5

Consider the potential energy curve shown in the figure below(a) Determine whether the force Fx is positive, negative, or zero at the five points indicated. (Enter ...

Question

Consider the potential energy curve shown in the figure below(a) Determine whether the force Fx is positive, negative, or zero at the five points indicated. (Enter your answers in the table below:)(b) Indicate points of stable, unstable, and neutral equilibrium. (Enter your answers in the table below:)(c) Sketch the curve for Fx versus x from x = 0 to x = 9.5 m: (Submit a file with a maximum size MB.)Choose FileMe selacledAne7C nas nol boon gradod YtpolntFx signEquillbriumSelec Selecl--Sulecl -S

Consider the potential energy curve shown in the figure below (a) Determine whether the force Fx is positive, negative, or zero at the five points indicated. (Enter your answers in the table below:) (b) Indicate points of stable, unstable, and neutral equilibrium. (Enter your answers in the table below:) (c) Sketch the curve for Fx versus x from x = 0 to x = 9.5 m: (Submit a file with a maximum size MB.) Choose File Me selacled Ane7C nas nol boon gradod Yt polnt Fx sign Equillbrium Selec Selecl-- Sulecl - Sulecl. Sulecl _ Sulacl Sulac- Suled Sulecl Solecl _. Neod Help?



Answers

For the potential energy curve shown in Figure P6.54 (page 190), (a) determine whether the force $F_{x}$ is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral equilibrium. (c) Sketch the curve for $F_{x}$ versus $x$ from $x=0$ to $x=9.5 \mathrm{m}$.

All right, so we're told to use f equals negative. Do you? Over D ex. Ah, in the ah, in the book. This is on page 187. Negative. Do you over D X and so do you. Over de acts is the slope, so that would be the opposite of the slope. All right, so at a the slope is zero. So the force is zero at B. The slope is negative. So the force is positive at sea, the slope is zero. So the force is zero at D. The slope is positive. So the forces negative and e. I'm not sure I drew that well enough to tell. Let me get to the actual problem in the book, E Looks like the slope is zero. So zero All right. No, we are told that unstable equilibrium is when the potential energy is maximum. So I see that points point a is the maximum and point He is a local maximum. And so I'm listing both of those as unstable, stable, stable equilibrium is when potential energy is a minimum and that's obviously at sea. Neutral equilibrium would be, ah, horizontal line, a period that is horizontal for a little distance. I don't see any of that in this graph, so nothing is labeled as neutral. Finally, we're supposed Teoh graph the force versus X. So that would be the slope of the line versus X. Um, I'm gonna make a little room here erasing this racing. This which I didn't even need to write anyway, So I'm gonna put this right below the graph, at least Aziz. Well, as I can think, I'm gonna erase this too. In this, in this, in this not of a racing, so I can put this right below the graph. So this is gonna be force in Nunes. So we said that the force is zero at a and at sea and at E now, the slope is maximum in magnitude when the slope is greatest. And it looks to me like the slope is greatest where it crosses the X axis. Now, initially, we have a negative slope, which would be a positive force. So the maximum positive force would be right about in here the maximum negative force and the slope looks, I guess the slopes a little bit less. The maximum negative force be right in here somewhere, but it would be slightly lower and magnitude kind of like that. So let me look at exactly what we're supposed to be doing again. Sketch. So I don't need it. No need that. I don't know if I need to put numbers on here. Um, the slope would be the derivative. Um, let's go ahead and put numbers on here. I'm going. Teoh use points here and here to approximate the slope in that region. So it looks to me like the point above is two comma one, and the point below here is three common negative one. So my slope is going to be. Why? To minus y one over x two minus x one. So negative one minus one three minus one is gonna be negative too. Over to negative one. So the obvious of the slope is gonna be positive one. So I'm saying that this maximum right here is about at one Newton the minimum force. I said the slope doesn't look quite as large in magnitude, so that's going to be a little bit less than negative. One new. All right, now, let's think about the shape of this graph. So the slope is close to zero here. Whoops. And its maximum here. But the slope changes gradually, so we don't see an abrupt change in slow. So the curve would look something like this. No, I went Teoh extra effort of finding an equation of this line and then taking the derivative of that equation. And what I found is that everything here is correct, except for the fact that my estimate of slope, which was right here was not very good. Um, when I took the derivative, I actually got, um here it's actually close to two point two. So this is close to 2.2, and then down here is close to, um to negative, too news. And I actually do see why. Ah, the reason is that ah three minus one is not correct. It's three minus two, which would give us one, which would give us the negative too. By the way, when I fit an equation to it, my actual equation was why equals negative 0.157 x to the fourth power plus 3014 x to the third power minus 1.5 to 8. Two x to the second power plus 20.6864 acts plus 3.9 and then the opposite derivative. Looks like this. Um, I figured this out using a spreadsheet. Ah, and a, um, curve fit on a spreadsheet. Okay, so that's it.

