5

An object having mass of 3kg, which is initially at rest at point A, starts its motion along frictionless path of A-C and finally; stops momentarily after it compre...

Question

An object having mass of 3kg, which is initially at rest at point A, starts its motion along frictionless path of A-C and finally; stops momentarily after it compresses the spring (k = 224 N/m) byxm The object starts moving in opposite direction after it stops momentarily What is the speed of the objectjust after it starts its motion in opposite direction if the high of the points A h A, and B,hB. is 4.6 m and 3.9 m, respectively; angle 8 of the inclined plane is 27 and the distance travelled on

An object having mass of 3kg, which is initially at rest at point A, starts its motion along frictionless path of A-C and finally; stops momentarily after it compresses the spring (k = 224 N/m) byxm The object starts moving in opposite direction after it stops momentarily What is the speed of the objectjust after it starts its motion in opposite direction if the high of the points A h A, and B,hB. is 4.6 m and 3.9 m, respectively; angle 8 of the inclined plane is 27 and the distance travelled on inclined plane; d, just before hitting the spring is 2 m? (Your result must be in m's and include digit after the decimal point: Maximum of 5% of error is accepted in your answer: Take & 10mls -



Answers

An inclined plane of angle $\theta=20.0^{\circ}$ has a spring of force constant $k=500 \mathrm{N} / \mathrm{m}$ fastened securely at the bottom so that the spring is parallel to the surface as shown in Figure $P 7.63 .$ A block of mass $m=2.50 \mathrm{kg}$ is placed on the plane at a distance $d=0.300 \mathrm{m}$ from the spring. From this position, the block is projected downward toward the spring with speed $v=0.750 \mathrm{m} / \mathrm{s}$ By what distance is the spring compressed when the block momentarily comes to rest? (FIGURE CAN'T COPY)

For this problem on the topic of energy conservation, we're told that a 0.5 kg mass is propelled up an incline by the use of a spring with spring constant 500 newtons per meter. The spring is initially compressed, but that he centimeters from its equilibrium position and sends the mass from rest firstly across a horizontal surface and then onto the plane. The plane has a length of four m an incline of 30° to the horizontal. The coefficient of kinetic friction between the mass and the surface is 0.35. And When compressed this, when the spring is compressed, the masses 1.5 m from the bottom of the plane. We want to find the speed of the mass as it reaches the bottom of the plane. The speed of the mass as it reached the top of the plane. And the total work by friction from the beginning to the end of the masses motion. Now the elastic potential energy is you spring. Yeah. And this is equal to half K X squared where K is the spring constant? And X is the compression. The mass loses energy which is the work done by friction, which is minus the frictional force, F F times the distance that the mass traveled. D. And this is equal to minus UK times M G. D. Due to friction. And therefore the kinetic energy at the bottom is given by K B. And K B is equal to a half M. The B squared which is equal to half K X squared minus the work done due to friction, Mieux, que times am times G times D. And so from here we can rearrange to find the speed of the block at the bottom of the plane. VB to be the square root of K X squared over two K X squared over em rather minus two UK jean times deep. And so since all these values are known if we substitute them in, we get this to be the square root of 500 newtons per meter times the compression of the spring, 0.3 m squared divided by The mass of the block, 0.5 Kg -2 times. The coefficient of kinetic friction is 0.35 Times the acceleration due to gravity 9.81 m/km2 Times a distance of 1.5 m which gives us the speed of the block at the bottom To be eight 93 meters per second. So that's the block speed just before it starts moving up the inclined plane. Now, for part B we have that to reach the top of the incline. The gravitational potential energy must also be considered. And the change of gravitational potential energy, delta U. G. Is equal to the potential energy at the top minus the potential energy at the bottom. Now, since the plane has lent l the an incline angle theater, the change in gravitational potential energy is MGl scientist to. And the kinetic energy at the top can then be calculated by subtracting the gravitational potential energy and work due to friction from the kinetic energy at the bottom. So Kay top is equal to okay at the bottom minus UK MG L. Sign theater minus mgl sine theta. And so by rearranging this equation, since we know half um the top squared is equal to K B minus UK mgl signed data minus MG al sine theta. We can find the speed of the block at the top of the incline, the top to be the square root of two over. Em into the kinetic energy at the bottom minus M G L. Into UK. Call sign data plus sign data. And so if we substitute the values into this equation, we get this to be the square root of two over 0.5 Kg. And the kinetic energy at the bottom. We can get from VB, which we calculated in part A and it's a half M V B squared which is 19 0.92 jules, yeah -0.5 Kg In 29.81 m/km2 times for meters multiplied by 0.35 Times The co sign of 30° plus the sign of 30 degrees. And so if we calculate this, we get the speed at the block at the top To be 4.08 m per second. And lastly, we want to find the total work done by friction from the beginning to the end of the motion of the mass. Now the total work done due to friction is equal to minus the frictional force ff in two D plus L, which is minus UK m g d minus UK mg. Call sign of theater times L. And so if we substitute our values into this equation, this is minus 0.35 times zero 0.5 kg Times 9.81 m/km2 Into 1.5 m less, four m times the call sign of 30 degrees. And so this gives us the work done due to friction for the blocks, entire motion to B -8 0.52 jules.

