Question to physics teacher, need your answer to it as well

[mysubaruimp]

A. You are trying to open a door that is stuck by pulling on the doorknob in a direction perpendicular to the door. If instead you tie a rope to the doorknob and then pull with the same force, is the torque you exert increased?
1.yes
2.no
A.. The answer is 2. The moment arm is not increased by adding the rope. In other words, rsinf remains the same.

i believe that for the purposes of your question, the answer is correct. but i believe for the real answer, it is wrong.

my question: i believe that the answer should be 1.Yes. i believe this because of the elasticity/stretching of the rope. if the rope you are pulling stretches, arent you exerting more force to pull that same object? For example: say the rope stretches 1" over its 6' length. it would take, say, 1lb of force to stretch that rope 1". after it stretches 1", it will not stretch anymore. if the door takes 50lbs of force to get unstuck, would you not need to apply 51lbs of force to the end of the rope to overcome the stretch in the rope, and to pull the door?

the numbers are all made up, just to have a better view of my argument, but i really do hope that you will respond to this. i hope that i explained it clear enough to understand, i tried my best.

thank you for your time,
-Ryan

 

[krab]

if the rope you are pulling stretches, arent you exerting more force to pull that same object?

No. Force is not "used up". Energy is used up. Let me explain. If the rope is stretchy, you use energy in stretching it (force times distance = work), but the force you apply after it is stretched is transmitted right through. So no; if the rope you are using stretches, you are not exerting more force to pull the same object; you are however, exerting more energy; some of that energy is stored in the stretched rope and can in principle be recovered.

Let's replace the rope with something even more stretchy, like a bungee cord. Pull on it with 50 pounds and it will stretch a lot, but keep a 50 lb. force on it, and that's exactly what the door will "feel". You could also rig up a pulley and apply the force by putting a 50 lb. weight on the end of the bungee. It would make not a whit of difference if the rope is a motorcycle chain or a bungee cord: the 50 lb. weight would ensure that the force at the door knob is 50 lb. in all cases.

 

[Doc Al]

tension in a rope

As long as the same force is used, the torque exerted on the door is the same with or without the rope.

In order to use the rope to pull with 50 lbs of force, that rope must be under 50 lbs of tension. Depending upon its elasticity, it will stretch a bit. But that's how the rope is able to "transmit" the force from your hand to the doorknob. Yes, you will have to pull the rope until it stretches enough to exert 50 lbs of tension, but as soon as you do you will be exerting 50 lbs of force on the door as well.

Imagine that instead of a rope a very stretchy bungee cord were attached to the doorknob. Sure, you may have to pull that thing until it stretches to three times its size to get 50 lbs of tension, but that's still all the force you need.

If I have missed your point, please feel free to rephrase your question and ask again.

Note: Looks like krab beat me to it! And we both used bungee cords as examples.

 

[2Pac]

Well, more force if you account for the weight of the rope.

 

[swansont]

Well, more force if you account for the weight of the rope.

The weight is down, so it's perpendicular to the tension and doesn't contribute to the torque.

 

[Ebolamonk3y]

remember the cross product! the weight is acting in the direction of the torque vector... depending on how you look at it...