Calculating Force for Mop with 5 ft Pole

[mikeb]

Hello everybody, I have simple problem (simple to you all) that I need the answer to. If I have a mop with a 5 foot long pole, how much force must I put on the pole to get 16 pounds of force on the mop head. One hand will be at the end of the pole and the other hand will be 2 feet from the first hand (mop head is 3 feet below the front hand.) The pole will be at a 45 degree angle from the floor. I would really appreciate it if you could show how you got the answer so I can tinker with it. Also, if the applied force is greater than 16 pound (resulting force?) can you give me an explanation.

Thank You.

 

[HallsofIvy]

The question as you asked it is slightly ambiguous. I assume that you mean "16 pounds of force on the mop head" downward.

Draw a picture: a right triangle with base angle 45 degrees. The vertical side represents the 16 pounds force downward. The hypotenuse represents the force you are exerting along the pole.

Since this is an isosceles triangle, both legs have "length" 16 pounds and, by the Pythagorean theorem, the length 16√(2) pounds. You must exert 15√(2) pounds along the mop handle to get 16 pounds force downward.

This is larger that 16 (about 1.4 times 16= 22.4 pounds) because part of the force goes downward and another (because of the 45 degrees, equal) part pushes the mop along the floor.

 

[mikeb]

Thank you for your reply. The 16 pounds of force must be on the floor so to clean. I assume you are telling me that the person mopping must push down on the pole (22.4 pounds) in order to produce the 16 lbs of force. I am trying to relate to others that a person can not do this effectively over a period of time. Thinking that way, would this be the same a a person bent over holding a 22.4 pound bucket off of the floor? Maybe you have a different analogy demostrating the impossiblity of this task..

Thank you

 

[HallsofIvy]

No, it's not the same thing. If you are holding up a 22.4 pound bucket, you are using only your arm and shoulder muscles. Pressing down on the mop you can use your own weight.

If you are trying to prove that you shouldn't be required to mop the floor, I'm afraid physics won't help you!

 

[mikeb]

Actually, I have invented some cleaning products some years ago. It has been a hard road but we are gaining some momentum now. I always explained the problem to my customer but have never put any scientic fact to it. By no means am I trying to get out of mopping, however, I would like to know how long the average person could consistantly apply a force of 16 pounds on the floor. Because of the body position, the force required etc. are we asking for the impossible.