Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date performed: 03-29-2017
Statement/ purpose: The purpose of this lab is to find the relationship between centripetal force and angular speed.
Theory/ introduction: This lab attempts to find the relationship between centripetal force and angular speed, or if "Centripetal Force=mr(omega)^2" is true. Centripetal force, or "centripetal force = mass x centripetal acceleration" is found from the force sensor in the middle of the disk while the angular velocity of the disk, or (omega), is found through the photo gate reading the tape attached to the end of the disk.
Three graphs will be made: a Force vs Mass graph, whose slope will give radius times omega squared, Force vs radius graph, whose slope will give mass times omega squared, and Force vs omega graph, whose slope will give mass times radius. Force will always be on the y-axis while the independent variables (mass, radius, or omega) will be on the x-axis.
We calculated our omega using the change in time from the first revolution to the 10th revolution (or 5th revolution for one of the trials). We used the constant radius and constant mass given to find and compare those values to the value of the slope.
Summary: First, the lab was set up like this.
The photo gate captures the angular velocity (the speed at which the disk rotates) by attaching a piece of tape at the end of the disk in order to find the angular velocity. The force sensor is set up in the middle with string attached between the sensor and the mass to find the centripetal force. Three situations were tested, such as collecting period and force data for different masses and fixed speed, same mass at fixed velocity, but different radii, and same mass at constant radius, but different rotational speeds.
 |
| This is the graph used to find force. |
 |
| This graph is used to find time from the 1st revolution to the 5th revolution. |
After gathering the data, we inputted it in three types of graphs: Force vs mass graph, Force vs radius graph, and Force vs omega graph.
Data Tables:
First Situation - Only radius is Varied
Trial 1
Mass = 200g
radius = 22.86cm
power = 3
Force Towards Center = 1.20N
Time at first revolution = 1.428 seconds
Time at 10th revolution = 14.769 seconds
Trial 2
Mass = 200g
radius = 29.24 cm
power = 3
Force Towards Center = 1.47N
Time at first revolution = 1.728 seconds
Time at 10th revolution = 14.88 seconds
Trial 3
Mass = 200g
radius = 34.29 cm
power = 3
Force Towards Center = 1.69 N
Time at first revolution = 13.36 seconds
Time at 5th revolution = 20.1 seconds
Trial 4
Mass = 200g
radius = 46.99 cm
power = 3
Force Towards Center = 1.98 N
Time at first revolution = 1.569 seconds
Time at 10th revolution = 15.6 seconds
Trial 5
Mass = 200g
radius = 58.42 cm
power = 3
Force Towards Center = 2.198N
Time at first revolution = 2.2 seconds
Time at 10th revolution = 17.4 seconds
Second Situation - Only mass is varied
Trial 1
Mass = 100g
radius = 46.99 cm
power = 3
Force Towards Center = 1.052N
Time at first revolution = 2.68 seconds
Time at 10th revolution = 17.02 seconds
Trial 2
Mass = 50g
radius = 46.99cm
power = 3
Force Towards Center = 0.57N
Time at first revolution = 1.54 seconds
Time at 10th revolution = 14.97 seconds
Trial 3
Mass = 300g
radius = 46.99cm
power = 3
Force Towards Center = 2.8N
Time at first revolution = 2.35 seconds
Time at 10th revolution = 16.46 seconds
Third Situation - Only Power (omega) is varied
Trial 1
Mass = 300g
radius = 46.99cm
power = 3.5
Force Towards Center = 5.39N
Time at first revolution = 1.245 seconds
Time at 10th revolution = 11.48 seconds
Trial 2
Mass = 300g
radius = 46.99cm
power = 3.8
Force Towards Center = 5.94 N
Time at first revolution = 1.12 seconds
Time at 10th revolution = 10.747 seconds
Trial 3
Mass = 300g
radius = 46.99cm
power = 4.1
Force Towards Center = 6.43 N
Time at first revolution = 1.46 seconds
Time at 10th revolution = 10.6 seconds
Calculated results:
 |
| Force vs. Radius Graph |
 |
| Force vs. Mass Graph |
 |
| Force vs Power (omega) graph |
Conclusion:
For the Force vs Radius graph, the slope was 2.729, which means the constant mass multiplied by omega squared. This value was less than the calculated value, which was 3.417.
For the Force vs Mass graph, the slope was 8.869, which means the radius multiplied by omega squared. This value was lower compared to our calculated value, which was 10.285.
For the Force vs Power graph, the slope was 1.733, which means the mass multiplied by the radius. This value was close to our calculated value, which was 1.4097.
A significant experimental error that may have affected the experimental data for the Force vs Radius graph and the Force vs Mass graph was the fact that the omega was varied due to the nature of the apparatus. Since the omega was varied, the slope values from the Force vs Radius graph and the Force vs Mass graph do not accurately reflect the actual omega value from the apparatus.
No comments:
Post a Comment