Name: Thea De Guzman
Title: The Conical Pendulum
Purpose: To test that the model for the centripetal acceleration vector that we developed is accurately
represented by a magnitude of v2/R, as predicted by Newton’s 2nd Law and a direction that is toward the
center.
Apparatus: the equipment used for this lab are stop watch, measuring stick, and a pendulum bob.
Sample Calculations:
sin θ = R/L
aideal = gtanθ
sin θ = 5/107.5
981tan2.67◦ = aideal
θ = 2.67◦
aideal = 45.7
v = 2πR/T
v = 2π(5)/2.1
v = 15.0 cm/s
Finding T
10.5/5
T = 2.1 sec
aexp = v2/R
a. aexp = (15.0)2/5
aexp = 45
Data & Calculations:
R (cm)
Θ
aideal
(prediction)
gtanθ
5
2.67
45.7
10
5.34
91.7
15
8.02
138.2
20
10.7
185.4
25
13.4
233.7
% Error
[ l(45.7 – 45)l / 45.7] * 100 = 1.53%
t (sec)
T (sec)
v (cm/s)
10.5
10.5
10.5
10.3
10.4
2.1
2.1
2.1
2.1
2.1
15.0
30.0
44.9
59.8
74.8
aexp
(actual)
v2/R
45
90
134.4
178.8
223.8
% error
1.53%
1.85%
2.75%
3.56%
4.24%
Summary:
1. Summary
a. The first purpose of the lab was the find a magnitude of v^2/R as predicted by newton’s 2nd law.
First of all, newton’s second law states that the acceleration of a body is parallel and directly
proportional to the net force and inversely proportional to the mass. To accomplish the first
purpose of the lab we first had to figure out the forcing acting on the pendulum bob. These were
Tsin( ) =mac . With these forces we can say sin( ) = R/L. After we were able to find angle theta.
We then used tan( ) to help find the ideal acceleration. We spun the bob around the paper the find
the amount of time it took the bob to spin fully around in 5 seconds. With this data we are able to
find v using sqrt(R)(aideal). Finally the experimental value of a comes from v^2/R. This shows
that the magnitude of v^2/R is true as predicted by Newton’s 2nd law.
b. The second part of the lab was to show that the direction of the acceleration of centripetal force
is towards the center of its circle. To prove this we drew vectors around a circle. Each vector
represents the velocity at a certain point. The difference between two vectors is perpendicular to
the center of the circle. This shows that the direction of acceleration is towards the center of the
paper.
B. Source of Error is always present in lab and there are three types of error which are human error,
systemic error, and assumption error.
Human Error –this may have occurred due to the sheet that may not have been correctly made
and corrected.
Human – this may have occurred when spinning the bob, one might not be able to get it into a
perfect circle
Human – this may have occurred when drawing the vectors the points of v may not be exactly
in center of circle.