# Document

```I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
Mass hanging from 2 supports unequally.
8 N
2 N
10 N
10 N
FNET = 0 N
Mass hanging from 2 supports equally. 5 N
5 N
7 N
3 N
10 N
10 N
FNET = 0 N
Trope
Trope
10 N
Mass hanging from 2 supports unequally.
FNET = 0 N
Equal angles
Trope = Trope
Trope + Trope &gt; Fg
FNET = 0 N
Unequal angles
Trope ≠ Trope
Trope + Trope &gt; Fg
FNET = 0 N
Trope
Trope
10 N
Equilibrium:
Forces on a body are balanced.
a = 0 N
FNET = ma m
a
= 0
/s2
a Constant speed (including stopped) and direction.
1) Approximately, how much does the 1,000 g mass weigh?
a) 1,000 g
b) 10,000 N
c) 10 N
d) 1 kg
0 2
20
18 newtons 4
?
16
14
A
B
C
D
12 10
6
8
1 Start
Question
1) Approximately, how much does the 1,000 g mass weigh?
a) 1,000 g
b) 10,000 N
c) 10 N
FBD:
d) 1 kg
16
14
Mass 10 N
hanging from 1 support:
FNET = 0 N
0 2
20
18 newtons 4
10 N
6
12 10
8
1,000 g = 1 kg
Fg = mg
2
Fg =(1 kg)(10 m/s ) Fg = 10 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Equilibrium:
FNET = ma = 0 N
Forces on a body are balanced.
a = 0 m/s2
Constant speed (including stopped) and direction.
Mass hanging from 1 support:
FNET = 0 N
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
10 N
2) What do the scales read in following configuration:
a) 10 N, 10 N
b) 5 N, 5 N
c) 10 N, 5N
d) 6.66 N, 6.66 N
0
?
2
20
18 newtons 4
A
B
C
D
16
14
12 10
8
6
0
?
2
20
18 newtons 4
16
14
12 10
6
8
2 Start
Question
2) What do the scales read in following configuration:
a) 10 N, 10 N
b) 5 N, 5 N
c) 10 N, 5N
d) 6.66 N, 6.66 N
FBD:
Mass hanging from 2 supports equally.
FNET = 0 N
0
2
20
18 newtons 4
16
14
6
12 10
8
0
2
20
18 newtons 4
16
14
6
12 10
8
5 N
5 N
10 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
10 N
Mass hanging from 2 supports equally. FNET = 0 N
5 N
5 N
10 N
3) What does the scale on the right read if the scale the left says 8 N?:
a) 8 N
b) 5 N
0
2
20
18 newtons 4
16
14
6
8
c) 10 N
d) 2 N
0
?
2
20
18 newtons 4
16
14
12 10
6
8
A
B
C
3 D
Start
Question
12 10
3) What does the scale on the right read if the scale the left says 8 N?:
a) 8 N
Mass hanging from 2 supports unequally.
FNET = 0 N
b) 5 N
c) 10 N
d) 2 N
FBD:
0
2
20
18 newtons 4
16
14
6
12 10
8
0
2
20
18 newtons 4
16
14
6
12 10
8
8 N
2 N
10 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
10 N
Mass hanging from 2 supports unequally.
FNET = 0 N
Mass hanging from 2 supports equally. FNET = 0 N
5 N
5 N
10 N
8 N
2 N
10 N
4) What do the scales the left each read now?
a) 8 N
b) 5 N
c) 10 N
d) 2.5 N
0
2
20
18 newtons 4
6
16
14
8
12 10
?
A
B
C
D
0
2
20
18 newtons 4
6
16
14
8
12 10
?
0
2
20
18 newtons 4
6
16
14
8
12 10
4 Start
Question
4) What do the scales the left each read now?
a) 8 N
5 N
d) 2.5 N
c) 10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
FBD:
5 N
b) 5 N
0
2
20
18 newtons 4
6
16
14
8
12 10
10 N
(no need to redraw)
Add this to the top of the page:
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
0
2
20
18 newtons 4
6
16
14
8
12 10
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
10 N
Mass hanging from 2 supports unequally.
