Normal Force Exerted: Min. Req'd for 63kg Climber

In summary, the climber in the "chimney" is supported by friction forces on his shoes and back. The minimum normal force he must exert is equal to his weight divided by the static coefficient of friction between his back and the wall. The diagram should show one force of gravity acting downward and two friction forces acting upward. The sum of forces in the vertical direction should equal zero, so the normal force can be solved for using the equations of motion.
  • #1
312213
52
0

Homework Statement


The 63 kg climber in Fig. 4-52 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.83 and 0.55, respectively. What is the minimum normal force he must exert? Assume the walls are vertical and that friction forces are both at a maximum.

The actual picture is of a man holding on to a rope with his back press against a right wall and his feet against a left wall.

Homework Equations


[tex]\Sigma[/tex]Fy=ma (sum of all forces equals to mass times acceleration, in case my symbols aren't same as the commonly used ones)
Ffr=[tex]\mu[/tex]FN
FG=mg (Gravity force equals mass times gravity)

The Attempt at a Solution


http://img301.imageshack.us/img301/6979/fbdyu9.jpg

The diagram that I thought that could be it,though I doubt it.

For 0.83:
[tex]\Sigma[/tex]Fy=ma
Ffr - FG = (63)(0)
[tex]\mu[/tex]FN - mg = 0
[tex]\mu[/tex]FN = mg
FN = mg/[tex]\mu[/tex]
FN = ((63)(9.8))/(0.83)
FN = 744N

For 0.55
[tex]\Sigma[/tex]Fy=ma
Ffr - FG = (63)(0)
[tex]\mu[/tex]FN - mg = 0
[tex]\mu[/tex]FN = mg
FN = mg/[tex]\mu[/tex]
FN = ((63)(9.8))/(0.55)
FN = 1123N

With these two numbers, I added for 1866.4N (using the two numbers but with more decimal places). I also subtracted 1123 by 744 for 378.7N.

Both ways were wrong.

I lack any confidence that any of this was done correctly. First off, how is the diagram supposed to be? The way my diagram is seems to lack reasoning, unless the two diagrams are combined. Since I am not sure if my diagram is right, I doubt my net equation is right either. Could some one help my understand how the correct diagram is?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Your diagram is pretty good - the same normal force on both sides, the two friction forces upward. But you should only have ONE force of gravity downward. Combine the diagram or at least the equations so you have only one sum of forces equaling zero. You will be able to factor out the FN and solve for it.
 
  • #3
I don't really understand what one force of gravity would mean. The way I understand that to be is that one of my side is left alone and the other one has 0 for Fg but that would result that whole side to equal zero (FN = ((63)(0))/(0.55) = 0) so I must be misunderstanding this.

Another thing is that is am I supposed to do a [tex]\Sigma[/tex]Fx=ma?
 
  • #4
The thing is the guy has only one force of gravity acting on him. One weight. If you want to get really sophisticated, that force would be at his center of mass and there might be a problem of one end of him falling while the other is secure. But don't worry about that!

Yes, use sum of forces equals ma which equals zero. You'll have mg down and the two friction forces up. Solve for Fn.
 

Related to Normal Force Exerted: Min. Req'd for 63kg Climber

1. What is Normal Force Exerted?

Normal Force Exerted refers to the force that a surface exerts on an object placed on it, perpendicular to the surface. It is also known as the contact force or support force.

2. How is Normal Force Exerted calculated?

The magnitude of Normal Force Exerted can be calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s^2). This is because the object's weight is equal to the Normal Force Exerted.

3. Why is the minimum required Normal Force important for a 63kg climber?

The minimum required Normal Force is important for a 63kg climber because it determines the amount of friction and stability the climber will have on the surface they are climbing. If the Normal Force is too low, the climber may slip or lose their grip, resulting in a fall.

4. What factors can affect the Normal Force Exerted on a climber?

The factors that can affect the Normal Force Exerted on a climber include the weight of the climber, the angle of the surface they are climbing on, and the coefficient of friction between the climber's shoes and the surface.

5. How can a climber increase the Normal Force Exerted on a surface?

A climber can increase the Normal Force Exerted on a surface by increasing their weight, using shoes with a higher coefficient of friction, or by changing their body position to increase the angle between their feet and the surface they are climbing on.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
880
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
708
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
987
  • Introductory Physics Homework Help
Replies
9
Views
12K
Back
Top