# physics question on torque for those who like to solve problems **URL:** \ **Category:** Factual Questions\ **Created:** [November 11, 2015, 4:17pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295 "2015-11-11T16:17:08Z")\ **Posts on this page:** 12\ **Page:** 1
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [November 11, 2015, 4:17pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/1 "2015-11-11T16:17:08Z")
I am presenting a solution to a physics problem to some high school students in my robotics club. I haven’t taught physics for a while so I wanted to check with straight dope experts to make sure I did the math right. Here is the problem. A mechanical arm supports 4 kg of water which is located a distance (d) from the fulcrum. According to the motor specs. the stall torque is 198.26 oz-in. I converted this to 221 Nm. Is this correct? Using torque = Fd found that without any mechanical advantage, the max distance the arm can be to lift the water is 35 cm. Is this correct? Assume a gear ratio of 10:1, the arm can now be 350 cm long. Is this correct? Thank you in advance straight dope braniacs!! ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 11, 2015, 4:57pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/2 "2015-11-11T16:57:39Z")
Your figure of 221 Nm can’t be correct, and I’m not sure how you got it, since a newton is more than an ounce, and a meter is much more than an inch. I get 1.4 Nm, with enough zeroes after the 1.4 that I suspect that that’s the motor’s actual rating, and that 198.26 is an overly-precise conversion. You apparently didn’t use your figure of 221 Nm in the next step, but instead somehow re-did the conversions, because 35 cm is the length of arm to get 1.4 Nm from a 4 newton force. But that’s still not right, because you have 4 kg of water, not 4 N. The weight of 4 kg of water will be nearly 40 N (more precisely, 39.2 N), so your actual answer will be closer to 3.5 cm. And that’s also assuming that the arm is perfectly horizontal, because torque isn’t just force times distance, it’s force times distance times the sine of the angle between them. Without more detail, I don’t know if this is what you want or not. ---
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [November 11, 2015, 5:21pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/3 "2015-11-11T17:21:20Z")
> [@Chronos](#): > > Your figure of 221 Nm can’t be correct, and I’m not sure how you got it, since a newton is more than an ounce, and a meter is much more than an inch. I get 1.4 Nm, with enough zeroes after the 1.4 that I suspect that that’s the motor’s actual rating, and that 198.26 is an overly-precise conversion. > > You apparently didn’t use your figure of 221 Nm in the next step, but instead somehow re-did the conversions, because 35 cm is the length of arm to get 1.4 Nm from a 4 newton force. But that’s still not right, because you have 4 kg of water, not 4 N. The weight of 4 kg of water will be nearly 40 N (more precisely, 39.2 N), so your actual answer will be closer to 3.5 cm. > > And that’s also assuming that the arm is perfectly horizontal, because torque isn’t just force times distance, it’s force times distance times the sine of the angle between them. Without more detail, I don’t know if this is what you want or not. Oops, you’re right, I wrote down the wrong number. It isn’t 221 Nm. It’s 1.4 Nm. That’s the number I used for the rest of the solution. ---
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [November 11, 2015, 5:53pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/4 "2015-11-11T17:53:16Z")
> [@Chronos](#): > > Your figure of 221 Nm can’t be correct, and I’m not sure how you got it, since a newton is more than an ounce, and a meter is much more than an inch. I get 1.4 Nm, with enough zeroes after the 1.4 that I suspect that that’s the motor’s actual rating, and that 198.26 is an overly-precise conversion. > > You apparently didn’t use your figure of 221 Nm in the next step, but instead somehow re-did the conversions, because 35 cm is the length of arm to get 1.4 Nm from a 4 newton force. But that’s still not right, because you have 4 kg of water, not 4 N. The weight of 4 kg of water will be nearly 40 N (more precisely, 39.2 N), so your actual answer will be closer to 3.5 cm. > > And that’s also assuming that the arm is perfectly horizontal, because torque isn’t just force times distance, it’s force times distance times the sine of the angle between them. Without more detail, I don’t know if this is what you want or not. And crap, you’re right about the 3.5 cm. I feel really dumb. I converted 0.035 m to 35 cm. Now, I’m probably wrong on the mechanical advantage part at the end. I think I would want a gear ratio of 10:1 to get to increase the length of the arm 10X. ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [November 11, 2015, 6:39pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/5 "2015-11-11T18:39:25Z")