FNET = 0 N
Mass hanging from 2 supports equally. FNET = 0 N
5 N
5 N
10 N
8 N
2 N
10 N
5) What do the scales on the left read now?
a) 8 N
b) 3.5 N
c) 7 N
d) 10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
?
A
B
C
D
0
2
20
18 newtons 4
6
16
14
8
12 10
?
0
2
20
18 newtons 4
6
16
14
8
12 10
5 Start
Question
5) What do the scales on the left read now?
a) 8 N
FBD:
7 N
3 N
10 N
b) 3.5 N
c) 7 N
d) 10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
0
2
20
18 newtons 4
6
16
14
8
12 10
0
2
20
18 newtons 4
6
16
14
8
12 10
Mass hanging from 2 supports unequally.
FNET = 0 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
10 N
Mass hanging from 2 supports unequally.
8 N
2 N
10 N
FNET = 0 N
Mass hanging from 2 supports equally. FNET = 0 N
5 N
5 N
7 N
3 N
10 N
10 N
Mass hanging from 2 supports unequally.
FNET = 0 N
6) What does the scale on the bottom read now?
a) 8 N
b) 5 N
c) 7 N
d) 10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
0
2
20
18 newtons 4
6
16
14
8
12 10
A
B
C
6 Start
Question
D
0
2
20
18 newtons 4
6
16
14
8
12 10
?
6) What does the scale on the bottom read now?
a) 8 N
FBD:
b) 5 N
c) 7 N
0
2
20
18 newtons 4
6
16
14
8
12 10
10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
10 N
(no need to redraw)
d) 10 N
0
2
20
18 newtons 4
6
16
14
8
12 10
7) Do the scales on the right read:
b) &gt; 5 N
c) = 5 N
C
D
to
ns
w
ne
10 8 6
12
B
14
?
16
A
18 20 0
0 0
20 20 2 2
4 4
18 newtons
18 newtons
16 16
6 6
14 14
8 8
12 10
12 10
2
4
a) &lt; 5 N
18 20
0
16 n
ew
2
to
14
n
?
s
12
10
8
4
6
7 Start
Question
7) Do the scales on the right read:
b) &gt; 5 N
c) = 5 N
10 8 6
12
ns
w
to
14
16
ne
18 20 0
0 0
20 20 2 2
4 4
18 newtons
18 newtons
16 16
6 6
14 14
8 8
12 10
12 10
2
4
a) &lt; 5 N
18 20
0
16 n
ew
2
to
14
n
s
12
10
8
6
4
10 8 6
12
ns
w
to
ne
16
14
18 20 0
2
4
Let's look at the Free Body Diagram for this situation:
18 20
0
16 n
ew
2
to
14
n
s
12
10
8
6
4
Let's look at the Free Body Diagram for this situation:
Its easier to see if we replace the scales with ropes:
Let's look at the Free Body Diagram for this situation:
Fg
The Force of Gravity pulls down on the mass.
Let's look at the Free Body Diagram for this situation:
(Same as the Table Vectors Lab)
The ropes counter the gravitational force. The 'up' tension must equal the downward force of gravity.
Tup
Fg
The Force of Gravity pulls down on the mass.
Let's look at the Free Body Diagram for this situation:
Tup
Trope
Fg = Tup
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Let's look at the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Let's look at the Free Body Diagram for this situation:
Notice that the tension in each rope has a vertical component equal Trope
to half the total force required to suspend the mass.
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Tup
Trope
Fg = Tup
Fg
Let's look at the Free Body Diagram for this situation:
Notice that the tension in each Tup
rope has a vertical Ty Ty
component equal Trope
Trope
to half the total Tx
Tx
force required to suspend the mass.
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Fg = Tup
Let's look at the Free Body Diagram for this situation:
Notice that the tension in each Tup
rope has a vertical Ty Ty
component equal Trope
Trope
to half the total Tx
Tx
force required to suspend the mass.
