Lab 19: Forces in Equilibrium
Don’t get tense!
Discussion: When a push or pull is at an
angle, we can break the force into a horizontal
Ty
component and a vertical component. The
vertical component represents the magnitude
of the push or pull up or down, and the horizontal
component represents the magnitude of force
sideways. If an object is not accelerating, then the
forces on that object in the horizontal directions
must cancel (add up to zero), and the forces on the
object in the vertical direction must cancel as well.
T (tension)
Θ
Tx
Purpose:
Using a graphing method, and using our trig functions (SOHCAHTOA) we
will verify that the forces on an object all cancel to equal a zero net
horizontal force and a zero net vertical force for a stationary object.
Materials:
mass hangars
force table with pulleys (3) and mass hangars (3)
box of assorted masses
Procedure:
1. Record the mass of an extra mass hangar (no string attached) to the
nearest gram. For this lab, you may assume that all the hangars are the
same mass.
2. Place the strings with mass hangars over the pulleys, so the mass
hangars can move freely. Move one pulley so that its string lines up with
the 270° mark on the force table. Gently tighten pulley clamp to force table.
3. Choose three identical (10 g works well) masses from your box of
masses. Weigh one to the nearest gram. Again, you may assume all
three are the same mass. Record this mass.
4. Place the masses on the mass hangars hanging from the pulleys.
Leave the pulley you clamped where it is. Loosen the clamps on the other
two pulleys, and slide them around the edge of the table until the knot in
the center of the strings is as close as possible to the center of the hole in
the middle of the table. Now your system is in equilibrium!
5. Make a sketch of your setup below draw your three strings, and
label the angles from the horizontal axis.
Label each string with the mass it
supports - that’s the brass mass plus
the mass hangar.
90°
180°
90°
0°
270°
6. Repeat steps 1-5 with
different, non-identical (10 g,
15 g, 20 g) masses. Sketch
below.
180°
0°
270°
Analysis:
1. Make two data tables - one for similar masses, one for different. In your
table, record the masses hanging from each string (brass mass plus
hangar) and the angle above the horizontal (for angled forces). Make T1
and T2 your angled vectors, make T3 the “downward” vertical vector (at
270°). NOTE: tensions are forces, measured in newtons; however, to
keep the numbers nice, we’ll “cheat” and leave our measurements in
grams.
Don’t fill in the components just yet.
Table 1: Identical masses
mass (g)
angle (°)
x component
y component
1
2
3
none
0
NET FORCE (g)
2. Make a scale diagram for each setup (two different diagrams - use a
WHOLE sheet of paper for each diagram). Again, make T3 the vector that
points straight down. Label all vectors and angles. Draw your x and y
components, measure them, and label their lengths on the diagrams.
3. Calculate the lengths of the x and y components for each vector
(SOHCAHTOA). Be sure to include sample calcs for each in your lab
report! Record these values in your data table. NOTE: vector
components can be negative. If your component points in the -x direction
(left) or -y direction (down), label its component as negative in your data
table.
4. Add up the x-components in each table and record under “Net force”.
Do the same for the y-components. Do the add up to zero, or at least
close? If so, your system is in equilibrium! If not, look for errors in your
calculations or data (be sure to include the mass of the hangars!)
Discussion: In your lab report, discuss what you’ve learned about
forces in equilibrium. What can you say about the net force in each
direction? There is no percent error here, but discuss why your vector
components may be slightly off (sources of error). Also discuss how you
might improve this lab.
Conclusions:
1. If you hang an object vertically from two wires at an angle, what forces
balance the weight of the object?
2. What happens to the tension in the wires if they are pulled more
horizontal? How do you know this? (A sketch might be helpful). Why is it
impossible to pull the wires completely horizontal?
3. A painting of mass 6.0 kg is hung on a wall with two wires, each
making an angle of 15° with the vertical.
all
a) Calculate the weight of the painting.
b) Sketch a vector diagram for forces acting on the painting. Label
forces and force components.
c) What’s the vertical component of the force on each wire?
d) Calculate the tension in each wire.
4. Would the tension in each wire be more or less if the angle were 75°?
Repeat the steps of problem 3 to calculate the new tension.