Name ___________________________________
Date _________________
Balancing Forces
Purpose:
The purpose of this lab is for you to gain more experience working with vector
quantities.
Discussion:
For this lab you will use an instrument called a force table. A ring is placed
around a pin in the center of the force table. Strings attached to the ring pull it in
different directions. The magnitude (strength) of each pull and the direction of the
pull can be varied. The magnitude of the string tension (strength of the pull) is
determined by the amount of mass, which is hung from the other end of the string.
The value of the pull in the string equals m*g, where m is the mass hanging from the
string and g equals 9.8 m/s2.
The force table allows you to demonstrate when the sum of forces acting on
the ring equals zero. Under this condition called equilibrium, the ring, when
released, will remain centered on the post. When the forces on the ring do not add
up to zero, the ring will be pulled to one side until stopped by hitting the post.
Forces are vector quantities, described by both their magnitude and
direction. We will use masses suspended from strings to exert force on an object – a
metal ring. The resultant is a single force calculated as the vector sum of the forces
exerted on the object. We will be able to calculate the magnitude and direction of the
resultant vector on the force table by examining the equilibrant, which is a single
force that establishes equilibrium by balancing two or more forces. So, the
equilibrant has the same magnitude, but opposite direction as the resultant.
Your task is to confirm that forces add as vectors. You will apply up to three
different forces to the ring and add them up. From this information you will predict
the magnitude and direction of a fourth vector that you need to apply to the ring in
order to bring into equilibrium. You will make this prediction by using algebraic
addition of vector components. Finally, you will check your prediction empirically.
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Procedure:
Part I:
1. Make sure the force table is level, and that you have four strings attached to
the ring.
2. Hang a known mass (no more than 300 g) from three of the strings, and
position the corresponding pulley so that the angle between each of the three
strings must be 90o. Do not make masses the same.
a. Calculate the tension in the first string, in Newtons. You may call the
magnitude of this force F1 and the corresponding angle 1.
b. Calculate the tension in the second string, in Newtons. You may call
the magnitude of this force F2 and the corresponding angle 2.
c. Calculate the tension in the second string, in Newtons. You may call
the magnitude of this force F3 and the corresponding angle 3.
d. You are going to figure out the magnitude F4, and the corresponding
angle 4.
3. Calculate the x and y components of F1, if any. Calculate the x and y
components of F2, if any. Calculate the x and y components of F3, if any.
Calculate F4 and 4.
4. Hang the mass necessary to produce F4 on a third string, and place its pulley
at a calculated angle, 4.
5. By making small variations in the mass and angle, decide what combination
will best keep the ring in equilibrium at the center of the table. Record your
answers in the bottom chart.
Part II:
1. Make sure the force table is level, and that you have four strings attached to
the ring.
2. Hang known masses (up to 300 g each) from three of the strings, and
position the corresponding pulleys by NOT having 90° angles between
them, not placing any of them on any of the four coordinate axes, and
placing them in quadrants 1 and 2 only. The choice of masses is up to you,
but don’t make them the same. All of the angles between the strings should
NOT be either 0°, 90°, 180°, or 270°.
a. Calculate the tensions in the strings, in Newtons. You may call the
magnitudes of these forces F1, F2 and F3, and the corresponding angles
1, 2 and 3, respectively.
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b. You are going to figure out the magnitude F4 and direction 4 of a
fourth force using mathematics, which should be applied to the ring in
order to establish equilibrium.
3. Calculate the x and y components of F1, F2, and F3. Set up the equations
Fx = 0 and Fy = 0, and solve them for F4,x and F4,y, respectively. Calculate
F4 and 4 from the components (Pythagorean Theorem and tan θ).
4. Hang the mass necessary to produce F4 on the fourth string, and place its
pulley at the calculate angle 4.
5. By making small variations in the mass and angle, decide what combination
will best keep the ring in equilibrium at the center of the table. Record your
answer in the chart.
Part III:
1. Make sure the force table is level, and that you have four strings attached to
the ring.
2. Hang known masses (up to 300 g) from three of the strings, and position the
corresponding pulleys at known angles. The choice of masses is up to you,
but don’t make them the same. None of the angles may be 0o, 90o, 180o, or
270o and their differences may not be any of these either. Place one force in
each of three quadrants. Calculate the tensions in the strings in Newtons.
You may call the magnitudes of these forces F1, F2, F3 and the corresponding
angles 1, 2, 3, respectively. You are going to figure out the magnitude F4
and direction 4 of a fourth force, which should be applied to the ring in
order to establish equilibrium.
3. Calculate the x and y components of F1, F2, F3. Set up the equations Fx = 0
and Fy = 0, and solve them for F4,x and F4,y, respectively. Calculate F4 and 4
from the components (Pythagorean Theorem and tan θ).
4. Hang the mass necessary to produce F4 on the fourth string, and place its
pulley at the calculate angle 4.
5. By making small variations in the mass and angle, decide what combination
will best keep the ring in equilibrium at the center of the table. Record your
answer in the chart.
6. Use the supplied graph paper to sketch, yes, sketch the vectors again
using a chosen scale between cm and N, just like in Ch. 3 lab. Draw the
three vectors tip-to-tail and determine the magnitude of the resultant
and also the equilibrant. Compare these values to F4 calculated in step
3. The resultants should match.π
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Summary:
Checklist: When you are finished you should have constructed or determined the
following items:
__________ 1.
A constructed vector summation (sketch from #6) for your
chosen experimental arrangement in Part III. Force vectors
must be clearly indicated and defined (angle included).
__________ 2.
A prediction for the expected value of each resultant vector
and resultant angle or direction. Your prediction will be found
by solving for the unknowns algebraically. SHOW ALL
MATH!! Your reasoning process is what I want to see.
__________ 3.
Experimental determination of F4 and 4. (Actually hanging
the masses, duh.)
Conclusion: How does observation (placing masses on the strings)
compare to prediction calculated from algebra and seen from
sketching? In other words did your calculated values and
measured values from the graph for the resultant vectors for each
part correspond to the actual mass that you added to the last
pulley? Use the rest of this sheet to answer this question, if
needed.
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