1

I'm doing a lab for my AP Physics class where I have to derive an equation for velocity. Trouble is when I do I get a value for velocity that is ±.

$$\pm \sqrt{g\cdot r\cdot cot(\Theta)}$$

In the past, I've ignored the + or - and just taken the +. I wonder though if that is okay? In real life situations, how can you mathematically decide on the + or the -?

Edit:

The lab specifically involves finding the velocity of a toy plane with a fan on the back producing thrust. The plane is attached to a string attached to the ceiling. The setup looks something like this.

I solve for velocity by writing two equations for the tension ($T = \frac{mg}{sin(\Theta)}$ and $T = \frac{m\cdot v^{2}}{r\cdot cos(\Theta))}$) and solving for v.

Zeke Medley
  • 13
  • Could you please show the original equation? – Botond Oct 21 '17 at 21:46
  • Please try to learn $\LaTeX$ first from https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Tengu Oct 21 '17 at 21:47
  • The sign could indicate a direction of a movement. But without more context it is hard to give a definite answer. – quid Oct 21 '17 at 21:54
  • @Botond I added the specifics of the lab. In this case, I assume that it is moving in the positive direction. In that case, what would the minus mean? – Zeke Medley Oct 21 '17 at 22:05
  • It's not 100% sure, but this is what I think: It does mean that the body would have the same Tension if it were moving in the opposite direction. It's like solving the $F=m*\frac{v^2}{r}$ for v. So you should choose the correct sign based on the situation. I suppose your task is to find the magnitude of the velocity, is it? – Botond Oct 21 '17 at 22:39

1 Answers1

1

When you solve the equation for the velocity of the plane you are really solving.. $$ v^2=\vec v \cdot \vec v = gr\cot\theta $$

This gives you the magnitude of $\vec v$ but says nothing about the direction.

Mathematically there is no way to determine this from the equation.

Physically I suspect that you assumed the velocity to be horizontal and perpendicular to the cable.

There is a real ambiguity about the sense of revolution, it could be either clockwise or counter-clockwise depending on initial conditions.

WW1
  • 10,497