We have force equals negative GDX off the force. Negative X cubed plus two x squared plus three x I had it was three x squared minus four x plus three I had When f equals zero, we can solve for three X squared minus four x plus three equals zero and the roots are X equals 1.87 and X equals negative. 0.535 The stable boy Oh, is X equals negative. 0.535 and the unstable point. Wow, He's at X equals 1.87 on this at Deter. Mined by that you being minimum over here and you being maximum.

In this question. It is about obtaining information from the potential energy diagram. So in this case, we are given this potential energy graph. Here we have a particle that is moving along the X axis acting on by a single conservative force. Okay, so there are seven parts in this question, in part A. Uh, we want to find her, uh, direction of the fourth at 0.8 when the particulars is released from rats. That 0.8. Okay. So from the potential energy diagram, you know, that force is equal to minus the u D X. Okay, so at a, um, the slope is, uh, negative. Okay, So f is positive. Okay. Which means that the force Yes, pointing right. Okay. Yeah. So, by convention, uh, positive means to the right. Okay. And then, uh, be proud be we want to find the direction of the fourth at point B. Okay, so at point B from the ground, you can tell that the U. D. X is positive. Okay, so if it's negative, Okay, So this means that the force is pointing left. Okay. And then in proxy, um, what value of X is the kinetic energy of the particle maximum. Okay, so for maximum Katie for maximum kinetic energy, Uh, that you is at minimum came hear from the graph. Okay. You mean yes. Ads. X equals to 0.75 and goes Okay, So at this point, the kinetic energy after pataca is that the maximum key? Then party was a false on the particular at sea Point C. And so at point C, the duty X is zero. So because zero So this means that no force exacting on the particle and see he false. Alright, in price e, we want to find the largest value of X reached by the particle. Okay, so, um, certify the value of X. Okay, you go back to the graph, and we actually draw a horizontal line across. Okay? And then this will be the point where the particle, uh, that's the maximum X that the particle rich again describe. That schedule is not exact. So I just referred back to the diagram on the book. Okay, so we draw. Hurry, draw a horizontal line from me. Thank you. It touches. Uh huh. Uh, potential energy graph again. Key. Okay at that. At that point, where explains to, uh, because the objects released at a So, uh so the U and A plus the kinetic energy of the paragraph A corresponds to the total energy of the system, the total energy of the party girl inside the system. So by just drawing another by just doing the horizontal lines is to represent the total energy line. Okay. And when the total energy matters potential energy Okay, that would be the turning point of the motion. Okay, So the largest value of X from the graph is equal to, uh, 2.2 m. Okay, then in F, we want to find the points, Uh, where you have stable equilibrium. Okay, that's stable. Equilibrium. Mhm. It refers to the minimum points of U X. Okay, so the answers, uh, X equals two 0.75 m and x equal to actually goes to 1.9 m. Okay. Okay, then in G, um, you want to find the points of unstable equilibrium. Okay. He refers to maximum points of U x. Okay, So the answer, it's point seat. Okay. Thanks to close to 1.4, he does. Okay, so these are the are the answers for this question, and that's all for this right?

