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Balanced Torques

Teacher/Instructor Matt Jones
Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

When the torques on either side of a fulcrum are equal, they are called balanced torques. A common example of balanced torques is two children on a see-saw. If the fulcrum is in the center of the see-saw, the two children must have equal mass for it to be balanced. If the fulcrum is not in the center, their masses must vary to create equal torques.

Balanced torques if you've ever been on a sea-saw you've experienced balanced torques right, if you're on side of the sea-saw and another person is on the other side if you're the same mass, you're applying the same force and you stay balanced. Well if I go to the park with my daughter she's 4, she weighs 40 pounds, I way almost 200 pounds, I'm applying a lot more force on my side than she is. So we're not going to be balanced, how can I ride on a sea-saw with my daughter if I have such a different mass than she does? Well if we remember what a torque is a torque is not just the force that's applied but it's the force that's applied at relative distance from a center okay. And in this case the balance torques, I'm going to talk about that center as being a fulcrum again like the middle of the sea-saw okay. So once I do that now I can figure out how far I need to be from the center to balance with my daughter so that we're about even and we can go up and down easily okay. So you'll see a lot questions where you're asked given 2 points and 2 forces and sometimes for example they'll ask you know they'll give you 1 distance and 2 forces or 2 forces in a distance.

Let's look in an example of that and how you might solve an equation like that okay. So again our sea-saw example, let's say I've got a force over here for 35 Newtons and it's 35 centimeters from the fulcrum and I've got another force over here and it's 30 Newtons but I don't know the distance it is. But notice this is a balanced torque so my sea-saw is even okay, so this times this must equal this times this. Alright so to write that equation we could say the force a times the distance a equals the force b times the distance b. And all we have to do is plug in the numbers, so my force a is 35 Newtons my distance a is 35 centimeters. My force b is 30 Newtons and my distance b I don't know that's what I need for. So I'm just going to leave that distance b.

Okay, so now I need to simplify this equation right so I want to get rid this so I divide this by 30 Newtons and I divide, I'm sorry I'm going to multiply these 2 and get 1,225 Newtons centimeters equals 30 Newtons times the distance okay. Now I need to simplify so I want to get rid of my 30 Newtons dividing this by 30 Newtons and this by 30 Newtons okay and when I do that I get again this cancels with this and this I can simplify into 40.83 my Newtons cancel and I'm just left with centimeters and that's my distance b. So the distance from the center here is 40.83 centimeters okay, which kind of makes sense because it's the greater force over here so this side is going to have to be a little further from the fulcrum to balance that force right. The torque needs to be the same by going out a little further okay.

Let's look at another one, a little bit more complicated. Now let's say we're getting 2 kids on one side of the sea-saw and 1 bigger kid maybe on the other side or 1 kid further out. How can we create a balanced torque with 2 forces on one side and one torque on another? Okay and you see this all the time on the play ground 2 kids on one side and 1 on the other. How do we figure that out okay again we can just add these torques together okay and they're going to equal this torque okay so let's put these 2 on one side and it's going to equal that one okay. So my distance, my first force is 50 centimeters from the center okay I apply the force of 25 Newtons so 50 times 25 plus this one is 10 centimeters from the fulcrum and the force I don't know okay. I need to figure out what the force is of that object okay.

This one I do know I've got a 50 centimeter distance and that's applying a force of 30 Newtons okay, so if I multiply 50 centimeters times 30 Newtons I see that this is 1,500 centimeters per Newton, centimeter Newtons I'm sorry centimeter per this is centimeter Newtons unit for torques okay and on this side I've got again 50 times 25 is 1,250 centimeter Newtons and then this one is the distance 10 centimeters times x the distance that I'm trying to solve for I'm sorry not distance, force I'm trying to solve for. Okay so again if we reduce that I've got this over here I need to get rid of that so I can make it negative and move it over here and subtract 1,250 from 1,500 I get 250. So I've got 10 centimeters times the force equals 250 centimeters Newtons and that can be simplified into 25 Newtons. So this person can be applying 25 Newtons 10 centimeters along with this person and that will equal a 30 Newton force that's 50 centimeters away okay. So this is an example for solving a more complicated balanced torque equation okay but it's simply just adding the different torques together and knowing that they're balanced I can solve it very easily.