Force on a fixed object- help settle a debate please

[yzfrocket]

Force on a fixed object-- help settle a debate please!

I was hoping to settle a debate with a friend. He is planning to install a rope climb from the ceiling of his home. The engineers told him that the load rating of the beam that the rope would be affixed to was 300 pounds. He happens to weigh 230 pounds. His concern was that varying pulling strength of individuals would affect the force exerted on the mounting location. In other words, two people of the same weight could exert a different amount of force on the beam that the rope is mounted to while climbing, depending on their strength and how explosively they climb the rope. My thought was that no matter what the strength of the person, they would still not be able to generate more force while hanging, than what their body weight is.

Could anyone set both of us straight? Neither of us have a physics or engineering background.

Thanks in advance.

 

[phinds]

Well think about this: suppose you want to jerk a barbell with enough force to get it 5 feet off the ground, based on your initial jerk --- that is, you are going to basically jerk it at ground level then let go and it should go up 5 feet. Then suppose you want to do exactly the same thing but you want the barbell to go 20 feet in the air. Do you think the two jerks will have the same force?

 

[yzfrocket]

I guess what has me questioning it is that in my scenario, the object generating the force( the person climbing the rope), is not stationary. The difference being, someone that weighs 230 pounds could stand on the floor and dead lift 700 pounds off the floor by pulling, but, that same person couldn't grab a cable overhead and pulled down the equivalent of 700 pounds without being affixed to the floor in some weigh because as soon as they tried to pull more than their body weight, they would merely lift themselves off the ground.

 

[phinds]

Absoultely right, but think about the rope. How strong does the rope have to be if the guy is climbing VERY slowly (basically a dead weight) vs how strong does it have to be if he give such a strong yank that he goes up in the air 5 feet just on the basis of the yank? How about if he gives a yank so hard that he goes up 100 feet?

I realize that thinking of a guy going up 100 feet by yanking on a rope is silly, but that's not the point. The point is that in math/physics it is often very useful to think about what would happen in extremes. The results in extremes are often different from non-extreme only in quantity, not in kind.

 

[KeithPickering]

Your friend is right. The climber's weight is only one of the two forces acting on the rope. The second is the force caused by the upward acceleration of the climber. According to Newton's Second Law

f = m a

Force = Mass x Acceleration

Since the climber isn't static -- he's moving upward on the rope -- this second, additional force must be added to the weight of the climber. Your friend weighs 230 lbs or 105 kg. Hanging from the rope and not moving, his acceleration (for force purposes) is the acceleration due to gravity (9.8 meters per second per second). The force of the hanging friend is then

F = 105 x 9.8
or
F = 1029 Newtons

To that we add the force caused by upward acceleration. Supposing your friend can accelerate from dead stopped into an upward movement of 1 m/s, and he can do that speed change in half a second. (That would be huge, but not impossible for a trained athlete). His acceleration would be 1 / .5 = 2 meters per second per second. His mass would be unchanged at 105, so the force from upward acceleration would be

F = 105 x 2 = 210 Newtons

and the total force on the rope (and the beam) would be 1029 + 210 = 1239 Newtons, which is 279 lbs.

If the beam is rated for 300, you may be on thin ice.

 

[SteamKing]

Just like weightlifters can't lift more than their own weight.

 

[sophiecentaur]

The biggest possible load would be the result of when a fall is arrested. The force involved would depend upon the modulus of the rope used and the time to break the fall (impulse = force times time). Pretty difficult to ascertain but the required support strength could need to be something up to the breaking stress of the rope, depending upon the maximum distance of a possible fall. Get some steel put in.

 

[nasu]

Just like weightlifters can't lift more than their own weight.

You mean that they CANNOT? Or is a typo?

They surely can. It's enough to look at some weightlifting results.
Lifting twice their weight is quite common.

 

[BruceW]

phinds has the right idea. Although I'm not sure his explanation was the simplest :) hehe, let me give another extreme: Suppose that the rope is right on the limit of breaking, what will you do? If it were me on the rope, I would be moving as slowly as possible. I would not want to cause any extra tension on the rope than is necessary.

Mathematically, as keith says, the tension in the rope is the force required to hold you steady against gravity, plus a force due to acceleration of your body. So if your friend is 230 pounds, and the beam can only take 300 pounds (which is equivalent to the tension in the rope), then I am pretty certain your friend could break the beam, just by using his strength on the rope. Of course, they might be using 300 pounds as a safe limit (i.e. it might actually break at 400 pounds, in which case your friend might be safe).

