AP Physics Lab
Name_________________
Roller Coasters
Partners_____________________________
1. Beginning ideas - What are my questions?
2. Tests - What did I do?
3. Observations - What did I see?
4. Claims - What can I claim?
5. Evidence - How do I know? What support can I make for these claims?
6. Reading/comparing - How do my ideas compare with other ideas (other students, books,
internet)?
7.
Reflection - How have my ideas changed?
8. Writing: What is the best explanation that explains what I have learned?
Where could this fit in real life?
In our studies?
Background Reading (handed out later)
When a filter is first dropped, the gravitational force is larger than the drag force, so the filter accelerates.
[Newton's Second Law of Motion]
Fy = ma = mg - Fdrag
However, as the filter accelerates and its velocity increases, the drag force also increases, by the
equation:
Fdrag = bvn
where b is the drag coefficient, that is determined by the shape of the object, and n is an exponent that is
also determined by the properties of the object. For most objects moving at low speeds, n is close to 2.
Let’s look at what happens as the object reaches terminal velocity, where acceleration is zero.
Fy = ma = mg - Fdrag = mg – bvn = 0
mg = bvn
Solving for this terminal velocity, vf:
vf = (mg/b)1/n
ln vf = (1/n)ln(mg/b)
ln vf = (1/n)[ln(m) + ln(g) – ln(b)]
For now, let’s let (1/n)[ln(g) – ln(b)] equal a constant, C, since these are all constant values.
Then:
ln vf = (1/n)ln(m) + C
Would it make sense to
1. Set up a data table? for mass, drop height, drop time, and velocity.
2.
3.
4.
5.
6.
7.
On standard Cartesian axes, plot terminal velocity vs mass?
On standard Cartesian axes, plot ln terminal velocity vs ln mass?
What does the slope of the line produced on the ln-ln plot represent?
What does the y-intercept on the log-log plot represent?
Plot fall time vs number of filters and discuss meaning of the graph
Graph terminal velocity vs mass on the computer and use the data analysis capabilities of Excel (or
another program) to plot an appropriate “best fit” curve. Attach the equation.
8. Determine a value for the velocity exponent, n, and compare it to the expected value of 2.
9. Determine a value for the drag coefficient, b.
10. What is the effect of the approximation made regarding the equality of the average and terminal
velocity on your answer for n?
11. What other factors affected your results overall?