Type:
Double
Date:____________
Objective: Torque II: Rigid Objects in Equilibrium I
Torque III: Rigid Objects in Equilibrium II
Homework: Do CONCEPT QUEST #’s (3, 5),
Do PROBLEMS #’s (3, 14) Ch. 9
Rigid Objects in Equilibrium I
Equilibrium of a Rigid Body
A rigid body is in equilibrium if it has zero “translational” acceleration and zero “angular”
acceleration. In equilibrium, the SUM of the externally applied forces is zero, and the SUM
of the externally applied torques is zero:
∑ Fx = 0
and
∑ Fy = 0
∑τ = 0
First condition of Equilibrium
Second condition of Equilibrium
CONSIDER THE FOLLOWING FORCES ACTING ON A BEAM. THIS COULD APPLY
TO A POST-LINTEL “BRIDGE” OR A “SIGN” SUPPORTED BY ROPES, ETC.
l⊥(1)
l⊥(2)
F1
F2
“PIVOT”
Fg = mg
First condition:
+→
+↑
∑F = 0
∑ Fx = 0
Second condition:
+
∑τ = 0
∑τ = 0
∑ Fy = 0
0
+ F1 + F2 - mg = 0
- F1* l⊥(1) + mg (0) + F2* l⊥(2) = 0
Applying the Conditions of Equilibrium to a Rigid Body
1. Select the object to which the equations for equilibrium are to be applied.
2. Draw a free-body diagram (FBD) that shows all the external forces acting on the object, each
force with its proper direction.
3. Choose a convenient set of x and y axes and resolve all forces into components that lie along
these axes.
4. Apply the equations that specify the balance of forces at equilibrium, namely:
∑ Fx = 0
and
∑ Fy = 0
5. Select a convenient axis of rotation. Identify the point where external force acts on the object,
and calculate the torque produced by each force about the axis of rotation.
6. Set the sum of the torques about the axis of rotation equal to zero, that is:
∑τ = 0
7. Solve any equations that arise from applying the conditions for equilibrium.
AP Physics “B”
Mr. Mirro
Date: ________
Rigid Objects in Equilibrium I
Ex 1: A woman whose weight is 530 N is poised at the right end of a diving board, whose length is 3.90 m.
The board has negligible weight and is bolted down at the left end, while being supported 1.40 m away
by a fulcrum as shown. [Cutnell9.3]
F2
W = Fg
F1
1.4 m
3.9
a. Find the forces F1 and F2 that the bolt and the fulcrum, respectively, exert on the board by
selecting the BOLT (left side) as the ORIGIN of the axis.
b. Repeat the analysis to find the forces that F1 and F2 exert on the board - this time by selecting the
FULCRUM (middle) as the ORIGIN of the axis.
Ex 2: A uniform 40 N board supports two children weighing 500 N and 350 N as shown. The support
(fulcrum) is under the center of gravity of the board and the 500 N child is 1.50 m from the center.
[Serway8.4]
F2
a. Identify the weight vector for the
board and label it Fw.
1.5 m
x
F3 = 350 N
F1 = 500 N
b. Using Newton’s Second Law, find the upward force exerted on the board by the fulcrum.
c. Choosing the fulcrum as the coordinate system, determine where the 350 N child should sit to
balance the system.
d. Repeat part (c), using another axis for the torque computations.
Rigid Objects in Equilibrium II
Ex 1: Consider a firefighter who weighs 875 N is on an 8.0 m long ladder that weighs 355 N as shown.
The ladder leans against a smooth vertical wall. The term “smooth” means that the wall can exert only a
normal force directed perpendicular to the wall and cannot exert a frictional force parallel to it. The
firefighter is 6.30 m from the bottom of the ladder. Assume that the ladder’s weight acts at its center
and neglect the weight of the fire hose. Find the forces that the wall and ground exert on the ladder.
[Cutnell9.4]
50°
Ex 2: A uniform, horizontal 300 N beam, 5.0 m long, is attached to a wall by a pin connection that allows
the pin to rotate. Its far end is supported by a cable that makes an angle of 53° with the horizontal. If
a 600 N person stands 1.50 m from the wall, find the tension in the cable and the force exerted on the
beam by the wall. [Serway8.6]