Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

(III) A $56.0-\mathrm{kg}$ person stands 2.0 $\mathrm{m}$ from the bottom of thestepladder shown in Fig. $65 .$ Determine $(a)$ the tension inthe horizontal tie rod, which is halfway up the ladder, $(b)$ thenormal force the ground exerts on each side of the ladder, and $(c)$ the force (magnitude and direc-tion) that the left side of the ladderexerts on the right side at the hinge onthe top. Ignore the mass of the ladderand assume the ground is frictionless.[Hint: Consider free-body diagrams foreach section of the ladder.]

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

a) $|170 \mathrm{N}|$b) 220 $\mathrm{N}$, 330 $\mathrm{N}$c) 280 $\mathrm{N}$, $52^{0}$

Physics 101 Mechanics

Chapter 12

Static Equilibrium; Elasticity and Fracture

Equilibrium and Elasticity

Cornell University

University of Washington

Hope College

McMaster University

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

04:17

04:42

For the stepladder shown i…

01:21

08:51

A stepladder of negligible…

07:34

09:23

01:37

05:33

A steplader of negligible …

00:52

04:16

05:50

so first considered the free body diagram for each side off the ladder. Now, because the two sides off the ladder are not identical, you must have both horizontal and vertical components. Tow the hinge, force off one side off the ladder on the other. So I have denoted the hinge force on horizontal and vertical direction. Bye. If EJ ej betweens hinge fourth horizontal and then it's it's f HIV means horizontal force for the vertical component on duh the same for the other side of the lateness. Now, if nl here is the normal fools on the ladder on one side off the ladder Ah, left side. And if n. R is the normal force on the right side. Now let's first to combine the angle Tita that we have. So we know that from here, these two distances we know that l cost ita has to be equal to be over too. This gift to be equally doe cost in worse off the overs to add No, they are given d to be equal to see the point nine made dash Oh, site B is given Toby but me Just check it once again. So yeah, the is 1.8 meters on DDE. L is given Toby. Don't point Fight makers, which is the length of the ladder. So we plug these to lose over here on bigger Tita to be equal to 68.9 degrees. Now let's ride the equilibrium in questions for the vertical forces on the ladder. Still, we have submission overs vertical to be equal to zero for equilibrium on dhe from here. So we have and F ankle, which is the normal force on the left. So over here, when we're spiting the equilibrium conditions when we're writing the vertical forces, we are writing this for the whole ladder. So we have to include the forces from either sides from both the sides off the ladder. So the F F end, unless it's in part minus Andy plus F, means vertical minus. If angel article, because on one side it goes upward and on the other side it goes downward. So there's a plus and minus, and that is equal to zero. From here we have an l less f and odd to the equal to mustangs gravity. So this abilities to cancel and B and I want this a Christian now that calculate dogs on the left side about the dog. Basically, you take this point into consideration when we have the hinge forces and take the talks about this point for the left side. So let me get straight talk on. We're taking talk for the N v a calculating talks for the left side. So there's l here and the physical to seal off our equilibrium. So this means we have as ml and another thing. I'm assuming clockwise stocks to be positive here. So they have f n l times the length from the force from the point off point where the forces acting on DDE the distance between the distance from the point off, where the forces acting so the point of consideration. So that distances l and then we have to multi plague my sign. Times 90 minus t damages this anger on Scient. I sign off 19 minus. Tita is co scientist. So that's what we don't you. So basically we are taking the force times the vertical component or the length were to goto this force on. We do the same thing for mg. So we have energy. The force times this distance, which is the vertical distance from the force to the point through which we are calculating the dark about which we can collect in the dark. So this distance right here is 0.2 l this Times co scientist. So that is the component. So they has 0.2 l dines was saying Tita So basically this equation, this land and this length is pretty sane. But here we had the land. Toby L Which is this lamp right here and here. That land is this lengths you're going toe then last we have Dr Goto Ft. So we have to multiply f David this distance so that will be equal to and over to dines Scientific. This is gonna go zero now let's call this a question. Could be a question one. Let me just right market with different colors. That's called this a question one. Now we do the same thing for the right side off the ladder. So we have that equal door negative. It's and right times off because tita plus ft things and oh, what to scientific And this is equal to zero. Let's call this to the equation. True. Now Let's abstract question due from me. Question one. So doing that, we get and left less f end right times and cost Tita minus mg. I see your point to Ah, go sign Tita