In this question. You have Ah, mess starting doll on this. Suppose that the fiction this surface No. I sliding down with a show of lost e he which is given to be 0.75 So just sickened. We're going to find over here is what is the distance that the spring is compressed when the block off mess actually comes toe a momentarily women a temporary stop. So we're gonna use energy conservation, right? And one of these simpler ways is to actually look at what is the change in our, you know, a gravitational potential energy. And she hit and the equate that to the energy in the spring. All right. And so let's say we have a final position, which we don't know it some compression off. Uh, let's see. X Right. So this is the distance that we want to find X. What we were firstly to know is feisty. Change in the sent off mess. When you block, we just x right. So from here, it moves until it we just x we changed color. You just x So at this point, what s D height, Right? So you want a fine the changing the height from here to here. So these are changing height. You give us the gravitational potential. Energy dubs off MGH. Now we know that this high bottom illness my but tennis is given s X plus D where the distance between the mess and or spring and it's given to be 0.3 meters. All right, To find a height, we take sign Peter of this You can't get the light. Multiply this by m g to get, uh GP. So this would tell us what is t ah gp that was lost or converted into other forms off energy. All right. And finally we used to energy conservation rule. That is the initial energy, which is kinetic initial kinetic energy pass and gpt must be equals to the final energy which is just e energy in the spring huff K X square Not really too soft. This equation for X you know they find what they saw. Ah, Compression. Yes. Pink. Not really, no sure. Kinetic energy is just half and V square gp were for Eddie investigator Sex rusty times 70 toe times empty goes to off. Thanks. Good. No, you need to do. Is to open up the breakfast over here and rearranged equation such that we had a quadratic equation is half X squared minus mg scientist toe off X minus off every square US mg Santita times deep. This is equals to cereal. No, we can't use the quadratic equation formula that IHS Xmas really close to negative B plus minus the square class for a C over to A In this case, our A because to off k o b c close to grief mg scientist and I will see supposed to negative off in the square, plus mg citatah time steep. What we need to do is just substitute the various ah federal scene. Now we know that for distance X cannot he a negative value. So what we can do is we can eliminate the negative Latif answer, which is you cannot be minus this value but county B plus All right, in order to get a positive distance and so putting in the values and solving for X, we should get final answer p 0.1 treat one. He took

