Lab Report 5_PHYS1100

docx

School

Brooklyn College, CUNY *

*We aren’t endorsed by this school

Course

1100

Subject

Mechanical Engineering

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by CountNarwhal3921

Lab Report 5 Circular Motion October 3, 2023

Objectives The goal of this three-part virtual lab was to help us understand concepts relating to circular motion and to use different formulas to find the necessary values. In the first exercise, we had to calculate the period (T) of a revolution (total time divided by number of revolutions) and the frequency (1/T) at different speeds. The second exercise focused on the relationship of the centripetal force to the mass of a rotating object, the radius of the circular path and the speed. First, six different random speeds were applied to a rotating object, and this speed was later calculated using the centripetal force, radius, and mass. A linear Fc vs. v^2 graph was constructed from the results. Next, we observed how the centripetal force changed as the mass of the rotating object was increased, and their relationship was shown on a graph (Fc vs. m). Similarly, the radius was also increased to see its effect on the centripetal force, and a third graph (Fc vs. 1/r) was made. For the last part of the lab, a video was watched where the radius of the rotating object and the number of cycles was kept constant, but the mass of the object was changed. The information from the video helped determine the period for each revolution, calculate the centripetal force and create a Fc vs. 1/T graph. Tabulated Results/Data Sheets B: Circular Force Lab Part 1: Dependence of the centripetal force ( F c ) on the speed of rotation ( v ) at a constant radius m = 1.5 kg r = 1.5 m Table 1 Random speed # Time for 5 cycles ( s ) Period, T ( s ) ω ( rad / s ) random speed v ( m / s ) F C ( N ) 1 5.66 1.13 5.55 8.3 68.59 2 11.24 2.248 2.795 4.2 17.48 3 9.38 1.88 3.35 5.0 24.73 4 13.08 2.616 2.402 3.6 12.86 5 6.78 1.36 4.63 6.9 47.55 6 6.52 1.30 4.82 7.2 51.76 Slope of F C versus v 2 (and give units!): 1.0 kg/m Expected slope (in algebraic form): mass / radius or m/r Numerical, expected value of slope: 1.0 kg/m Percentage difference between expected and measured slope values: 0% Part 2: Dependence of the centripetal force ( F c ) on the mass of rotating object ( m ) at a constant radius

Random speed # 6 and radius, r = 1.5 m . Table 2 Mass (kg) Time for 5 cycles ( s ) Period, T (s) ⍵ (rad/s) v (m/s) Fc (N) 1.5 6.48 1.30 4.85 7.2 51.74 1.6 6.48 1.30 4.85 7.2 55.32 1.7 6.50 1.30 4.83 7.2 58.75 1.8 6.60 1.32 4.76 7.2 62.23 1.9 6.58 1.32 4.77 7.2 65.57 2.0 6.46 1.29 4.86 7.2 69.20 Slope of F C versus m (and give units!): 34.34 m/s 2 Expected slope (in algebraic form): (velocity) 2 / radius or v 2 /r Numerical, expected value of slope: 35 m/s 2 Percentage difference between expected and measured slope values: 0.96 % Did the period, T change? Explain: The period, T, did not vary significantly over the 6 trials. The radius remained constant over the trials, which means that the object needed to travel the same amount of distance to complete one revolution. Additionally, as the mass increased, the Fc also increased, so the change in mass did not affect T. Part 3: Dependence of the centripetal force, F c on radius, r for a constant rotating mass, m m = 1.5 kg , and random speed, v # 6 Table 3 r ( m ) Time for 5 cycles ( s ) Period, T (s) ⍵ (rad/s) v (m/s) Fc (N) 0.5 2.16 0.432 14.5 7.2 155.44 1.0 4.34 0.860 7.31 7.2 77.79 1.5 6.46 1.29 4.86 7.2 51.81 2.0 8.74 1.75 3.59 7.2 38.95 Does the period, T change? Explain: The period, T, in this experiment did change significantly over the 4 trials depending on the radius. T is the amount of time it takes for the object to complete one revolution, therefore, it would be expected that with a smaller radius, it would take less time to complete a revolution (because the object is traveling less distance), thereby decreasing T. Slope of graph of F C versus 1/ r (and give units!): 77.683 kg * m 2 / s 2 Expected slope (in algebraic form): mass*(velocity) 2 or mv 2 Numerical, expected value of slope: 78 kg * m 2 / s 2 Percentage difference between expected and measured slope values: 0.055%

