Trask Jeffrey 9/28/2007 Section A PHY 110 Lab 4: Centripetal Force
Purpose: The purpose of this lab is to experimentally demonstrate that centripetal force and acceleration exist by comparing them to the acceleration due to gravity.
Abstract: In order to measure centripetal force, a string with a small weight on one end and a large weight on the other was run through a tube, then spun so that the centripetal force and the weight force equaled the weight force of the larger mass. The process was measured and documented in the data table below. This procedure allowed the effects of centripetal acceleration and force to be observed and defined. Centripetal acceleration is an inward-directed vector quantity perpendicular to the velocity of an object. Centripetal acceleration, unlike other accelerations, is still present even without a change in speed because the direction is constantly changing. Centripetal acceleration is mathematically defined as a c
v2 r
or a c
4 t
2
2
r
. Centripetal force is defined as an inward-directed
external force required to make a body follow a circular path at constant speed. Mathematically, this is expressed as Fc
m 4 t
2 2
r
, which is derived from the centripetal
acceleration equation when force equaling mass times is acceleration added to the equation.
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Data: r (m) T (s) v (m/s)
Fc (Newtons)
4 t
2 2
=total time/revs. =2r/T =m .20 .20 .20 .35 .35 .35 .
velocity v. radius
0.4 0.35 0.3
r
.43 .39 .36 .53 .44 .49
2.92 3.22 3.49 4.15 4.99 4.49
.85 1.04 1.22 .98 1.43 1.15
radius (m)
0.25 0.2 0.15 0.1 0.05 0 0 1 2 3 velocity (m/s) 4 5 6
2
Centripetal Force v. radius
1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 Radius (m) 0.25 0.3 0.35 0.4
Questions: 1. As radius increases, centripetal force stays the same, or at least very similar. This is because the period increases as well as the radius, and the two increases balance each other out. 2. If the velocity increases, the radius increases as well, because the acceleration stays the same, so as per the equation a c keep the equation true. 3. Fc
m 4 t
2 2
Centripetal Force (N)
v2 r
, the radius must increase in order to
r
9 .8
.5
4 t
2 2
.2
t = .63s
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Discussion: Using the percent derivation formula, our answers for the first radius point were determined to be 5.78% off from the weight force of the object, and our secondradius point answers were 20.74% off. An average deviation of 13.26% is not perfect or even preferable, but it is close enough to demonstrate the intended points in the lab.
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