# physics problem: a yoyo in a car **URL:** \ **Category:** Factual Questions\ **Created:** [February 24, 2005, 3:48am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641 "2005-02-24T03:48:43Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Br\_er\_Lapin](https://avatars.discourse-cdn.com/v4/letter/b/e79b87/32.png) [@Br\_er\_Lapin](https://boards.straightdope.com/u/Br_er_Lapin)\ **Post date:** [February 24, 2005, 3:48am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/1 "2005-02-24T03:48:43Z")
So, I had my first test in my physics class today. On the test, there was an extra credit problem. The problem was this: > [@](#): > > A yoyo in a car is dangling at an 80\* angle to the vertical axis. Find the acceleration of the car. I left it blank, having absolutely no idea how to go about solving such a thing, and I’m becoming more and more convinced that it’s impossible. Someone please help me. I, was well as my lab partner, will go crazy if forced to wait until Monday to have it explained. [sub](disclaimer: I promise I’m not trying to get homework help, and the above detailed situation is entirely true.)[/sub] ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [February 24, 2005, 3:55am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/2 "2005-02-24T03:55:12Z")
Let me ask you this: what causes the yo-yo to dangle at an angle instead of being vertical? ---
**Author:** ![Br\_er\_Lapin](https://avatars.discourse-cdn.com/v4/letter/b/e79b87/32.png) [@Br\_er\_Lapin](https://boards.straightdope.com/u/Br_er_Lapin)\ **Post date:** [February 24, 2005, 3:59am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/3 "2005-02-24T03:59:13Z")
> [@scr4](#): > > Let me ask you this: what causes the yo-yo to dangle at an angle instead of being vertical? Well, I imagine that would be because…the car is accelerating… and… um… I don’t know. We didn’t discuss situations like these, which is why I’m so flustered and confused. ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [February 24, 2005, 4:25am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/4 "2005-02-24T04:25:15Z")
This may have some ideas for you [Tension, Free Body Diagrams and Speed](http://physics.about.com/cs/freebodydiagrams/a/conicalpendulum.htm) > [@](#): > > A 1kg mass hangs from a fixed point on a 1m long, light, inextensible, string. It has a velocity v that is entirely horizontal, and so it moves in a horizontal circle. This circle is centered on the vertical line below the point of support, and the string makes an angle of 45 degrees with the vertical at all times. This is known as a conical pendulum. > > a) What is the tension in the string when the mass is moving? > > To find the tension in the string, we look at the free body diagram. When the mass is in circular motion, the net force is exactly horizontal, so the vertical component of the tension must exactly cancel the weight of the mass. > > T sin(45o)=mg > T=14 N > b) Find the speed of the mass. > > The centripetal force is the horizontal component of the tension: > Fc=mv2/R=Tcos(45o)=10N > > As the rope is 1m long, the radius of the circular motion is sin(45o). > > v2=7.1(m/a)2 > v=2.66m/s ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 24, 2005, 4:50am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/5 "2005-02-24T04:50:08Z")
If the yo-yo were hanging at a 45[sup]o[/sup] angle, instead, what do you suppose that says about the relationship of the acceleration due to gravity and the acceleration of the vehicle? Think in terms of a vector diagram. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [February 24, 2005, 5:14am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/6 "2005-02-24T05:14:35Z")
Another way to think about it is this: if the string is hanging at a constant angle in the car, then the yo-yo must have the same acceleration as the car, right? Now draw a free-body diagram. The only forces acting on the yo-yo are the tension in the string and gravity. You can figure out what the tension is by the fact that it cancels out gravity (since the yo-yo isn’t accelerating up or down)… and you should be able to take it from there. Eighty degrees from the vertical? Damn, that car is pulling some serious g’s. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [February 24, 2005, 9:22am UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/7 "2005-02-24T09:22:32Z")
Sorry, I meant to get back to this thread sooner… The key to understanding the question is that gravity is indistinguishable from acceleration. A 1kg object exerts 9.8 N of force on the floor because gravitational acceleration of 9.8 m/s/s is acting on the object. Now, if that 1kg objects is in the car, and the car is accelerating, what are the forces on that object? If you know the effect of the forces (i.e. causes the yo-yo to dangle at 80 degrees), what can you say about those forces? ---
**Author:** ![InvidiousCourgette](https://avatars.discourse-cdn.com/v4/letter/i/e47c2d/32.png) [@InvidiousCourgette](https://boards.straightdope.com/u/InvidiousCourgette)\ **Post date:** [February 24, 2005, 12:37pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/8 "2005-02-24T12:37:22Z")
> [@MikeS](#): > > Eighty degrees from the vertical? Damn, that car is pulling some serious g’s. My thoughts as well. I always found that such questions produced “real world” answers. Unless I got my solution wrong, this one fails that test. ---
**Author:** ![Shade](https://avatars.discourse-cdn.com/v4/letter/s/2bfe46/32.png) [@Shade](https://boards.straightdope.com/u/Shade)\ **Post date:** [February 24, 2005, 2:38pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/9 "2005-02-24T14:38:03Z")
> [@InvidiousCourgette](#): > > My thoughts as well. I always found that such questions produced “real world” answers. Unless I got my solution wrong, this one fails that test. I first read it as ‘80 degrees to the horizontal’; in fact, it seems likely that was the original intent and someone typo’ed somewhere. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 24, 2005, 4:01pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/10 "2005-02-24T16:01:11Z")