Everyone, This is the problem is gone. Contribution off energy as soul In the figure there is inclined plane having inclination 20 degree at the bottom. Off it I spring off in constant 500 Newton permit er is fixed and at the top of it there is a block off must 2.5 KD at at the state's off while 3 m from this big it is thrown towards the spring with the speed off 1 75 meter per second. We have to fire compression industry not to see it. We have to apply contribution off energy according to contribution off energy A knish ALS kind of technology Initial gravitational potential energy initial spring energy Yeah, it's called toe Final Kind of technology Final gravitational potential energy Final spring energy No substitute the value and each other kind of technology. Half M v I script gravitational potential energy you can find by and D H Final kind of technology zero because it is coming Moment Lee addressed is initial spring energy Europe because it is unexpressed. You know, gravitational potential energy becomes zero on it is half x squared. Uh huh. Half and yeah, Mhm. Yeah. Edge will be deep Bliss. Hex. Sign off Ito. Mm. Into G edge. Just a moment. No half and re I squared. Plus MGH having this value is there. Toe half gives square. No substituting the value. Uh huh. Mask off. The body is given to 25 Any silver cities? Why am 75 ever? 2.5 and two G 9.8 D is given three 13 m. Sign off 20. Yeah, it's going toe half cage 500. Mhm. And to access for solving this value for eggs, they will get Yeah, 0.135 After solving this quality execution value off actually will get 13 point meter, that's all. Thank.

Well, most of the block em is equal to one kilogram on super inconstant key is equal to 200 Newtons Newton's burn meter And, uh, Peter, please. Well inclined plane angled upward, the horizontal by an angle equal to 40 degrees. And also, uh, Shawn, in the figure D is equal to zero point six meters, we'll end the problem. The figure shows that de is equal to 0.6 meters. Okay, on the initial kinetic energy of the block. Uh, okay. Eyes the initial kinetic energy of the block, and it's equal to 16. Jules, and, uh, the block compresses the sip ring by a distance off X is equal. Do 0.2 meters. Well, let's go party. Let us apply Conservation of energy weeks is kinetic energy Initial bliss. Ah, potential energy initial equals. Um kinetic energy final Bless potential energy if I know Plus, uh, w s, which is the work done by the simpering W ass is the worried them by the supreme on. And this could be returnees. Uh, fanatic initial. Ah, plus, But kinetic energy in jobless potential energy initial is a cool too, uh, finding kinetic energy Plus me. LF it's equal to m g d sign pita m g d Sign Peter. And work done by the simpering is given by half Gak square, huh? Ok, X squared. Okay. I'm not putting the values. Uh, any some kinetic energy? Oh, bless. 16 is equal to one month. Supply by one multiplied. I 9.8 multiplied by, um, they're 0.6. Bless. 0.2. Sign of 40 unless one divided by two multiplied by C. Bring constantly just 200 newtons per meter. 200 multiply x squared, which is 0.2 square. And, uh, therefore, we have here. Okay, f um Well, here you eyes the initial dramatic energy. Uh, KF and you fr the kinetic and potential energies in deep endpoint on W s is the word than by the simpering. And therefore, uh, we have kinetic energy. Initial kick I initial is equal to ah, six point minds. Extra old six point mine six. Um, Jules. Okay, so 6.96 Jules. All right, so now, um, like a soul Barbie. Okay, well, this is not initially dramatic Energy dropped. This is the final kinetic energy story X equal. This explained 96 yours and in part B, we will find out, Um, the initial kinetic energy and initial kinetic energy ki I is equal to, uh, zero less one multiply by 9.8 multiplied by, um, 0.6 plus 0.4 into sign or 40. 40. Um bless. Huh? Um, multiplied by 200 multiplied by zero point for scare Swear. So we have a kid. I initial kind of kick energy is equal to 22.3 jewels and off the problem. Thank you. For what you


