Static Equilibrium –
Analyzing Objects at Rest (Ch 7-1)
An object in equilibrium has a “net force”
zero
of ________, which means that all forces
balance
on the object must __________.
For example: Use spring scales to
support a 10 N weight…
10 N
5 N
What would happen to the
force in the spring scales if the
angle between the spring scales
were increased, as shown?
The force in each spring scale
increases
____________, because the pull is now
horizontal
partially in the _____________ direction.
This is in addition to the 5 N (half of the
vertical
weight) in the ________ direction that
each spring scale must support.
Drawing force vector diagrams to scale
illustrate that the tension in the spring scales
must increase as the angle between them
increases:
The two tension vectors added “head-
weight
to-tail” balance the _______ vector.
As the angle between the spring scales
continues to increase (becoming more
horizontal), the force continues to increase
_________.
Demos:
• Lift 1 kg mass with thread. As the angle, q,
increases, tension increases, until thread
breaks
________.
• Lift 0.5 kg mass with thread. The breaking
larger
angle, q, will be ________ than with 1 kg mass.
As the spring scales would approach
horizontal, the required force would
infinity
approach ___________!
Why?
In order to support a weight (downward
upward
force), there must be __________ force. But,
when pulling exactly horizontally, there is
NO
____ force in the upward direction!
impossible
Application: It’s ____________ for a cable,
rope, or chain to be pulled perfectly
horizontal. Demo: Cable must _____! sag
Applications and Examples
• Power lines, Clothes lines, Suspension
bridge cables, etc. always sag!
Why do power lines sometimes snap
during a bad ice storm?
The weight of the ice
HUGE
produces __________
increases in tension
___________________,
because the lines are
pulled so close to
horizontal.
Why, then, don’t we sag them more?
Cost and Safety!
• Which would be easier?
OR
OR
New Vocabulary term:
What’s a “boom”?
On a sailboat, a “boom” On a crane, a “boom” is
is the long pole along the part of the system used
bottom of the rigged sail. to lift heavy objects to
large heights.
• A 100 lb weight is supported
by a cable and light “boom”.
If the cable makes a 30° angle
with the boom, calculate the
tension in the cable and the
force in the boom.
100
FBD: sin 30
100 lb T T
T 200 lbs
30°
Fboom
Or 30-60-90…
Fboom 100 3 173lbs
W = 100 lb
• How can your knowledge of physics be
used to move a heavy object such as a
car stuck in the mud? Assume there is a
tree nearby and you have a strong cable
or chain.
Tie cable tightly
between car and
tree…
Then… sit on it!
Calculate the tension created in the cable,
assuming the cable made a 5° angle with the
horizontal on each side, and the weight of the
person is 200 lbs. (Hopefully this force is enough to
move the car!)
FBD: (Not drawn to scale)
T T
½W 5° 5° ½W = 100 lbs
W= 200lbs
100
sin 5
T 100
sin 5
1147 lb!!
T Note: After calculating T, do NOT double it!!