1. Forces in equilibrium
So this means…
• There is no acceleration
• The sum of the forces = 0
• Further…
– The sum of force in the x-direction = 0
– The sum of forces in the y-direction = 0 ΣFx = 0
ΣFy = 0

2. Example
A cafe sign with a mass of 65.5 kg is being held up by 2 cables as shown in
the picture to the left. Calculate the tension in each of the ropes.
X Direction
T2 cos35 T1 cos19
T2 T1 T1 0.866T2
T2sin35 T1sin19
T2cos35 T1cos19
T2 sin 35 T1 sin 19 mg
Catsup & Mustard 0.574T2 0.326T1 642
0.574T2 0.282T2 642
0.856T2 642
mg T2 750 N T1 = 650 N

3. What if the object is not in
equilibrium?
If it is not in equilibrium, then what’s going on
with its motion???
It is changing in some way!!
It can be….stopping, slowing down, speeding
up, changing direction, beginning to move…
USE NEWTON’S
ACCELERATING! SECOND LAW!!


4. What if the object is not in
equilibrium?
1. Draw a free body diagram
2. Break vectors into components if needed
3. Find the NET force by adding and subtracting forces
that are on the same axis as the acceleration.
4. Set net force equal to “ma” this is called writing an
EQUATION OF MOTION.
ΣFx = max ΣFy = may
NOTE: To avoid negative numbers, always subtract the
smaller forces from the larger one.

5. example
A bucket attached to a rope is lifted from a well. The mass of
the bucket and the water in the bucket are 10.0 kg, and the
tension in the rope is 100 Newtons. What is the acceleration
1. of the bucket? diagram
Draw a free body
2. Break vectors into components if
needed
3. Find the NET force by adding and
subtracting forces that are on the same
axis as the acceleration.
4. Set net force equal to “ma” this is called
writing an EQUATION OF MOTION.
a = 0.2 m/s2

6. Example
An elevator with a mass of 2000 kg rises with an
acceleration of 1.0 m/s/s. What is the tension in the
supporting cable? Equation of Motion
T
FNET = ma
T - mg = ma
T = ma + mg
T = (2000)(1) + (2000)(9.8)
T= 21,600 N
mg

7. elevators
• Maximum tension in • Minimum tension
elevator occurs
T occurs when there is
T
when Tthere is an
- mg = ma a downward
mg - T = ma
upward ma + mg
T = acceleration acceleration
T = ma - mg
a
a
mg
mg

8. elevators
• There are typically 3 phases to an elevators motion:
– At a constant speed
– When it comes to a stop
– When it starts moving
• As a result, the tension on the elevators rope WILL
change, AND the weight you read on a scale will change