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Fg = Tup
These are the same:
Ty
Tup
Ty
Let's look at the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Let's look at the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Let's look at the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
To see the tension in the ropes we construct the parallelogram around the resulting Tup.
Fg
Let's look at the Free Body Diagram for this situation:
Tup
pe
T ro
Trope
Trope
ro
T
Fg
pe
Fg = Tup
Fg
We see that the tension in the ropes is greater than the force of gravity on the mass.
Let's look at the Free Body Diagram for this situation:
FBD:
Trope
Trope
10 N
Equal angles
Trope = Trope
Trope + Trope &gt; Fg
FNET = 0 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
10 N
Mass hanging from 2 supports unequally.
8 N
2 N
10 N
FNET = 0 N
Mass hanging from 2 supports equally. 5 N
5 N
Trope
10 N
3 N
10 N
10 N
FNET = 0 N
Trope
7 N
Mass hanging from 2 supports unequally.
FNET = 0 N
Equal angles
Trope = Trope
Trope + Trope &gt; Fg
FNET = 0 N
a) left
b) right
B
C
6
2 4
A
?
s
?
4
20 tons
6
w
ne
8
1
8
16
10
14 12
0
2
n
20
to
w
ne
8
18
0
16 4 2 1
1 1
0
c) both the same 8 Start
Question
a) left
b) right
?
2 4
s
6
?
4
20 tons
6
w
ne
8
1
8
16
10
14 12
0
2
n
20
to
w
ne
8
18
0
16 4 2 1
1 1
0
c) both the same Hints:
1. Which way is the mass pulled?
2. Which scale pulls more 'up'?
a) left
b) right
s
2 4
4
6
20 tons
6
w
ne
8
1
8
16
10
14 12
0
2
n
20
to
w
ne
8
18
0
16 4 2 1
1 1
0
c) both the same Hints:
1. Which way is the mass pulled?
2. Which scale pulls more 'up'?
Again, the Free Body Diagram for this situation:
FBD:
Unequal angles
Trope ≠ Trope
Trope + Trope &gt; Fg
FNET = 0 N
Trope
Trope
10 N
I would suggest you take notes like this:
FBD's for Equilibrium:
Forces on a body are balanced.
Equilibrium:
a = 0 m/s2
FNET = ma = 0 N
Constant speed (including stopped) and direction.
TENSION IS CONSTANT THROUGHOUT A SUPPORT!
Mass hanging from 1 support:
1,000 g = 1 kg
Fg = mg
Fg =(1 kg)(10 m/s2) Fg = 10 N
10 N
FNET = 0 N
Mass hanging from 2 supports unequally.
8 N
2 N
10 N
10 N
FNET = 0 N
Mass hanging from 2 supports equally. 5 N
5 N
7 N
3 N
10 N
10 N
FNET = 0 N
Trope
Trope
10 N
Mass hanging from 2 supports unequally.
FNET = 0 N
Equal angles
Trope = Trope
Trope + Trope &gt; Fg
FNET = 0 N
Unequal angles
Trope ≠ Trope
Trope + Trope &gt; Fg
FNET = 0 N
Trope
Trope
10 N
Again, the Free Body Diagram for this situation:
Tup
Fg = Tup
Fg
Again, the Free Body Diagram for this situation:
Tup
Fg = Tup
Again, we can see the tension in each rope by constructing the parallelogram.
Fg
Again, the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
Again, we can see the tension in each rope by constructing the parallelogram.
Fg
Again, the Free Body Diagram for this situation:
Tup
Trope
Trope
Fg = Tup
Again, we can see the tension in each rope by constructing the parallelogram.
Fg
Again, the Free Body Diagram for this situation:
The left rope does more of the pulling Trope
'up' so feels the greater tension.
Tup
Trope
Fg = Tup
Again, we can see the tension in each rope by constructing the parallelogram.
Fg
END
```