You’re still being imprecise. Which I suspect is due to hurry. One can’t successfully teach anything in a hurry. The inevitable mistakes really buffalo the students. Is the 10:1 gear ratio you’re thinking of from motor:lever arm or from lever arm:motor? Bottom line: If you want 10x the lever arm you’ll need the motor shaft to turn 10x the revs of the lever arm shaft. You’ll also need some margin. If the motor stalls at 1.4 Nm you’ll want to plan to extract no more than ballpark 90% of that, so 1.25 Nm. Otherwise operation becomes slow and erratic. You’ll also need to allow for friction losses in any gear train. WAG another 10% for that, plus a small additional factor for each additional gear in the train above two. And another factor for whether you’re using high quality, or cheap-ass, or even homemade gears. But that’s all engineering, not physics. ---
**Author:** ![Ornery\_Bob](https://avatars.discourse-cdn.com/v4/letter/o/da6949/32.png) [@Ornery\_Bob](https://boards.straightdope.com/u/Ornery_Bob)\ **Post date:** [November 11, 2015, 7:57pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/6 "2015-11-11T19:57:12Z")
This whole thing becomes childishly simple if you leave the torque in English units. 4Kg is 141 oz. The motor is putting out 198 oz-in so 198/141= 1.4 so the lever arm can be 1.4 inches long. Of course, as others have said, you don’t want to ever stall the motor, so you need fudge factors. In real life, you would simply figure the torque required at the speed you want and buy an appropriate gearmotor. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 11, 2015, 8:25pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/7 "2015-11-11T20:25:24Z")
> [@](#): > > Quoth **LSLGuy** : > > And another factor for whether you’re using high quality, or cheap-ass, or even homemade gears. I would have guessed that, for a robotics club, he’s using Lego gears, which are pretty high-quality for plastic, except that 10:1 isn’t an easy gear ratio to get from those (the largest and smallest standard gears are 40 teeth and 8). ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [November 11, 2015, 9:07pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/8 "2015-11-11T21:07:28Z")
40 and 8 gives us 5:1, so all we need are a shaft and a 2:1 pair and we’re rockin’ and rollin’. Or for most homebrew robots, a stallin’ and a sputterin’ 😃 ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [November 11, 2015, 9:49pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/9 "2015-11-11T21:49:49Z")
> [@LSLGuy](#): > > One can’t successfully teach anything in a hurry. The inevitable mistakes really buffalo the students. +1 Well put. ---
**Author:** ![blood63](https://avatars.discourse-cdn.com/v4/letter/b/97f17d/32.png) [@blood63](https://boards.straightdope.com/u/blood63)\ **Post date:** [November 12, 2015, 12:52am UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/10 "2015-11-12T00:52:30Z")
> [@Chronos](#): > > I would have guessed that, for a robotics club, he’s using Lego gears, which are pretty high-quality for plastic, except that 10:1 isn’t an easy gear ratio to get from those (the largest and smallest standard gears are 40 teeth and 8). Not at all. We build big robots, with elaborate drive trains etc. and compete in FIRST competitions. My son just joined. There is a lot to learn. Thanks for everyone’s help. ---
**Author:** ![Isilder](https://avatars.discourse-cdn.com/v4/letter/i/cc9497/32.png) [@Isilder](https://boards.straightdope.com/u/Isilder)\ **Post date:** [November 12, 2015, 12:03pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/11 "2015-11-12T12:03:54Z")
> [@Chronos](#): > > And that’s also assuming that the arm is perfectly horizontal, because torque isn’t just force times distance, it’s force times distance times the sine of the angle between them. Without more detail, I don’t know if this is what you want or not. You could take it that the arm will move through horizontal , and horizontal arm is where the motor must produce most torque, as moving the water horizontally takes (toward) 0 force… ( a speed of a nanometer a millenia is implied to be sufficient to prevent motor stalling… Not in practice but the OP didn’t specificy a minimum speed… ) ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 12, 2015, 2:44pm UTC](https://boards.straightdope.com/t/physics-question-on-torque-for-those-who-like-to-solve-problems/737295/12 "2015-11-12T14:44:54Z")
Of course, if you can get it moving enough beforehand, you could coast through the stall angle.