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Physics Lab Report - CENTRIPETAL FORCE
General College Physics I (PHYS 1441)
The University of Texas at Arlington
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Introduction:
Centripetal force is the required force to keep any object in accelerated motion within a curved path. This force is directed towards the center of path’s curvature and depends on the radius constant speed, and mass from the path’s center. Within this lab the role in circular motion of radius,mass and centripetal force is tested in three different conditions speed is then obtained from the average time it takes in completing a complete circle.
Objective
Verify the relationship played by the variables within the equation Fc = m( V 2 / r) as we keep the value of two of these variables constant varying the third and measuring the fourth variable.
Theory An object with mass (m) moving along a circle of radius ( r ) with continuous speed (v) is allowed to accelerate regardless of the constant vector of velocity, because the direction of the vectors change continuously. Instantaneous acceleration is referred to the acceleration of a moving body at any given time. In a circle the direction of the instantaneous acceleration unit vector, points towards the center. Through Ac = v 2 /r we are then able to calculate the magnitude of the instantaneous acceleration. The subscript c derives from referring the acceleration directed towards the center as centripetal force. Within Fc=m(V 2 / r), we are able to see the that F=ma indicates the need of a net force required to produce an acceleration. In the experiment the spinning mass will be the object going under the circular motion. Properly setting the apparatus, will allow for the spring connecting the spinning mass and the rotating shaft, to provide the force. By using, v = r/T it is easier to obtain the speed of the 2휋 spinning mass. T, refers to the time it takes to complete one revolution around.
In this experiment, the relation of Newton’s Second Law and of Fc = m( V 2 / r) will be verified. In order to accomplish this two of these variables will remain constant as we vary the third and measure the fourth. By the conceptual realization and with the combination of Fc=m(V 2 / r) and v = 2휋r/T for the period of T, we are able to infer the effect on T from the variation of one variable. Graphs for part A:
Graphs for part B:
❏ Spin the rotating shaft. Notice that as it spins faster and faster, the radius of the circle on which the spinning mass moved will get larger and larger. If the base begins to rock try adjusting the counter weight on the horizontal arm to stop the rocking. ❏ Adjust the speed of the rotation until the spinning mass moves in a circular path, passing directly over the pointer. ❏ Maintain this speed. A good method to do this is by alternately using your index and middle fingers to spin the shaft as if they were walking on a treadmill. ❏ While maintaining this motion, measure T by clicking Start and allow 10 to 15 rotations to be recorded. Then click Stop, after which the spinning may be ceased. ❏ Located at the bottom of the Table window is the mean value for the period, T. If the standard deviation value displayed in the table is greater than .01s, redo the measurement. ❏ Record the mean value in Data Table C ❏ Calculate the value for the speed. Remember to use the current radius value, r. Record this value. Changing the Radius, r ❏ Change the Radius by 1 cm, using the dimples present on top of the rod.
Data Sheet C: Starting value of r: .14 ± .002 m Constant value of Fc : 5 ± 2 N Constant value of m: .401 ± .001 kg Expected Trend for T as Force Increases: T should increase. Table for part C:
r (m)
T
(Mean value) (s)
Speed v ± Sv (m/s)
v 2 ± S(v 2 ) (m 2 /s 2 )
.14 .5938 1 ± .0701 2 ±.
.15 .6172 1 ± .0629 2 ±.
.16 .6440 1 ± .0679 2 ±.
.17 .6508 1 ± .0697 2 ±.
.18 .6701 1 ± .0688 2 ±.
The slope of the straight line for v 2 vs. r = 15 ± 2 (m 2 /m ) Calculated value of Fc /m = 14 ± 147 (N/kg) Percent error of two values : 6 % Graph for part C:
Summary: Overall, the lab was as a success in verifying the relationship within the equation
Physics Lab Report - CENTRIPETAL FORCE
Course: General College Physics I (PHYS 1441)
University: The University of Texas at Arlington
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