> [@InvidiousCourgette](#): > > My thoughts as well. I always found that such questions produced “real world” answers. Unless I got my solution wrong, this one fails that test. Yeah, that’s a helluva car, innit? 😃 ---
**Author:** ![Finagle](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@Finagle](https://boards.straightdope.com/u/Finagle)\ **Post date:** [February 24, 2005, 4:10pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/11 "2005-02-24T16:10:56Z")
"A yoyo in a car is dangling at an 80\* angle to the vertical axis. Find the acceleration of the car. " Acceleration is zero. The car’s parked on a hill. A very steep hill. ---
**Author:** ![Mollie\_Magill](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mollie_magill/32/20882_2.png) [@Mollie\_Magill](https://boards.straightdope.com/u/Mollie_Magill)\ **Post date:** [February 24, 2005, 4:22pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/12 "2005-02-24T16:22:52Z")
To solve you will need to know your trig. ```auto |\ |y\ 9| \ .| \ 2| \ n| \ | \ | _______ \ x ``` Solve for x where angle y=80 degrees. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [February 24, 2005, 4:31pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/13 "2005-02-24T16:31:59Z")
> [@Maus Magill](#): > > Solve for x where angle y=80 degrees. And if the car is on Earth, use 9.8 instead of 9.2 N. 😉 ---
**Author:** ![Finagle](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@Finagle](https://boards.straightdope.com/u/Finagle)\ **Post date:** [February 24, 2005, 4:43pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/14 "2005-02-24T16:43:05Z")
> [@Q.E.D.](#): > > Yeah, that’s a helluva car, innit? 😃 Well, it could be a car rapidly decelerating due to a collision. Which, when one thinks of it, would be one of the natural consequences of playing with a yoyo while you’re driving. If this is the case, you’d have to change the sign on the solution. ---
**Author:** ![Munch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/munch/32/5281_2.png) [@Munch](https://boards.straightdope.com/u/Munch)\ **Post date:** [February 24, 2005, 4:50pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/15 "2005-02-24T16:50:38Z")
> [@Finagle](#): > > Acceleration is zero. The car’s parked on a hill. A very steep hill. B’rer, if you get a chance, I’d like to know how your professor would have graded (pun intended) an answer that explains the yo-yo’s angle as a result of being on a hill. That’s a good answer, Finagle. ---
**Author:** ![Br\_er\_Lapin](https://avatars.discourse-cdn.com/v4/letter/b/e79b87/32.png) [@Br\_er\_Lapin](https://boards.straightdope.com/u/Br_er_Lapin)\ **Post date:** [February 24, 2005, 10:13pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/16 "2005-02-24T22:13:48Z")
> [@](#): > > I first read it as ‘80 degrees to the horizontal’; in fact, it seems likely that was the original intent and someone typo’ed somewhere. There was a bit of a disagreement about the exact problem… I swear it was 40\* with no axis mentioned, but I posted the problem as she remembered it because I never know what’s going on and she generally does. For my purposes, the numbers aren’t as important as “how the hell does this work?” > [@Maus Magill](#): > > Solve for x where angle y=80 degrees. 55.6? :dubious: You guys are killing me here. Except **Finagle** …that’s a hell of an answer. I’ll try to slip it in on Monday if the opportunity presents itself. ---
**Author:** ![FatBaldGuy](https://avatars.discourse-cdn.com/v4/letter/f/ecd19e/32.png) [@FatBaldGuy](https://boards.straightdope.com/u/FatBaldGuy)\ **Post date:** [February 24, 2005, 10:18pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/17 "2005-02-24T22:18:53Z")
I’d just like to jump in here to observe that this thread is a perfect example of the rationale behind the “Don’t ask us to do your homework for you” policy on the board. I love how everyone has jumped in here not giving the direct answer to the problem but giving helpful hints to get the OP thinking in the right direction. This is the way that this kind of question should be handled. ---
**Author:** ![Mycroft\_H](https://avatars.discourse-cdn.com/v4/letter/m/898d66/32.png) [@Mycroft\_H](https://boards.straightdope.com/u/Mycroft_H)\ **Post date:** [February 24, 2005, 10:31pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/18 "2005-02-24T22:31:16Z")
[QUOTE=Bre’r Lappin] 55.6? :dubious: [QUOTE] I don’t believe that’s correct, but I will defer to the true mathematicians/physicists. Remember the Sine = opposite/hypotenuse, Tangent = opposite/adjacent rules. (Hint, only one is appropriate.) And the 80° may be incorrect as that wodul be almost straight back, but once you have the concept figured out (aren’t we nasty 😃 ?) you can recalculate for any angle. ---
**Author:** ![Br\_er\_Lapin](https://avatars.discourse-cdn.com/v4/letter/b/e79b87/32.png) [@Br\_er\_Lapin](https://boards.straightdope.com/u/Br_er_Lapin)\ **Post date:** [February 24, 2005, 10:41pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/19 "2005-02-24T22:41:37Z")
> [@Fat Bald Guy](#): > > I love how everyone has jumped in here not giving the direct answer to the problem but giving helpful hints to get the OP thinking in the right direction. This is the way that this kind of question should be handled. That’s pretty much what I wanted, but I’m now more confused than when I started out. Basically, there’s no way for us to have solved this problem without being geniuses, or reading ahead in the book, because none of this is based off anything we learned so far. I appreciate everyone’s help, and I don’t want to give off the impression that I’m ignoring everyone’s replies and waiting for the answer, I just haven’t a clue what to do with the information you’ve provided. ---
**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:** [February 24, 2005, 10:46pm UTC](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641/20 "2005-02-24T22:46:35Z")
I have to point out that parking the car on a hill won’t work, since the yo-yo would still hang vertically. [Next page](https://boards.straightdope.com/t/physics-problem-a-yoyo-in-a-car/291641.md?page=2)