How does speed affect acceleration in a circular motion?
Variables
Independent: speed (rev/s)
Dependent: acceleration
Control: radius of "circle", mass of object
Controlling methods
always measure the length of the string to make sure it is the same length (60cm)
add a paper clip beneath the holding rod- by keeping it at the same position while performing the experiment, we know the radius is constant
use the same hanger for every trial to keep the mass constant
a plastic tube is used for holding to avoid exerting any extra force on the motion sensor
Methods for data collection
use a force sensor to measure an accurate force that can be used to determine the acceleration
Procedure
measure length of string and reset position of paper clip so that (hanger) - (paper clip) = 60cm
hang force sensor on the other end of the string and connect it to a computer
set metronome to a certain bpm, hold on to the tube and sensor, start swinging according to the metronome's tempo
swing until reaching 15s
record revolutions/trial and the force reading on logger pro, repeat above steps
convert rev/s to m/s for speed
find net force/mass for acceleration
Labeled diagram
Recorded raw data
Processed raw data
speed calculation: (rev/s) * 2(pi)(0.6m) = m/s
acceleration calculation: net force/mass = m/s^2
there is a constant mass of 18.8g for the hanger
Presentation of Processed Data
y= 0.00173v^2
slope= curved, the faster speed (either direction), the more acceleration there is
y intercept= (0,0) = when there is no speed, there is no acceleration
Conclusion
The lab shows the relationship between acceleration and speed. From the graph we can see that the points are in positive relationship, but the model is not clear. A linear model can fit, but it cannot explain the slight curvy tilt at the tail of the data. The most sensible take is a power function. By testing the function we found that the exponent is roughly 2, leaving the model to be generalized as a square function. This makes sense because by logics, if we swing the mass in the opposite direction (which gives us negative velocity), the acceleration will still be positive, leading us to the equation of centripetal acceleration, a = v^2/r.
Evaluating Procedures
A weakness of the experiment is the upper and lower limits of tempo. If we have a low bpm, we cannot swing the hanger fast enough for it to move in a horizontal circle, making errors in the data. If we go too fast, it might get dangerous and hurt students in the classroom, leading to a data set with a small range. The accurate matching of tempo might also be an uncertainty as some students are weaker at hitting the beat.
Improving the Investigation
Using an automatic swinger would make tempo matching more accurate and thus giving more accurate results
a swinger could also raise the upper limit of bpm as there is no risk of hitting anyone during the experiment