Also, the idea of a load: most of the time, the load is assumed to be stationary (or moving at steady speed). In which case, the load is equal to the mass of the load, times gravity. But if the object is being accelerated (for example a climber, pulling himself up), then the load is going to be greater. (In the sense that the force on the beam will be greater).

 

[AlephZero]

Of course, they might be using 300 pounds as a safe limit (i.e. it might actually break at 400 pounds, in which case your friend might be safe).

Don't go there, unless you think playing Russian Roulette "might be safe" because you might not fire the bullet!

If the safe limit is 300 lb, then assume something will break at 300 lb, unless you want to die young.

As sophiecentaur said, the biggest loads are likely to be if you slip and stop your fall using the rope. In that case the minimum load on the rope would be about double your body weight, and it could easily be more than that.

Climbing in an average height room, you would have to be fairly unlucky to kill yourself by falling and hitting the floor. On the other hand falling, hitting the floor, and pulling the ceiling down on top of you could be more serious.

 

[crissyb1988]

To that we add the force caused by upward acceleration. Supposing your friend can accelerate from dead stopped into an upward movement of 1 m/s, and he can do that speed change in half a second. (That would be huge, but not impossible for a trained athlete). His acceleration would be 1 / .5 = 2 meters per second per second. His mass would be unchanged at 105, so the force from upward acceleration would be

F = 105 x 2 = 210 Newtons

and the total force on the rope (and the beam) would be 1029 + 210 = 1239 Newtons, which is 279 lbs.

If the beam is rated for 300, you may be on thin ice.

Im just trying to imagine if the climber moved upward at a constant velocity. Just thinking about it conceptually it seems the rope would have a higher tension when moving with const velocity then if the person was stationary. But thinking about it some more it seems logical that constant velocity and stationary state would yield the same tension on the rope. ?!?

 

[BruceW]

good point. I think that if the object's acceleration truly was zero, then the tension is not affected. But in many situations, the acceleration will not be zero. For example, a person climbing a rope might cover roughly the same vertical distance every few seconds, but the person's acceleration will definitely not be zero. Unless you are a super-fit climber, you are going to be pulling yourself up with one arm, then grab further up the rope with your other arm, then repeat the process (with the role of each arm reversed). So your speed is going to go up to some peak value, then go pretty much all the way to zero, then up to peak value and so on. So the speed is going to be changing all the time, so there will be acceleration and deceleration.

If you are a super-fit climber, then maybe your vertical speed would be more steady than an average person's. But it is still not going to be completely steady.

 

[crissyb1988]

good point. I think that if the object's acceleration truly was zero, then the tension is not affected. But in many situations, the acceleration will not be zero. For example, a person climbing a rope might cover roughly the same vertical distance every few seconds, but the person's acceleration will definitely not be zero. Unless you are a super-fit climber, you are going to be pulling yourself up with one arm, then grab further up the rope with your other arm, then repeat the process (with the role of each arm reversed). So your speed is going to go up to some peak value, then go pretty much all the way to zero, then up to peak value and so on. So the speed is going to be changing all the time, so there will be acceleration and deceleration.

If you are a super-fit climber, then maybe your vertical speed would be more steady than an average person's. But it is still not going to be completely steady.

Yes i had the same thoughts after thinking about it some more. I was thinking about how the climber would change arms and each time he would jerk the rope. But if he was smooth in his motion his centre of mass would be moving upwards at a constant velocity. If he had at least one hand on the rope at any given time he would only need to pull down on the rope at exactly his body weight force (because he only has to overcome the acceleration of gravity as he is moving with a constant velocity) . anyway I'm just thinking out aloud here

 

[BruceW]

exactly. That's why I mentioned a 'super-fit' climber, because he/she would be much more able to be smooth in his/her motion.

 

[sophiecentaur]

Even a super-fit climber can sneeze and generate an extra g of acceleration, just when he / she doesn't want it.

 

[BruceW]

yeah, we need some kind of terminator! :)

 

[sophiecentaur]

Or an electric motor?

 

[BruceW]

too boring, haha. Yeah, that is a good point though. From this discussion, I would expect the tension (as a fraction of weight) would vary much less for something like an elevator, compared to a person climbing a rope.