Download Equilibrium Problems - Warren Hills Regional School District

EQUILIBRIUM :
Equilibrium is the mathematical representation of Newton's 1st Law.
Basically, it says that when an object is (a) at rest, or (b) moving with a constant velocity,
then the sum of the force vectors equals zero (F = 0).
Static Equilibrium
Static equilibrium occurs when an object is at rest. Although any number of forces can
be present, typically there are 2 or 3 present in a given situation (like you sitting in your
seat, for example). Visually, the force vectors would appear as shown below:
2 Forces
+
3 Forces (Lab Situation)
 Fx = 0
= 0
Fy = 0
In this case, use components, as we did
way back in the Vectors section.
Dynamic Equilibrium
Dynamic equilibrium occurs when an object moves with a constant velocity. We have
observed this while zooming down the hallway.
v
Fair
mg
Usually, friction is present. Friction depends on only 2 factors :
(1) the smoothness of the surfaces in contact (called the coefficient of friction, )
(2) how much one surface "presses" into the other (called the normal force, FN).
These 2 factors are represented in the expression
Ff max = FN
Equilibrium Problems
1.
Nicole, Emma and Lauren have had enough of physics class. They go outside to
play tug of war to release some stress but they don’t have a rope handy. So they
decide to use Tim. Nicole pulls on Tim with a force of 25 N to the north. Emma
applies a second force of 20 N to the east. Find the magnitude and direction of
the force Lauren needs to apply to produce equilibrium.
(32 N, 51 S of W)
2.
An object in equilibrium has 3 forces acting on it. A 33 N force acts to the north,
and a 44 N force acts at 60 N of E. What is the magnitude & direction of the
3rd force?
(74.3 N, 73 S of W)
3.
3 forces are in equilibrium. A 200 N force acts directly to the south.
F1 acts at 45 North of East , and F2 acts at 53 North of West.
Determine F1 and F2.
(121 N, 143 N)
4.
A 150 N sign is supported equally by two wires as shown. What is the tension in each
of these wires?
30o
50o
Eisner’s
Cove
5.
Flaherty decides that he has had enough of school and joins the circus. His job is
to walk the tightrope. He weighs 600 N. When he stands on a small platform in
the middle of the tightrope, it causes the tightrope to make an angle of 10 at
both ends with the horizontal. Find the tension in each half of the tightrope.
600 N
(1728 N)
6.
A sign weighing 200 N is supported by a wire that makes a 30 angle with the
horizontal and a “boom”, which exerts a horizontal force outward from the wall.
Find the tension in the wire and the force exerted by the boom.
30
Brian Q’s
Bakery
(400 N, 346 N)