So understand that in the first half, force equals forex in the second half. Fourth egress. Four minus four x so forth request negatively Utx So do you d X equals forex. So solving 40 that the U equals integration for X g X plus two X square. Let's see on over here you have do you equals negative fdx. So for X minus four dx in addition so that big guns two X squared minus four x I see Now we have to find the continuity off this at X equals half so at X equals zero born five we get From here we get u equals half the sea. From here we get Equus half minus to see. That's called They see one that's got the sea do So this is C one and this is state. Do me so if we choose that you at X equals zero equals one, if we choose that you at X equals zero equals zero, then see one was 20 Andi se do goes to one. So using that we will draw the scarves. Ah, this is nearly four x and negative two x squared. So when we draw the car. This would come out to be all negative. That's X on. That is you. So this will go like this for the first half. And then this is go like that for the fast second half and then it would become horizontal.


Similar Solved Questions

5 answers
Honfbnzl "DOnion uh [espect t0 " {or Lt E ofvo- Aa easutcd expression fot I In Icta angle- Riound. Find Yout 4nsto Vo- ut Afor &x ball- FOINTS) velocity horizonu l [ Express with Eround evislince (22 throun sc height = 8.) A ball is 1 whcn = it hits from the 'neglect = aunchcd trveled; - You may It is ball has gravity) distance - acceleration 5 due and g (the
honfbnzl "DOnion uh [espect t0 " {or Lt E ofvo- Aa easutcd expression fot I In Icta angle- Riound. Find Yout 4nsto Vo- ut Afor &x ball- FOINTS) velocity horizonu l [ Express with Eround evislince (22 throun sc height = 8.) A ball is 1 whcn = it hits from the 'neglect = aunchcd tr...
5 answers
Istion -Heln Ien ememss %5 allkched topoII 0 #Iin ie Ilo ? ef tvo rJSs 058 (ocs cocn Sin IcIl9 TotecC. #etsei J7one-J.ECcn 802 $ Whalis tre Anelic energy Ine sys'em?MckPanoriJ; 478CA
Istion - Heln Ien ememss %5 allkched topoII 0 #Iin ie Ilo ? ef tvo rJSs 058 (ocs cocn Sin IcIl9 TotecC. #etsei J7one-J.ECcn 802 $ Whalis tre Anelic energy Ine sys'em? Mck Panori J; 478 CA...
5 answers
Problem 5.1Differentiate the following functions:(a) f(r) tan-'(r _ V1+7) (6) g(x) = arccos btacose ,0 < I<t,a > b > 0 a+bco: %
Problem 5.1 Differentiate the following functions: (a) f(r) tan-'(r _ V1+7) (6) g(x) = arccos btacose ,0 < I<t,a > b > 0 a+bco: %...
5 answers
Unit 2- Epoxidation and Sterol In-class activity Draw an acid-calaylzed reaction between an equimolar amount of glycerol and butanoic acid.H2'Oh2 Draw the structure of oleic acid at pH 7, and provide mechanism for the following reactions: a) reaction with hydrogen peroxide and waler(H}b) reaction with hydrcgen peroxide and sodium borohydride
Unit 2- Epoxidation and Sterol In-class activity Draw an acid-calaylzed reaction between an equimolar amount of glycerol and butanoic acid. H2 'Oh 2 Draw the structure of oleic acid at pH 7, and provide mechanism for the following reactions: a) reaction with hydrogen peroxide and waler (H} b) r...
5 answers
We define a relation; S Oll R? {0} as follows: If we have two vectors v and & , WC say "SW if the angle from { to " is multiple of m/2. Is S a1 equivalence relation on R2? Would the aSWeI change if we define aleW relation the same Wa] Oll R: {0}?
We define a relation; S Oll R? {0} as follows: If we have two vectors v and & , WC say "SW if the angle from { to " is multiple of m/2. Is S a1 equivalence relation on R2? Would the aSWeI change if we define aleW relation the same Wa] Oll R: {0}?...
5 answers
$1 mathrm{~kg}$ of ice at $0^{circ} mathrm{C}$ is mixed with $1 mathrm{~kg}$ of steam at $100^{circ} mathrm{C}$. What will be the composition of the system when thermal equilibrium is reached? Latent heat of fusion of ice $=3 cdot 36 imes 10^{5} mathrm{~J} mathrm{~kg}^{-1}$ and latent heat of vaporization of water $=2 cdot 26 imes 10^{6} mathrm{~J} mathrm{~kg}^{-1}$.