minus two f b. I don't want to scientist, and that is equal procedure. So basically, we did this obstruction in order to get you off the FT. That if if we subtract this, we get rid off ft. And we don't need toe evaluate this force. So no, we do this. And let's substitute the values and soul for okay, Just a minute. So yeah. So we did this in order to solve for ft not to get rid off. In order to get rid of a piece, you will have to add the at these two equations. But we did the subsection, So we will find the force. No, um, if the attention force from here. So now let's lake Let me the street from my scent. And so basically, if you do the substance Regine, you'll arrive like this. No, Andi, we already evaluated this time to be equal to mg so we can directly luck. Andy over here on this will eliminate the work off calculating S N L and F N R. Separately and plugging them into Equus. This a question. Either one or two and then finding a 52. This makes our calculations lot more simpler. So we do that like the value of Tita that we just can't connect it to 68.9 degrees. So, doing that and solving for everything, you get the state of the equal do 1 69 point. A whole new gun. Let me just write. The value is that might need to use. So we have mosque to be given 56 Katie gravity. You know what? This is 9.8 media, ballistic and scratch. Tita is only the evaluated back in the previous slide on Yes, this is all you need. You don't need land here because these just cancer long each of the bones on DDE. So doing that, you get ft to be equal to 1 69.4 Newton. Now it's do part. So to find the normal fools on either side. Okay, So if n. L and F and R so we already have the old question for both left and right, so first, let's pick this aggression and sol for an R. So now that you have if you can plug this value off FDA over here on obviously the land cancers from Border Dome so you don't need to use l to find an r on then, blud, the value off Tita in here and over here on dso for an art. So doing that you get as an art of the equal door 219 point five minutes is basically I'm writing in the back of. So you're using the question to To find if an r now to find if an l which is the normal force on the left side So instead off doing the long calculation sort of going the long way and saw the cushion one mother to have f n r you can directly plugged the value off and on over here. Let's call this a question three. And since you know what mg really you can find if an l so you can also choose to solve this A question, a question one. But, uh, this one just you might need toe do more calculations in orderto solved this a question for offended So this is this a question Jews in this equation is makes the calculations lot more easier. So let's do back so f n l will be mg minus offend, right? Simply plug this value over here on, you know, the mass and acceleration due to gravity. With these two vandals on DDE, we get as an elder the equal door 29.3 Newton. So this is my using you question too now for the last where we have to find the hinge force components for the right side. So this is for the left side of the question. So this is non, well, fools on the right, and this is normal force Under left Mom refined the hint force components. So basically f HIV and F h h. For that, we really use the force components. Let's find the hinge force components from the free body diagram for the right side. So let's write the It's a Newton's second law for the right side off the liner. So we have the security. Is Edo on this equal to zero for Calabria. This gives us have and write minus f Etch Vito be equal to zero and from here since you already have an I. You see that HIV is a gold O f on that gives 219.5 Newton. Now solve this. So we have each edge. If it's it dying minus ft. You called zero follicle librium. So if EJ will be equal to ft on DDE Ft. Began gloated over here. So if Etch Etch will be also control on 69.4 now that have the body the vertical and horizontal components for the pinch force, we can find the magnitude of the force using by to get us to your own. So basically, add the squares off both the components and take that was over. So doing that you get the magnitude to be called you to 77 1 teen now the fi off the hinge, which is this anger? The scan. We found my baking dan in Ross off the vertical gun running off the hitch, or raj the horizontal sought after a vertical component of bands such F HIV over the horizontal gone woman. So doing that you get fired to be 50. Do Nick

View More Answers From This Book

Find Another Textbook

02:16

Acar skids to a halt Where did its kinetic energy go?To potential energy…

01:45

Two ice skaters, Clark and Charles_ are practicing in the preparation for co…

02:09

Pulling out of a dive; the pilot of an airplane guides his plane into a vert…

01:51

The rotating systems shown in the figure differ only in that the two identic…

02:06

Explain what must happen in order for an Oxygen atom to become positively ch…

01:05

"For a stretched string of length L with fixed ends, the resonant frequ…

An astronaut on Mars attaches a small brass ball to a 1.00 meter length of s…

00:55

Which of the following is not an intensive quantity?a)Pressureb)…

04:34

A certain helium-neon laser pointer; emitting light with a wavelength of 632…