Torque....?

Question

Harry is finding it very difficult to muster enough torque to twist a stubborn bolt with a wrench and he wishes he had a length of pipe to place over the wrench handle to increase his leverage. He has no pipe, but he does have some rope. Will torque be increased if he pulls just as hard on a legnth of rope tied to the wrench handle?

a) Yes
b) No

Dr. D. - I appreciate it and am aware. It's an individual who I've come to know alternatively as “Dr. H” aka Tom Flood/Thomas Flood/Floodtl/(Ω)Jack/ (Ω)flood IR/(Ω)floodtl/(Ω)flood/BekkiC/(Ω)Lord Kelvin/The Physics Guy/et al. This person regularly creates new inane persona. He seems to also have some sort of obession with me. Who knows why. To me, it really has become more sad than annoying. I very much appreciate your noticing the difference! :)

The answer is b, no. The twisting force or torque that is applied to the stubborn bolt depends not only on the applied force but also on the legnth of the elver arm upon which the force acts. This relationship can be visualized by recalling your experiences with wrenches or see-saws. The greater the leverage, the greater is the torque. By attaching the rope to his wrench, Harry increases the distance from the bolt to the location of the applied force, but he doesn't increase the lever arm. That's because the lever arm is not the distance from the pivot point (bolt) to the applied force, but rather the distance to the LINE OF ACTION of the applied force. The lever arm is always at right angles to the line of action of the applied force. It is also the shortest distance between the line of action and the pivot point. When Harry uses the rope he does not change the length of the lever arm.

By definition, torque is equal to force multiplied by the lever arm. We can picture torque...

geometrically -- it's twice the area of a particular triangle. Let the altitude of the triangle be the lever arm and the base of the triangle be the force vector. Remember that the area of a triangle is one-half the altitude multiplied by the base. In our case, altitude = lever arm, and base = force. So the area is equivalent to half the torque. If you sketch it out you will see that whether or not the force is applied directly to the wrench handle or from a rope tied to the wrench handle, the area of the triangle formed by the applied force and the pivot point is the same in both cases (same base and altitude), so the torque is the same.

Answer 1

a) A provisional yes. As previous answers have said, it won't help in the obvious setup, pullng lengthwise on a rope tied to the handle. This is kind of a cheat, but it doesn't need any aids like pulleys, and it has worked for me when I wanted to apply a force way beyond my capability to a car bumper, and had only a rope but no pulleys. He ties the rope to the wrench handle and ties the other end of the rope to a tree, cinched up as tight as he can get it. Then he pulls sideways on the middle of the rope. The mechanical advantage is potentially huge.

Answer 2

Dr. H. You might want to know that someone else is using your name and picture.
http://answers.yahoo.com/my/profile;_ylt=AtzVJKUTxR4pZdWEbGPCyDL_xQt.;_ylv=3?show=KFWNBuTXaa

OK now to the question. If he can get the rope in pulley system like diagram 2a in the site below, then it will help him.
http://en.wikipedia.org/wiki/Pulley#How_it_Works

Assuming that he pulls with his maximum force, the torque will only increase if the distance from the bolt increases. A rope cannot accomplish that. But with the pulley system, he can double the force, thus increasing his torque.

*Addendum*
He can use the rope to yank at the wrench, similar to an old lawn mower. With the rope he is able to exert a higher impact force, which will increase the torque momentarily so he can at least crack the nut.

Answer 3

Answer b is correct.
Why didn't anyone simply explain that the rope does not increase the level arm, therefore the torque does not increase. Dr H has created a strange culture of competition from Answerers leading to all kinds of "what ifs". What ever happened to the classic approach of using the given information to solve the physics problem? Sad.

Answer 4

I don't think so, he would have to pull harder. What about the stretch of the rope? Does that effect torque?