Here are some sample graphs of Fuc vs Vtan and Fuc vs. Angular Velocity

And here's the analysis for the Fuc v. Angular Velocity graph. The trend follows y=ax^2, "y" is the Fuc in Newtons, and x is the angular velocity in rad/s. When you're doing dimensional analysis, 'rad' doesn't really count as a unit, so the unit for angular velocity is basically 1/s. That angular velocity is squared in the equation means that the unit for x^2 is 1/s^2. The units on the left-side of the equation are Newtons, or kg*m/s^2 which means that the units on the constant "a" in the equation have to combine with the units on x^2 to give the same units. So what the heck is kg*m, well, it suggests that you have things that you held constant in the data collection that had units of kg and meters. Your stopper mass didn't change, so that's the kg, and your radius didn't change, that's the meters. When this group multiplies those two things together, they get something darn close to 0.0083. So the general form of their equation would be

Fuc=radius*mass (of thing going in a circle)*angular velocity^2

Fuc=mr(w)^2

For the Vtan version of the lab, x^2 in the equation has the units (m/s)^2 because you're squaring the Vtan, so what are the units on that constant? What would you multiply times the m^2/s^2 (that we get from x^2) in order to get kg*m/s^2, it needs to bring kg into the equation, and get rid of the "squared" on the meters. So kg/m it is then. That makes the general form of that equation

Fuc=m(Vtan)^2/r

So now, get some practice with those two equations by attacking the worksheet you picked up on the way in today!

## No comments:

## Post a Comment