PHYSICS
=
Historical Background
Galileo mathematically described the lever, as shown in Figure 10.1. It should be mentioned that
the lever was most probably identified first by Archimedes (287-212 B.C.). This is typical in the
history of science. Ideas develop through the centuries, and even millennia. Science is an
incredible collection and synthesis of ideas from all over the world and through out human
civilizations.
f
F fulcrum Rf = rF
r R
Figure 1. The lever.
The “R’s” are the distance from the fulcrum (lever arms), and the “F’s” are the forces at each end.
For a relatively small force, a large force can be produced. This idea is called leverage. A small
force gains leverage as its distance from the fulcrum increases.
Leverage is a ‘special case’ contained in Newtonian mechanics. The quantity, rF, is called
TORQUE. That is, T=rF. From Newton’s 2nd Law, it can be shown that if an object is not
rotating, then the sum of the Torques on that object must be zero, ?
T = 0.
In the next experiment we’ll learn about another definition of Torque that Newton defined. What
is significant about this other definition is that it explains the precession of the Earth, a truly
magnificent formulation for the 17th Century. Precession is usually attributed with gyroscopic
motion, which is governed by Torque.
=
Governing Principle
The expression Fr = fR was generalized by Newton. Newton showed this to be a direct result of
the principle of equilibrium. Newton stated that if a system was not accelerating, then the sum of
the external forces must be zero. Similarly, Newton stated that if a system was not angularly
accelerating, then the sum of the external torques must be zero.
Figure 10.2 shows a rigid body acted upon by several forces. If the system is not rotating, then
the sum of the torques caused by the forces must be zero. That is, F1r1 – F2r2 – F3r3 = 0. A
positive sign is assumed for counterclockwise rotation and a negative sign for clockwise rotation.
r3
r1
r2
F2 F3
F1
Figure 10.2. Rigid body under several torques.
Experimental Procedure
For the problems, use the following diagrams and equations. Use a ruler clamp to hang and
balance a meter stick from a ring stand.
r1 r2
m1r1 = m 2 r2
m2
m1
r3
r1
r2
?T = 0:
m3 r1m1 g – r2 m 2 g – r3 m3 g = 0
m1 m2
r1 x
mcm
m1r1 = mcm x
m1
=
Experimental Data: Experiment 9
For the given values, determine the unknown quantities. Verify the results experimentally by
constructing the configurations. Show all calculations explicitly and neatly.
Case 1: r1 = 5 cm, m1 = 500 g, m2 = 100 g.
r2 = _________(calculated)
r2 = _________(experimental)
Case 2: r1 = 20 cm, r2 = 30 cm, m1 = 500 g, m2 = 200 g, m3 = 100 g.
r3 = _________(calculated)
r3 = _________(experimental)
Case 3: r1 = 25 cm, r2 = 10 cm, m1 = 500 g, m2 = 250 g, r3 = 20 cm.
m3 = _________(calculated)
m3 = _________(experimental)
Clamps were used to hold the weights in this experiment. If each clamp weighed 17 g, how
would this affect your answers in Cases 1 and 2?
r2 = _________(Case 1)
r3 = _________(Case 2)
75
PHY 101 LAB NAME___________________________
Torque & Equilibrium
Case 4: r1 = 10 cm, m1 = 100gm + weight clamp .
(you have to use trial and error to find x, start with x about 8 cm)
x = _________(experimental)
mcm =________(calculated from data)
Case 5: x = 10 cm, m1 = 100gm + weight clamp .
r1 = _________(experimental)
mcm = ________(calculated from data)
Calculate the average mass of the meter stick from Cases 4 and 5. Measure the mass of the meter
stick with an electronic scale and calculate the percent error. Use the electronic scale reading as
an accepted value.
mcm = _________(average)
m cm =_________(scale)
% error = _________
=