A simple ladder problem (equilibrium)

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In summary: Thanks for the help!In summary, the equilibrium problem is a difficult one that Fermat has been struggling with. There is a ladder with static friction against a wall. The person climbs up the ladder, and there is a maximum frictional force the ground can exert on the ladder at its lower end. The man can climb up the ladder until the ladder starts to slip, and then the actual frictional force is greater.
  • #1
NutriGrainKiller
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First test on equilibrium tomorrow, and I'm very sure there is going to be a ladder-type problem on it where I have to determine normal forces, frictional forces when someone is on the ladder up a certain distance, and how far can the person go up before it starts to slip. I don't know if you guys are familiar with masteringphysics.com or not, but it is an online homework system where it automates questions similar to that in the book. I've gotten pretty far in the problem, but for some reason I can't complete the 2nd two problems. Here is the exact problem on mastering physics:
A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 160 N. The coefficient of static friction between the foot of the ladder and the ground is 0.40. A man weighing 740 N climbs slowly up the ladder.
A)What is the maximum frictional force that the ground can exert on the ladder at its lower end?
B)What is the actual frictional force when the man has climbed 1.0 m along the ladder?
C)How far along the ladder can the man climb before the ladder starts to slip?
I drew a diagram and a free-body diagram of the problem, and was able to get the answer to A through the requirements for equalibrium. Here is my work:
(Fnet)x: Fs-Fw=0
(Fnet)y: Fn-Fp-Fg=0
We have Fp and Fg, so Fn = Fp+Fg or Fn = 900
Since Fs <= Us*Fn we have (Fnet)x: Us*Fn-Fw=0, or Fw=(.4)*(900), so Fw = 360. And since Fs<=Us*Fn, Fs = Fw, so Fsmax=360. This is the answer to A.
I am confused as hell when it comes to B. It is difficult to explain because you cannot see my free-body diagram, but I will do my best to describe it.
Don't know how to use tao, so I'll just use lowercase t.
(tnet)=tn+ts+tp+tg+tw=0. I am choosing the origin to be at the lower end of the ladder where Fn and Fs are, so those would equal zero because they have no moment arm. So here is the new equation:
(tnet): -(Fp)(R)Sin()-(Fg)(R)Sin()+(Fw)(R)Sin()=0. With the values we have
(tnet): -(740n)(1m)sin(53.13)-(160n)(2.5m)sin(53.13)+(Fw)(5m)sin(36.87)=0.
I found 53.13 and 36.87 through basic trig. Here are my questions: I am solving for a new Fw (normal force coming from the wall) in this equation right? i.e. I would NOT be using the value I obtained earlier. After I get that I plug it back into (Fnet)X to get Fs, which would be my answer - right?

My final answer was 301.3, which is NOT right - The correct answer is 171n. Why :confused:

When it comes to part C I'm not sure how to go about it because I don't fully understand the answer to part B. I'm guessing you solve for the unknown moment arm in the tnet equilibrium equation.

Thanks guys

pink floyd says hi :cool:
 
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  • #2
You've got your angles the wrong way round!

Or, you should be taking cos instead of sin, and vice versa.

The distance from the bottom of the ladder to the wall is 3 m.
3m is not the height up the wall to the top of the ladder
 
  • #3
Oh, btw, it's a 3-4-5 triangle, with cos@ = 3/5, sin@ = 4/5. It makes calculations a bit simpler if you recognise that :smile:
 
  • #4
Thanks Fermat :)

btw for searching purposes the answer to B is 171n and C is 2.7m.
 
  • #5
Yeah, I got those answers too.
 

1. What is a simple ladder problem and why is it important?

A simple ladder problem is a physics problem that involves a ladder leaning against a wall and finding the point of equilibrium, or balance, where the ladder will not fall. It is important because it demonstrates basic principles of physics and can be applied to real-world situations.

2. What factors affect the equilibrium of a ladder?

The factors that affect the equilibrium of a ladder include the weight of the ladder, the angle at which it leans against the wall, the surface friction between the ladder and the wall, and the weight of any objects placed on the ladder.

3. How do you calculate the point of equilibrium for a simple ladder problem?

To calculate the point of equilibrium, you need to use the principle of moments, which states that the sum of the clockwise moments must equal the sum of the counterclockwise moments. This can be represented mathematically as Mcw = Mccw. By setting up and solving this equation, you can find the point at which the ladder will be in equilibrium.

4. Can the equilibrium of a ladder be affected by the placement of objects on the ladder?

Yes, the equilibrium of a ladder can be affected by the placement of objects on the ladder. The weight and position of these objects can change the overall weight distribution of the ladder and therefore impact its equilibrium point.

5. How can the concept of equilibrium in a simple ladder problem be applied to real-world situations?

The concept of equilibrium in a simple ladder problem can be applied to real-world situations such as construction, where ladders are commonly used. Understanding the equilibrium point of a ladder can help ensure its stability and prevent accidents. It can also be applied to other structures and objects that rely on a balance of forces, such as bridges or cranes.

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