anonymous
  • anonymous
for the seesaw depicted in the diagram, which of the following will happen? A. The seesaw will rotate clockwise B. The seesaw will rotate counterclockwise
Physics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
We can determine this by finding the sum of the moments of the system with respect to the origin.\[\huge \sum_i^n \text{M}_{o_i}=\sum_i^n \vec{\text{F}}_i \times \vec{r}_i\]
anonymous
  • anonymous
We need to keep in mind that we must include the direction of the moment in order to find the net moment about the origin/fulcrum.

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anonymous
  • anonymous
If we establish the convention that counter-clockwise is positive, then the moment due to the force to the left of the fulcrum is positive and the moment due to the force on the right is positive. If the net moment is positive, then it is counter-clockwise. If it is negative, it is clockwise.
anonymous
  • anonymous
I see that you have bumped this question, so I'll try to break it down a little bit more. In order to see how the fulcrum/see saw will rotate, we have to observe the moment or torque (they're synonymous in this case) produced about the fulcrum. The equation I posted above is the equation to find the net torque/moment about the fulcrum (the point at which the seesaw rotates). In our case, this formula that looks complex, actually is really simple and can be reduced as the following:\[\huge \sum \text{M}_o=(\text{F}_{\perp1}*r_1)+(\text{F}_{\perp2}*r_2)\]
anonymous
  • anonymous
The forces are simply the weights of the boxes! Recall that \[\text{Weight}=mg\]\(r\) is simply the radius from the fulcrum to the box. You're given all these values, which makes this problem a simple plug and chug to find your answer! Next, we have to include signs. And in order to do so, we must state a convention of what is positive and what is negative. Contrary to forces, moments/torques do not have a horizontal or vertical positive convention. Instead, we use clockwise and counter-clockwise to convey what's positive/negative. How do we know which is which? Here's the cool part: we get to choose! It's a convention and no matter if we choose counter-clockwise to be positive or clockwise to be positive, we will end up with the same answer in the end (signs will be different, but conceptually the answer is the same). Now let's look at a diagram of what will happen.|dw:1449287514302:dw| If we push down on the left side, we see that the lever will go down on that side, and therefore the torque being produced is counter-clockwise. On the opposite side, the torque produced is clockwise. So which one's positive? Again, we get to choose! So let's choose that counter-clockwise is positive. Therefore, the left torque is positive and the right torque is negative! Knowing this, our equation finally becomes: \[\huge \sum \text{M}_o=(\text{F}_{\perp1}*r_1)\color{red}{-}(\text{F}_{\perp2}*r_2)\] Notice the minus instead of the plus. If our net torque comes out to be positive, that means that, like we stated in our convention, the seesaw will rotate counter-clockwise. If it comes out to be negative, then it is clockwise. If you have any questions, please speak up and let me know!

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