Similar Solved Questions

5 answers
Miobts and Maloalsfcldna Are nolnecoecl droer PinnnQuminna alox 5fatrrh ArapnasePootras eTelspnat meiacnage?IneihaseWhichZ-Cell:early and tata slaga ol ba &am0 phase 0l mosie Wmel phaer4in caitne struclure label304-In rcwttiz tie euclure abelecLnccn Cempusemito5ig ?6-What two main changes are taking pLic: " cellI-Senuence b7cdiaaranizfrom fust%o last:8-'hat is Irie and producC milass ? 9-Whal Main dirferenco %# een Cylokinesis planis a7d anmals?
Miobts and Maloals fcldna Are nolne coecl droer Pinnn Quminna alox 5fatrrh Arapnase Pootras e Telspnat meiacnage? Ineihase Which Z-Cell: early and tata slaga ol ba &am0 phase 0l mosie Wmel phaer 4in cai tne struclure label30 4-In rc wttiz tie euclure abelec Lnccn Cem puse mito5ig ? 6-What two ma...
5 answers
Hon mnuch nolxet Atert Then deribels and aurrage secd ttatel Lener7 Tha blloales tNla Petnea Ele bak kilometen pr hoar for # Bampka o rotdrrtBpeed Ln/E) Tua 32 a} DTncu AeOne DAD E WO DT uTFind the lincu rcgranlon cquatia;contltlou cocibcicdiAeHeamanLhnLAL AIcon-nriondttcrnuliontcEpretulerpretetton:
Hon mnuch nolxet Atert Then deribels and aurrage secd ttatel Lener7 Tha blloales tNla Petnea Ele bak kilometen pr hoar for # Bampka o rotdrrt Bpeed Ln/E) Tua 32 a} DTncu AeOne DAD E WO DT uT Find the lincu rcgranlon cquatia; contltlou cocibcicdi AeHeaman LhnLAL AI con-nrion dttcrnulion tcEpret uler...
5 answers
3.A 2.26 kS rcsistor is connected to an AC voltage source with an mms voltage of 230 V (a) What is the maximum potential difference across the resistor (in V)? ?V (6) What is the maximum current through the resistor (in A)? 2A (c) What is the rms current through the resistor (in A)? ?A What is the average power dissipated by the resistor (in W)PPW
3.A 2.26 kS rcsistor is connected to an AC voltage source with an mms voltage of 230 V (a) What is the maximum potential difference across the resistor (in V)? ?V (6) What is the maximum current through the resistor (in A)? 2A (c) What is the rms current through the resistor (in A)? ?A What is the a...
5 answers
For Ihe exponential function y = logaX where a > and a+1, find the following Find the domain(-0,0) (0,60) [0,00)(-0 0E (~6,0Find Ihe renge 6,0) (0,0)[0,0o)oe0,0iFind ary intorcuplsCilck
For Ihe exponential function y = logaX where a > and a+1, find the following Find the domain (-0,0) (0,60) [0,00) (-0 0E (~6,0 Find Ihe renge 6,0) (0,0) [0,0o) oe 0,0i Find ary intorcupls Cilck...
5 answers
Determine the digevergence or convergence of the sequences below: If the sequence converges determine the limiting value {F"vn n4+3n + 10 Jn=1 n + 4 n=[
Determine the digevergence or convergence of the sequences below: If the sequence converges determine the limiting value {F"vn n4+3n + 10 Jn=1 n + 4 n=[...
5 answers
Aqueous hydrochloric acid (HCL) will react with solid sodium hydroxide (NaOH) to produce aqueous sodium chloride (NaCl) and liquid water (Hzo) Suppose 8.4 of hydrochloric acid mixed with 14.9 of sodium hydroxide Calculate the minimum mass of hydrochloric acid that could be left over by the chemical reaction; Be sure your answer has the correct number of significant digits_Do
Aqueous hydrochloric acid (HCL) will react with solid sodium hydroxide (NaOH) to produce aqueous sodium chloride (NaCl) and liquid water (Hzo) Suppose 8.4 of hydrochloric acid mixed with 14.9 of sodium hydroxide Calculate the minimum mass of hydrochloric acid that could be left over by the chemical ...
5 answers
Assertion: Cork cambium and vascular cambium are lateral meristem. Reason: Both are involved in secondary growth of plant by addition of cells in lateral direction of main axis.
