- #1
Valerie Prowse
- 25
- 0
Homework Statement
Hi everyone,
I am doing a lab currently (and it looks like a few other people on here have had similar questions...) and I'm having trouble with one of the concepts. I had to drop a ball from a height and measure the movement with a motion sensor, which was graphed with the Logger Pro program. I had to create a quadratic equation for a few of the curves created in the graph, which the program does automatically. I have attached a picture (hopefully it is clear enough) of the resulting graph and the quadratic equations for 4 of the curves.
Homework Equations
Ax^2 + Bx + C
y = yo + vo(t) - 1/2 g(t)^2
The Attempt at a Solution
The first part of the question is:
"Write a clear interpretation of the meaning of each parameter in this equation."
Which I understand well enough. I do understand how the quadratic equation relates to the kinematic equation y = yo + vo(t) - 1/2 g(t)^2.
A = 0.5g
B = vo
C = yo
What I'm having problems with is the following part:
"From the fit results of each interval, you should notice that the B (parameter) increases as the ball makes a new bounce. If B is interpreted as the initial velocity of the ball for the corresponding bounce, this seems to contradict the observed loss of mechanical energy after each bounce. Provide an explanation of this apparent discrepancy."
I don't understand why, for example in the first interval, B = 15.31, and C = -11.85, yet A seems fairly close to the actual value of 0.5g. Furthermore, I don't understand why B and C are in fact getting larger in the later intervals when C should be 0 (if it really is y0) and B should be getting smaller because the ball, in real life, is losing energy. I think I may have worked out from other posts on here that B and C are not the actual v0 and y0 values (although still not too sure why), but I think I may have worked out how to find them. For example, for the first interval, the bounce actually begins at t = 1.25 and the max height (y = 0.742) is reached at t = 1.65 (this is in the table on the left), so I worked out that, for the bounce to actually begin at t = 0, then max height is reached at t = 0.4, so (t' = t-t0) and y0 = 0:
y = y0 + v0(t) - 1/2g(t)^2
v0 = (y + 1/2g(t)^2 ) / t
v0 = 3.71
Does this make sense? If so, why does the graph tell me that B (or v0) = 15.31? What is the significance of this number? The only thing that I can think of is that y0 = -11.85, literally... so the intercept occurs at y = -11.85 (which obviously is impossible since the ground is at 0m but maybe the computer doesn't know that?) and at this negative intercept
Any help is appreciated! :)