A definition of the problem and selection of variables - How do changes in tangential speed affect centripetal acceleration? The independent variable is speed in m/s and the dependent variable is centripetal acceleration in m/s^2. The radius of the circle and the mass of the object being lassoed overhead were controlled for.
The controlling variables - The same object was used for each trial to keep mass constant. The radius of the circle created via spinning the object was held constant by marking 0.60 meters on the string with a marker and ensuring that only this length is spinning.
A developed method for the collection of data - a force sensor was hooked up to the bottom of the string that was spinning, measuring the force of tension pulling the string and the object towards the center. This tension force provides the net force acting on the object which can be divided by the mass of the object aftering weighing. This provides the centripetal acceleration. Someone used a stopwatch to measure the time the object was spinning and they counted the number of times the object completed a full rotation. This provided the angular speed in rotations/s which could be converted to m/s to get the tangential speed by multiplying this by 2(pi)(r), or 3.78 meters/rotation.
The procedure—what you did in the lab. Bullets or sentences are fine; this section should be CONCISE. Focus on the main details: what did you measure, how did you measure it, and how many trials did you do. (No need to describe the lab setup; that’s what your diagram is for).
The controlling variables - The same object was used for each trial to keep mass constant. The radius of the circle created via spinning the object was held constant by marking 0.60 meters on the string with a marker and ensuring that only this length is spinning.
A developed method for the collection of data - a force sensor was hooked up to the bottom of the string that was spinning, measuring the force of tension pulling the string and the object towards the center. This tension force provides the net force acting on the object which can be divided by the mass of the object aftering weighing. This provides the centripetal acceleration. Someone used a stopwatch to measure the time the object was spinning and they counted the number of times the object completed a full rotation. This provided the angular speed in rotations/s which could be converted to m/s to get the tangential speed by multiplying this by 2(pi)(r), or 3.78 meters/rotation.
The procedure—what you did in the lab. Bullets or sentences are fine; this section should be CONCISE. Focus on the main details: what did you measure, how did you measure it, and how many trials did you do. (No need to describe the lab setup; that’s what your diagram is for).
- Centripetal acceleration was measured by finding the tension force using the force sensor hooked up to the bottom of the string of a spinning object. ac=(net force)/(mass)
- The force sensor was plugged into logger pro which provided the tension force of the object over time. The average tension force over these time periods was eyeballed
- Tangential speed was measured by counting the number of rotations completed in the given time frame
- Consistent speed was ensured because the click of a metronome at varying bpms marked the start of a new rotation. The person spinning the object ensured that every rotation lined up for consistent speed.
- 5 trials were conducted
raw data
processed raw
Tangential speed (m/s) = Angular speed (rotations/sec)*2*pi*.60m
0.60m is the radius
0.60m is the radius
Presented data
The linear model, Ac=Av, does not work because a negative acceleration implies a change in direction of net force. The tension net force was only ever pulled downward, thus the acceleration must always be positive, lying above the x axis. This means a simple parabolic model would fit better, as it only covers the upper half of the coordinate plane. A negative speed implies a change in direction of the spinning of the object above the head. In our case, this was from counterclockwise to clockwise.
Simple parabolic model: Ac= Av^2
This implies a x-intercept and y-intercept of (0,0) because when speed is zero, nothing is accelerating forward. No motion of the object is happening so nothing is accelerating
Ex: 120m/s^2 = A(9.05)^2
A = 1.47 1/m.
1/1.47 m = 0.68 m or about 0.60 m RADIUS. Thus, A = 1/r and thus
Centripetal Acceleration (m/s^2) = (velocity)^2/(r)
There is a noticeable gap in the middle of the graph because it is impossible to spin the object at lower speeds above our heads while keeping a steady circle. More force would be necessary.
Evaluating Procedures - There is human error in spinning the object overhead. Timing the spinning in line with the metronome’s click is based off a person’s own internal clock which is not always accurate. There is also the uncertainty of all the data points between (0,0) and the first point that could not be found. There could be more trials which would give a more accurate representation of the natural world’s behavior in our experiment.
Simple parabolic model: Ac= Av^2
This implies a x-intercept and y-intercept of (0,0) because when speed is zero, nothing is accelerating forward. No motion of the object is happening so nothing is accelerating
Ex: 120m/s^2 = A(9.05)^2
A = 1.47 1/m.
1/1.47 m = 0.68 m or about 0.60 m RADIUS. Thus, A = 1/r and thus
Centripetal Acceleration (m/s^2) = (velocity)^2/(r)
There is a noticeable gap in the middle of the graph because it is impossible to spin the object at lower speeds above our heads while keeping a steady circle. More force would be necessary.
Evaluating Procedures - There is human error in spinning the object overhead. Timing the spinning in line with the metronome’s click is based off a person’s own internal clock which is not always accurate. There is also the uncertainty of all the data points between (0,0) and the first point that could not be found. There could be more trials which would give a more accurate representation of the natural world’s behavior in our experiment.