Circular Motion Lab
Name: Kyle Collins
Lab Partner: Parker Fairchild
Date: 17 December 2014
Purpose: This lab's purpose is to determine the forces acting upon a pendulum in motion.
Theory: Centripetal force is defined by the equation below. Here, centripetal force is equal to the force of tension. It is the force that keeps an object in circular motion moving in the same circular path. The free-body diagram shows the forces and quantities involved in the circular motion of a pendulum bob. This picture shows mg crossed out in the third step of the equation; note that this is the result of zeroing the weight in experimental technique.
Lab Partner: Parker Fairchild
Date: 17 December 2014
Purpose: This lab's purpose is to determine the forces acting upon a pendulum in motion.
Theory: Centripetal force is defined by the equation below. Here, centripetal force is equal to the force of tension. It is the force that keeps an object in circular motion moving in the same circular path. The free-body diagram shows the forces and quantities involved in the circular motion of a pendulum bob. This picture shows mg crossed out in the third step of the equation; note that this is the result of zeroing the weight in experimental technique.
Experimental Technique: A pendulum was first set up. This consisted of a force sensor attached to a rotary motion sensory (used for bearings) with a rod attached to the bottom of the force sensor. Attached to this rod were masses which would swing through a photogate to measure velocity. For this set of ten run-throughs, velocity was the value being varied. Before each swing, the zero button was pressed to effectively remove weight (mg) from the equation, leaving us with tension, or centripetal acceleration. The velocities, along with the constant mass and radius for each run, were recorded in a data table. The tension was measured in Datastudio by finding the point on the force vs. time graph that corresponded with a velocity point from the velocity vs. time graph. This tension was then compared to the tension found from using the equation above, and the percent difference was measured.
Data And Analysis: Since velocity is the value being varied, the radius and mass must stay constant. The radius was set at 45cm, or .45m, and the mas was set at 299.85g, or .29985kg. All data was collected from one run-through. Raw data can be seen below. By using the equation from the theory section, in conjunction with measured masses (column A), velocities (column B), and radii (column C), centripetal force was calculated, shown in column D.
Next came analyzing the force vs. time and velocity vs. time graphs. This involved moving the xy tool over a velocity vs. time data point to find the x-coordinate. Then, the corresponding x-coordinate was selected for the force vs. time graph and the y-coordinate (the measured force from the table above) was recorded as column E. The sign of the number does not matter in this case because the force still acts in the same direction in the real world.
After both the measured and the calculated forces were found, they were compared using a percent difference equation and recorded as column F in the data table.
Conclusion: This experiment successfully showed the intricate relationship between mass, velocity, and radius of a swinging pendulum. The data indicates that as velocity decreased when mass and radius remained constant, the force measured also dropped. Unfortunately, there was a high percentage of error, ranging from seven to thirteen percent. A significant amount of error likely came from the fact that the pendulum was not directly in line with the photogate. This means the pendulum was past the point where force was highest when the force was being measured, which would have skewed results. Another point to note is that the post the entire mechanism was attached to swayed fairly significantly during testing, and this sway was possibly another source of error. Lastly, there were some numbers involved in calculation, like the diameter of the pendulum bob, that the computer rounded up from the actual value, added a small portion of the error percentage.
References: Giancoli, D. (1998). Circular Motion; Gravitation. In Physics: Principles with applications(5th ed.). Upper Saddle River, N.J.: Prentice Hall.
References: Giancoli, D. (1998). Circular Motion; Gravitation. In Physics: Principles with applications(5th ed.). Upper Saddle River, N.J.: Prentice Hall.