Static equilibrium with unequal angles, Purpose, Pre-lab question – PASCO ME-6855 Tension Protractor User Manual
Page 6: Theory
®
T e n s i o n P r o t r a c t o r
E x p e r i m e n t 1 : S t a t i c E q u i l i b r i u m w i t h U n e q u a l A n g l e s
4
Experiment 1: Static Equilibrium with Unequal Angles
Purpose
The purpose of this experiment is to verify that the vector
sum of the forces acting on an object in equilibrium is zero.
Pre-lab Question
If an object is suspended by two strings at two different
angles, as shown in Figure 1.1, which string will have the
greater tension?
Theory
The vector sum of the forces acting on an object in equilib-
rium is zero:
(eq. 1-1)
This requires that the sum of the force components in the x- and y-directions must each
separately be zero:
(eq. 1-2)
(eq. 1-3)
For example, if three forces are acting on an object (as shown in Figure 1.2), Equation 1-2
yields
(eq. 1-4)
(eq. 1-5)
This can also be interpreted as requiring the magnitudes of the x-components of the forces
to be equal and opposite:
(eq. 1-6)
(eq. 1-7)
Equipment Needed
Suggested Part
•
(2) Tension Protractors
ME-6855
•
(2) Large Table Clamps
ME-9472
•
(3) 90 cm Steel Rods
ME-8738
•
(2) Multi Clamps
SE-9442
•
Hooked Mass Set
SE-8759
•
Braided Physics String
SE-8050
•
Balance
SE-8723
String #1
String #2
Figure 1.1
F
i
i
∑
0
=
F
ix
i
∑
0
=
F
iy
i
∑
0
=
Figure 1.2
F
2 y
F
1x
F
2 x
F
1 y
θ
2
θ
1
F
1
F
2
F
3
F
3y
=
F
2x
F
1x
–
0
=
F
2
θ
2
cos
F
1
θ
1
cos
–
0
=
F
2 x
F
1 x
=
F
2
θ
2
cos
F
1
θ
1
cos
=