Assertion: Cork cambium and vascular cambium are lateral meristem. Reason: Both are involved in secondary growth of plant by addition of cells in lateral direction of main axis....
1 answers
Find the indicated extremum of each function on the given interval. Absolute maximum value on $(0, \infty)$ for $$f(x)=5 x-2 x \ln x$$
Find the indicated extremum of each function on the given interval. Absolute maximum value on $(0, \infty)$ for $$f(x)=5 x-2 x \ln x$$...
5 answers
(r-Jul_ (rju61-Jur = ()w(2 = fJuj = (4)d(1=Zu = (418"ultze (M)iIu-2(uydeL} J41 J0 Ju0 4ILA Dotung slyiurXo| 4jeJ #eW (nd 91pbudneojuxod
(r-Jul_ (rju 61-Jur = ()w (2 = fJuj = (4)d (1=Zu = (418 "ultze (M)i Iu-2( uydeL} J41 J0 Ju0 4ILA Dotung slyiurXo| 4jeJ #eW (nd 91 pbud neojuxod...
1 answers
A sample of nickel is heated to $99.8^{\circ} \mathrm{C}$ and placed in a coffeecup calorimeter containing $150.0 \mathrm{g}$ water at $23.5^{\circ} \mathrm{C}$. After the metal cools, the final temperature of metal and water mixture is $25.0^{\circ} \mathrm{C} .$ If the specific heat capacity of nickel is $0.444 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}$ what mass of nickel was originally heated? Assume no heat loss to the surroundings.
A sample of nickel is heated to $99.8^{\circ} \mathrm{C}$ and placed in a coffeecup calorimeter containing $150.0 \mathrm{g}$ water at $23.5^{\circ} \mathrm{C}$. After the metal cools, the final temperature of metal and water mixture is $25.0^{\circ} \mathrm{C} .$ If the specific heat capacity of ni...
1 answers
For each of the points given in polar coordinates, find two additional pairs of polar coordinates $(r, \theta),$ one with $r>0$ and one with $r<0$. $$\left(1.3, \frac{3 \pi}{4}\right)$$
For each of the points given in polar coordinates, find two additional pairs of polar coordinates $(r, \theta),$ one with $r>0$ and one with $r<0$. $$\left(1.3, \frac{3 \pi}{4}\right)$$...
5 answers
What is the pH of a 0.99 M solutionof Al(H2O)3+6 if the Ka for the hydrateis 1.4×10−5?Round your answer to the nearest hundredth.
What is the pH of a 0.99 M solution of Al(H2O)3+6 if the Ka for the hydrate is 1.4×10−5? Round your answer to the nearest hundredth....
5 answers
Locust Inc. owes $19,000.00 to be repaid by monthly payments of$510.00. Interest is 7% compounded monthly.(a)How many payments will Locust Inc. have to make?(b)How much interest is included in the 13th payment?(c)How much of the principal will be repaid in the 10thpayment period?(d)Construct a partial amortization schedule showing details of thefirst three payments, the last three payments, andtotals.
Locust Inc. owes $19,000.00 to be repaid by monthly payments of $510.00. Interest is 7% compounded monthly. (a) How many payments will Locust Inc. have to make? (b) How much interest is included in the 13th payment? (c) How much of the principal will be repaid in the 10th payment period? (d) Constru...
5 answers
Sin % dx (1) Vcos €
sin % dx (1) Vcos €...
5 answers
(b) Determine the general solution of the given differential equationdy = 4- + 4y = 4x + 3cos(2x) dx2 dx
(b) Determine the general solution of the given differential equation dy = 4- + 4y = 4x + 3cos(2x) dx2 dx...
5 answers
8_ For any positive integer k, let Ak {x € Q: 0 < x < 1/k} and Bk {x € Q : 0 < x k}. What are the following sets?U Ai i_1bUBi i=1nA;d_Bi
8_ For any positive integer k, let Ak {x € Q: 0 < x < 1/k} and Bk {x € Q : 0 < x k}. What are the following sets? U Ai i_1 b UBi i=1 nA; d_ Bi...

-- 0.018702--