PASCO ME-8949 EQUAL ARM BALANCE - Manual

P A S C O
s c i e n t i f i c
EQUAL ARM BALANCE
MAXIMUM TOTAL MASS NOT TO EXCEED ONE KILOGRAM
ME-8949
F
θ
r
Instruction Sheet
for the PASCO
Model ME-8949
EQUAL ARM BALANCE
012-05921A
12/95
$1.00
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teach science
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Introduction
The PASCO Model ME-8949 Equal Arm Balance was
designed to be used in a vertical position to compare
weights hung vertically from it to standard weights. This
balance can also be used in a horizontal (or vertical) posi-
tion to show that torques about its axis of rotation must be
of the same magnitude if it is to remain in an equilibrium
position. The Balance can be used with hanging weights
or with applied forces measured with spring scales.
Equipment
The ME-8949 Equal Arm Balance consists of a symmet-
ric molded plastic arm attached to a low friction, freely
rotating brass axle. Masses can be suspended from the
grooves on top of the plastic arm or from the loops on the
bottom of the arm. If an outer loop or groove is used, a
mass difference of about 2% between the two ends of the
balance is detectable.
Additional Equipment Required:
Use a Base and Support Rod (ME-9451), or a Universal
Table Clamp (ME-9376B) rod for basic support. Then use
a Right Angle Clamp (SE-9444) or Multi-Clamp (SE-9442)
to attach the Equal Arm Balance to the support rod.
For vertical observations with hanging masses:
– 2 SE-8703 Slotted Mass Hangers with SE-8726
Slotted Mass Set and/or
– 1 ME-9348 Mass and Hanger Set and/or
– 2 SE-8705 Hooked Mass Sets
For horizontal observations with applied forces:
– 2 SE-8716 5N Metric Spring Scales or
– 2 SE-8715 2N Metric Spring Scale or
– 2 SE-8714 1N Metric Spring Scale
Theory
The vector sum of torques with respect to the axis of rota-
tion of an object must be zero if the object is to remain in
a state of rotational equilibrium. If a force is applied to
the Equal Arm Balance at one of the grooves or loops the
torque exerted on the Balance can be calculated.
The magnitude of the torque,
τ
, is given by the product of
the magnitude of the moment arm vector, r and the force
vector, F and the sine of the angle between the extension
of the moment arm and the line along which the force
vector acts. Thus,
τ =
rF sin
θ
Torque is actually a vector. Its direction can be found
from the moment arm and force by using a right hand
rule. The moment arm is defined as the vector pointing
from the axis of rotation to the point of action of the
force. Lay the fingers of the right hand along r . Your
thumb will point perpendicular to the plane containing
vectors F and r . Curl your fingers toward F . The direc-
tion your fingers curl is the direction of the torque.
Axle with
bearings
Molded plastics body Mass holder loops
P A S C O
s c i e n t i f i c
EQUAL ARM BALANCE
MAXIMUM TOTAL MASS NOT TO EXCEED ONE KILOGRAM
ME-8949
Axis of rotation
Figure 1: Equal Arm Balance
Grooves
Figure 2: Calculating Force
© 1996 PASCO scientific
Written by Priscilla Laws. Based on Units 5, 12, and 13
of the Workshop Physics Activity Guide. Published by
John Wiley and Sons (1996). Permission was granted by
the publisher for these adaptations .