Daniel Hanna, Tyler Kolby, Trey Seabrooke, Ryan Partain
Central Net Force Model Lab
Objective: To determine the mathematical and graphical relationship among radius, tension, and speed for an object rotating by a spring.
Procedure:
- Obtain necessary items for lab
- Measure mass of washers making sure you have ten times the mass of a single washer.
- Measure string and mark off at any increments ending up with a final distance being ten times as long as the increment.
- Choose a constant radius to spin apparatus at and increase hanging mass after every trial
- Take clock reading after 20 rotations for every trial.
- Record data and graph.
- Choose constant mass of hanging mass and spin apparatus again changing radius every trial.
- Take a clock reading after 20 rotations for every trial.
- Record data and graph.
Data Table:
Graphs:
V vs. r
V^2 vs. r
V vs. F
V^2 vs. F
Analysis and Conclusion
1. A) The original graphical relationship found for the data was quadratic.
B) We developed our mathematical equation by squaring the velocity (found on our y-axis).
C) The equation developed from our data is from the y=mx+b equation. For the data in the graph of v^2 as the y values and Force of tension as the x values, we developed the equation v^2=(.284r/m)Fnet. With the v^2 vs. radius graph we developed the equation: v^2=(6.652 Fnet/m)r. The units of these graphs can be related through the equation Fnet (or centripetal acceleration)= v^2/r.
D) the generalized equation for the experiment is Fnet=v^2/r.
2. Centripetal force is the force acting upon an object when the object is moving in a circular, continuous direction. The force is directed towards the center of the fixture of the object or the center of the system. For this lab, the centripetal force is directed towards the hand of the student that was holding the tube on the string while the string with a rubber stopper was swinging in a circular, rotational motion around the hand of the student. The equation for centripetal force is as follows: Ac= m(v)^2/ r, or the centripetal acceleration is equal to mass times the velocity squared, all over the radius.
According to Newton's laws of motion, if the forces acting upon an object are balanced, then the object in motion will continue in motion in a linear path. For an object traveling in a circular path, because the acceleration is constantly changing direction, the forces acting upon the object are unbalanced. This allows the object to continue motion in an ever changing directional state.
3. The errors in this experiment were most likely the clock management, the system in place was one student watching the student swinging the weights in the circular motion. The student watching would call "time" when the other student started swinging, this indicated a third student to start a timer. When the first student counts that the second student has swung the rope 20 times in a row, he says "time" again. Because their is no possible way to count for the elapsed time between between when one student notices the 20th spin has swung by, and motioning time is to be stopped, this is the flaw in the experiment.
If the students were to repeat the experiment, the student who was watching and counting the swings of the rope should have their finger readily placed on the timing button to cut down elapsed time and to cut out the middle man as well in this process. All though they limit student participation, the error has been reduced.
