r$ is the separation of the two atoms of the molecule and $A$ and $B$ are positive constants. This potential energy is associated with the force that binds the two atoms together. (a) Find the equilibrium separation - that is, the distance between the atoms at which the force on each atom is zero. Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is (b) smaller and (c) larger than the equilibrium separation?

A $\mathrm 2.0 \mathrm{kg}$ breadbox on a frictionless incline of angle $\theta=40^{\circ}$ is connected, by a cord that runs over apulley, to a light spring of spring constant $k=120 \mathrm{N} / \mathrm{m},$ as shown inFig. $8-43 .$ The box is released from rest when the spring is unstretched. Assume that the pulley is massless and frictionless. (a) What is the speed of the box when it has moved 10 $\mathrm{cm}$ down the incline? ( b) How far down the incline from its point of release does the box slide before momentarily stopping, and what are the (c) magnitude and (d) direction (up or down the incline) of the box's acceleration at the instant the box momentarily stops?

A 700 g block is released from rest at height $h_{0}$ above a ver- tical spring with spring constant $k=400 \mathrm{N} / \mathrm{m}$ and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring 19.0 $\mathrm{cm} .$ How much work is done (a) by the block on the spring and (b) by the spring on the block? (c) What is the value of $h_{0} ?$ (d) If the block were released from height 2.00$h_{0}$ above the spring, what would be the maximum compression of the spring?

You drop a 2.00 $\mathrm{kg}$ book to a friend who stands on the ground at distance $D=10.0 \mathrm{m}$ below. If your friend's outstretched hands are at distance $d=1.50 \mathrm{m}$ above the ground (Fig. $8-30 ),$ (a) how much work $W_{g}$ does the gravitational force do on the book as it drops to her hands? (b) What is the change $\Delta U$ in the gravitational potential energy of the book-Earth system during the drop? If the gravitational potential energy $U$ of that system is taken to be zero at ground level, what is $U(\mathrm{c})$ when the book is released and $(\mathrm{d})$ when it reaches her hands? Now take $U$ to be 100 $\mathrm{J}$ at ground level and again find (c) $W_{g}$ (f) $\Delta U,(\mathrm{g}) U$ at the release point, and (h) $U$ at her hands.

A watermelon seed has the following coordinates: x=5.0mx=5.0m y=8.0m,y=8.0m, and z=0mz=0m . Find its position vector (a) in unit-vector no- tation and as (b) a magnitude and (c) an angle relative to the positive direction of the xx axis. (d) Sketch the vector on a right-handed coor dinate system. If the seed is moved to the xyzxyz coordinates (3.00m(3.00m 0m,0m),0m,0m), what is its displacement (e) in unit-vector notation and as (f) a magnitude and (g) an angle relative to the positive xx direction?

In the 1991 World Track and Field Championships in Tokyo, Mike Powell jumped 8.95m,8.95m, breaking by a full 5 cmcm the 23 -year long-jump record set by Bob Beamon. Assume that Powell's speed on takeoff was 9.5 m/sm/s (about equal to that of a sprinter) and that g=9.80m/s2g=9.80m/s2 in Tokyo. How much less was Powell's range than the maximum possible range for a particle launched at the same speed?

A projectile is fired horizontally from a gun that is 45.0 mm above flat ground, emerging from the gun with a speed of 250 m/sm/s . (a) How long does the projectile remain in the air? (b) At what horizontal distance from the firing point does it strike the ground? (c) What is the magnitude of the vertical component of its velocity as it strikes the ground?