$1 mathrm{~kg}$ of ice at $0^{circ} mathrm{C}$ is mixed with $1 mathrm{~kg}$ of steam at $100^{circ} mathrm{C}$. What will be the composition of the system when thermal equilibrium is reached? Latent heat of fusion of ice $=3 cdot 36 imes 10^{5} mathrm{~J} mathrm{~kg}^{-1}$ and latent heat of vapor...
5 answers
(0 pls) Final paramelrie cqualions for the lin? ol inlerseetion ofth? planesZr+4y+2 = and r-3y 22 = 0(10 pts) The space cuve r(t) = cuS sin t} is the infersection of two surfaces Find che equations of the two Sufaces and sketch the graphs_(5 Tls) Findlth? TNR Irame cun ut"Ano IOSIr(t) -In t 410}.
(0 pls) Final paramelrie cqualions for the lin? ol inlerseetion ofth? planes Zr+4y+2 = and r-3y 22 = 0 (10 pts) The space cuve r(t) = cuS sin t} is the infersection of two surfaces Find che equations of the two Sufaces and sketch the graphs_ (5 Tls) Findlth? TNR Irame cun ut"Ano IOSI r(t) - In ...
1 answers
Sketch and find the area of the region $R$ described in terms of the given parametric curves. $R$ is the closed loop bounded by $x=t^{3}-4 t, y=t^{2}$ $(-2 \leq t \leq 2)$
Sketch and find the area of the region $R$ described in terms of the given parametric curves. $R$ is the closed loop bounded by $x=t^{3}-4 t, y=t^{2}$ $(-2 \leq t \leq 2)$...
1 answers
Graph each function using shifts of a parent function and a few characteristic points. Clearly state and indicate the transformations used and identify the location of all vertices, initial points, and/or inflection points. $$f(x)=\sqrt{x+2}-1$$
Graph each function using shifts of a parent function and a few characteristic points. Clearly state and indicate the transformations used and identify the location of all vertices, initial points, and/or inflection points. $$f(x)=\sqrt{x+2}-1$$...
5 answers
D)logz(x + 7) ~ 10g2l (2x) = 3eJlog(3x + 6) = 1 + logx
d)logz(x + 7) ~ 10g2l (2x) = 3 eJlog(3x + 6) = 1 + logx...
5 answers
Sinx c0s3x dxSelect one: cos2r a 2cos4r + c)nbsinZrsinar + € 8cos2c C.costr + c 8dsin2z 2sin4r + c 2
sinx c0s3x dx Select one: cos2r a 2 cos4r + c )n b sinZr sinar + € 8 cos2c C. costr + c 8 d sin2z 2 sin4r + c 2...
5 answers
2 yer Ii answer 6 probability to single that of distributed the Gediraainig thermometer with readings sajpid at reading treeezor randomly Jo 88 between and selected batch 8 and standard of thermometers H 'Rourd are
2 yer Ii answer 6 probability to single that of distributed the Gediraainig thermometer with readings sajpid at reading treeezor randomly Jo 88 between and selected batch 8 and standard of thermometers H 'Rourd are...
5 answers
Repeat Exercise $4,$ but assume that the top of the triangle is located 3 m below the surface of the water.
Repeat Exercise $4,$ but assume that the top of the triangle is located 3 m below the surface of the water....
5 answers
When k>1 the products are favored. Does this mean that equilibrium goes left, towards the reactants to even it out?
When k>1 the products are favored. Does this mean that equilibrium goes left, towards the reactants to even it out?...
5 answers
The rectangular box has a length of 8 cm, a width of 10 cm and a height of 8 cm.A cylinder with a radius of 2.1 cm is cut out of the box.Find the volume of the cylinder and use it to
The rectangular box has a length of 8 cm, a width of 10 cm and a height of 8 cm. A cylinder with a radius of 2.1 cm is cut out of the box. Find the volume of the cylinder and use it to...
5 answers
If the probability of passing test is 0.64, what is the probability of {failing the next two tests?0.360 B: 0.410 0.130 D:0.64
If the probability of passing test is 0.64, what is the probability of {failing the next two tests? 0.360 B: 0.410 0.130 D:0.64...

-- 0.019847--