Uniform Circular Motion (Lab 7)
Introduction
Uniform circular motion is motion of an object in a circular path with constant speed. The speed is constant not the velocity. Velocity is a vector quantity having both magnitude and direction. In uniform circular motion, the velocity changes uniformly as its direction changes. Change in velocity per time is the definition of acceleration. We know accelerations are produced by forces according to Newton’s Second Law of motion:
F = ma (1)
The purpose of this exercise is to determine the force acting on an object in uniform circular motion.
The magnitude of the acceleration of an object in uniform circular motion is called the centripetal acceleration (ac) and is given by:
XXXXXXXXXX)
where v is the speed of the object and r is the radius of the circle in which it moves. The direction of the acceleration is radially inward, i.e. toward the center of the circle. [Centripetal means “center-seeking”.] The force which causes this acceleration, and therefore is in the same direction, is called centripetal force.
In this exercise, you will make measurements of the time, t, for an object (in this case it is a ladybug) to rotate N (1, 2, 3, …) times around a circle at a constant speed. Since 2r is the circumference of the circle in which the object moves, the total distance traveled is N(2r). Knowing that speed is the distance traveled divided by the time taken, it can be written:
XXXXXXXXXX)
Sketch
The object is attached to a string. The string pulls the object toward the center of the circle in which it moves. Thus, it is the string that provides the centripetal force.
Procedure
Go to the simulation site at Unifrom Circular Motion Intro
1) Select “Intro”
https:
phet.colorado.edu/sims/cheerpj
otation/latest
otation.html?simulation=rotation
2) move the red ladybug along the string to a certain position, for example, the outside circle of the green ring. Take the ruler measuring from the center point of the circle to the red ladybug (the white spot in the middle of the ladybug’s back). This is the radius r.
3) Set the angular speed to 30 (degree/s)
4) have your stopwatch (use your cell phone) ready to measure the time for 5 turns. 360o x 5 = 1800o
5) Click “play” and almost at the same time click your stopwatch
6) When exactly 5 turns, click stop on your stopwatch and record your time.
7) Do this for 5 times. Keep the same radius and angular speed.
Data
Set Data table1
Mass m(kg)
Radius r(m)
Set angle speed ω (degree /s)
0.020
3
30
Time recorded table2
1st trial--
2nd---
3rd--
4th --
5th --
Analysis
Compute the speed of the object using Equation (3), but using ti (from table2, i=1, 2, 3, 4, 5) for t. Compute its acceleration using Equation (2), and then the force that the spring exerts on the object using Equation (1).
Analysis table3
1st trial
2nd trial
3rd trial
4th trial
5th trial
Since we set the angular speed ω = 30 degree /s = XXXXXXXXXXradian/s at the beginning of the simulation, then speed V= r*ω = 3*0.5236 = 1.571m/s – this is our expected V value.
Calculate the V average from table3 (speed row), comparing with expected V value, then calculate the percent e
or (take expected V value as the true value).
% e
or = |true value – exp. value| / true value X 100%
Conclusion
Discuss the e
or