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

C: Online video Table 4 r ( m ) Number of cycles Time measured (s) Period, T ( s ) Hanging mass (kg) Fc (N) 0.63 20 10.54 0.527 0.200 1.96 0.63 20 12.09 0.6045 0.150 1.47 0.63 20 14.43 0.722 0.100 0.95 Slope of graph of F C versus 1 / T 2 (and give units!): 0.601 kg*m Expected slope (in algebraic form): (mass * 4π 2 * radius) or m4π 2 r Mass of rotating object, obtained using slope of graph (show calculation): 24 g (calculation shown in calculation section below under Table 4) Calculations

Original Data Sheets

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Graphs

Discussion of Results

In this experiment we worked on measuring the velocity, time, and revolutions of an object on a circular path. In comparing the measured and predicted values, the differences weren’t too great. For example in Table 1, our expected slope of Centripetal Force (Fc) vs. v 2 , was 1.0. Upon inputting our answers to our graph, our measured slope was 1.0 as well, giving us a 0% difference. A reason for this is that our mass (1.5 kg ) and radius (1.5 m ) were unchanged in this portion of the experiment (as shown in the calculations, the slope is equal to m/r). It’s also noticeable that with greater velocities, the periods were measurably shorter. In Table 2, again the difference between the expected and predicted slopes was below 1% at 0.96% difference. In keeping a constant velocity and radius, we saw that a changing mass did not have a great effect on the period and time of one revolution. In Table 3, the percentage difference between our expected and measured slopes was 0.055%, which used a constant velocity and mass, but a varying radius. Finally, in Table 4 we were able to discover from our calculations that by decreasing the mass of the hanging object, the centripetal force decreased and the period and time it took for a full revolution on a set radius, increased. We saw that there was a linear relationship between Fc and 1/T 2 and were able to calculate the weight of the rotating mass using the slope of the graph which was equal to m4π 2 r. Since this was an entirely virtual lab, our sources of error were relatively limited. Even still, our main possible source of error was based on how accurately we could start and stop the timer. If we hesitated or missed the trackpad of our laptop that could have affected our results. We tried to mitigate this error by having the same person doing the stopping and starting each time. In terms of our initial certificate that we got, there were larger errors in parts 1-3 and parts 7. This was due in part to not realizing that the topic that we needed to calculate for was being changed, or by misreading the instructions and therefore using the wrong formula/calculations and inputting the incorrect result. We managed to fix this error in the middle of the experiment by carefully reading what the directions told us. Conclusion In this virtual lab experiment, we tested centripetal force and circular motion with different variables changed; such as changing the speeds, radii, or masses of the rotating mass. In the initial portion of our experiment, which experimented with circular motion, we were shown how to measure the period correctly and then calculate for it. Much of the beginning of the experiment did not give us tabulated results, rather gave us an idea of how certain calculations are done, for example how to calculate for RPM, period, and velocity. In this experiment we saw that if we increase the mass of an object, the angular velocity of the rotating mass will decrease. Also if we increase the radius, the angular velocity will also decrease, and vice versa. Since the lab was entirely virtual, the amount of errors that we could make in performing the procedures was limited to misreading the instructions or by inconsistently stopping and starting the timer. It is also noted that with smaller radii, and a consistent mass, the centripetal force (Fc) and angular velocity will increase. Since the angular velocity increased, the time it takes for one revolution, the period, is shorter. Like with changing the radius, increasing the speed led to shorter periods

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

and greater centripetal forces. Changing the mass had very little effect on the angular velocity and period, and only a small change to the centripetal force was noticed. Post-Lab Questions 1. In Part C, what provides the centripetal force on the whirling mass? The hanging mass of 200g is what is providing the centripetal force through the tension of the string. Without the mass, the whirling mass won’t stay in circular motion, and would move in a tangent along the proposed circular path. 2. How is it possible that a body moves at a constant speed and is still in accelerating motion? In the example of spinning a mass on a string, an object does just this. Velocity is a vector, and so is acceleration. The speed can be constant but since the object has a direction, spinning around, it is accelerating. For example, acceleration measures the change in velocity over time, otherwise known as the change in speed or direction, or both, over time. Since the speed is constant, and the direction of an object being spun around is changing, the object is accelerating while still keeping a constant speed. 3. When a car is going around a circular track with constant speed, what provides the centripetal force necessary for circular motion? The centripetal force needed for circular motion is the force that would drag the car towards the center of the track. This force is the force of friction on the turned tires. The sideways force of this friction, because the wheels are turned provides the centripetal force. If there were no friction, the car would move tangentially and would simply travel in a straight line, regardless of if the wheels are turned. If a car slips on a slippery road, there is still some friction, and this would cause the car to “spin out” and travel in a circular path. This is the same idea as if a car tried to turn on an icy circular track. Because there would be no friction, it would just travel in a tangent relative to the circle.