Isaac Parenteau
02/25/2007
PHY-1041
Static Equilibrium with a Force Table
Abstract: The purpose of this lab is to see how an item can stay in equilibrium by using
force vectors.
Theory: A system is said to be in equilibrium when the net forces acting in x, y, & z
directions are all equal to zero. In this lab you will verify this condition by analyzing a
system with unbalanced forces acting upon it, and calculate the fourth force required to
restore equilibrium. The vector sums will be determined analytically.
Equipment:
Various Masses
String
Force Table
Procedure:
Obtain 3 masses and 3 angles and convert the masses to weight by multiplying the mass
by the force of gravity (9.8). Then hang the masses on the force table at the 3
predetermined angles and then calculated the resultant force and angle. The resultant
force is the square root of the sum of the x component squared plus the sum of the y
components squared. The Resultant angle is the inverse tan of the sum of the y
components over the sum of the x components. The Resultant force is the force required
for equilibrium but the angle has to be 180 degrees from the resultant angle to make it
equal. Place the 4th mass on the table and see if everything is equal.
For my experiment, I used the following mass and angles: 1 Kg, 0.5 Kg and 0.2 Kg and
0°, 100°, and 210° respectively. Then I converted the mass into Force (N) by multiplying
the mass by the force of gravity (9.8)
Mass (Kg)
1
0.5
0.2
Force (N)
9.8
4.9
1.96
Angle (degrees)
0
100
210
Next I had to find the resultant Force and angle by using the Sum of the y components
and the sum of the x components. To find the y components I multiply the force by the
sin of the angle that corresponds to that angle, and the sum is the sum of these
components. The x component is the force multiplied by the cosine of the angle that
corresponds to that angle, and the sum is the sum of these components.
∑y= sin (0) * 9.8 + sin (100) * 4.9 + sin (210) * 1.96 = 3.85N
∑x= cos (0) * 9.8 + cos (100) * 4.9 + cos (210) * 1.96 = 7.25N
The resultant force = √ (∑x2 + ∑y2) or √ (3.852+7.252) = 8.2N
To find the mass needed, I divided 8.2N by 9.8 and calculated a mass of 0.836 Kg is the
equivalent mass of the above vectors.
Next I calculated the resultant angle by taking the inverse tan of the y components
divided by the x components: tan-1(3.85/7.25) = 27.96°. To be in equilibrium the same
force of 0.836 Kg would have to be applied 180° degrees from the resultant angle:
180 + 27.96 =207.96. So a mass of 0.836 Kg at an angle of 207.96° will equalize all the
masses.
0.5 Kg @ 100°
1 Kg @ 0°
0.2 Kg
@ 210°
Equilibrium Force 0.836 Kg @ 207.96°
To equalize the forces that are in the table a Force of 8.2N at an angle of 207.96° need to
be applied. When I applied the force it was slightly off and the mass was not in
equilibrium. I had to move the mass to 210° to get the center to be at the center so the
difference is off from 2° from the calculated results to the actual results.
Summary:
When all forces acting on a body equals zero then that objects is in equilibrium and not
moving. To get an object to be in equilibrium then the vectors need to be drawn and the x
and y components need to be broken down to find the resultant. By using the formulas
done in the lab I found the sum of the x components and the y components. Then by
taking the square root of the sum of the squares I found a resultant force. Next by take the
inverse tan of the y components over the x components and found the angle. This angle is
the resultant angle of all the forces and their angles together. If the force is placed 180°
from the resultant angle then it will equalize the whole system of vectors. This lab was a
good representation on how equilibrium works.