give answer in 2 step with explanation at the end of each step and final answer at the end:
P
:
0
1
The members
o
f
a truss are pin connected
a
t
joint
O
.
Determine the magnitudes
o
f
F
1
and
F
2
for
ε
l
o
n
Set
θ
=
6
0
°
.
Aflic:
⿱
f
x
+
=
0
o
r
λ
f
y
=
0
+
→
t
f
x
=
0
→
f
2
s
i
n
9
0
°
+
f
1
c
o
s
6
0
°
-
5
c
o
s
3
0
°
-
7
(
4
5
)
=
0
hat
(
f
)
f
y
=
0
→
f
2
c
o
s
3
0
°
+
5
s
i
n
3
0
°
-
7
*
3
5
-
f
1
s
i
n
6
0
°
=
0
6
9
x
1
=
f
2
s
i
n
7
0
=
-
f
1
c
o
s
6
0
+
9
*
9
3
Substitute
e
q
3
into
e
q
2
f
2
→
k
n
,
f
1
→
k
nP:01
The members of a truss are pin connected at joint O.
Determine the magnitudes of F; and F; for equilibrium.
Set = 60°. Et y
*
. => x oN 2 pr)
Athy 9 |p tacet
£txz0 ov ery:o Th d
. RESP,
D5 Fm0 =2 fr sides hese -seosts- 304) 0 ERE Aree
3 Be
=? hites3dy Sudd-ad -fignbo zo p. yd
2 fon?
i
[TPR fi
Fes 107 =f Loses 4.93
Subavnere eq 3 imo eqn
[AUP NY
Question:
give answer in 2 step with explanation at the end of each step and final answer at the end:
P
:
0
1
The members
o
f
a truss are pin connected
a
t
joint
O
.
Determine the magnitudes
o
f
F
1
and
F
2
for
ε
l
o
n
Set
θ
=
6
0
°
.
Aflic:
⿱
f
x
+
=
0
o
r
λ
f
y
=
0
+
→
t
f
x
=
0
→
f
2
s
i
n
9
0
°
+
f
1
c
o
s
6
0
°
-
5
c
o
s
3
0
°
-
7
(
4
5
)
=
0
hat
(
f
)
f
y
=
0
→
f
2
c
o
s
3
0
°
+
5
s
i
n
3
0
°
-
7
*
3
5
-
f
1
s
i
n
6
0
°
=
0
6
9
x
1
=
f
2
s
i
n
7
0
=
-
f
1
c
o
s
6
0
+
9
*
9
3
Substitute
e
q
3
into
e
q
2
f
2
→
k
n
,
f
1
→
k
nP:01
The members of a truss are pin connected at joint O.
Determine the magnitudes of F; and F; for equilibrium.
Set = 60°. Et y
*
. => x oN 2 pr)
Athy 9 |p tacet
£txz0 ov ery:o Th d
. RESP,
D5 Fm0 =2 fr sides hese -seosts- 304) 0 ERE Aree
3 Be
=? hites3dy Sudd-ad -fignbo zo p. yd
2 fon?
i
[TPR fi
Fes 107 =f Loses 4.93
Subavnere eq 3 imo eqn
[AUP NY
This is AI generated Response.
Asked by: Pagal
Created at: 2025-09-05 04:28:04
Final Answer:
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Let's solve this problem step by step, as you requested.
---
### **Step 1: Write the Equilibrium Equations**
**Explanation:**
- At joint O, for equilibrium, the sum of forces in both x and y directions must be zero.
- Forces are broken down into their x and y components (as shown in the diagram).
#### **Sum of forces in the x-direction:**
\[
\sum F_x = 0
\]
\[
F_2 \sin 90^\circ + F_1 \cos 60^\circ - 5 \cos 30^\circ - 9 \cos 60^\circ = 0
\]
\[
F_2 (1) + F_1 (0.5) - 5 (0.866) - 9 (0.5) = 0
\]
\[
F_2 + 0.5 F_1 - 4.33 - 4.5 = 0
\]
\[
F_2 + 0.5 F_1 = 8.83
\]
---
### **Step 2: Sum of Forces in the y-direction**
**Explanation:**
- Set up the equation for vertical equilibrium using the force components.
#### **Sum of forces in the y-direction:**
\[
\sum F_y = 0
\]
\[
F_2 \cos 30^\circ + 5 \sin 30^\circ - 7 - F_1 \sin 60^\circ = 0
\]
\[
F_2 (0.866) + 5 (0.5) - 7 - F_1 (0.866) = 0
\]
\[
0.866 F_2 + 2.5 - 7 - 0.866 F_1 = 0
\]
\[
0.866 F_2 - 0.866 F_1 = 4.5
\]
\[
0.866 (F_2 - F_1) = 4.5
\]
\[
F_2 - F_1 = \frac{4.5}{0.866} = 5.20
\]
---
### **Now, solve the two equations:**
1. \( F_2 + 0.5 F_1 = 8.83 \)
2. \( F_2 - F_1 = 5.20 \)
#### Substitute \( F_2 = 5.20 + F_1 \) into the first equation:
\[
(5.20 + F_1) + 0.5 F_1 = 8.83
\]
\[
5.20 + 1.5 F_1 = 8.83
\]
\[
1.5 F_1 = 8.83 - 5.20 = 3.63
\]
\[
F_1 = \frac{3.63}{1.5} = 2.42~\text{kN}
\]
Now substitute \( F_1 \) back into equation 2:
\[
F_2 = 5.20 + 2.42 = 7.62~\text{kN}
\]
---
## **Final Answer**
- **\( F_1 = \boxed{2.42~\text{kN}} \)**
- **\( F_2 = \boxed{7.62~\text{kN}} \)**
---
**Summary:**
- Step 1: Write and simplify the equilibrium equations for x and y directions.
- Step 2: Solve the two simultaneous equations to find the magnitudes of \( F_1 \) and \( F_2 \).
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P:01
The members of a truss are pin connected at joint O.
Determine the magnitudes of F; and F; for equilibrium.
Set = 60°. Et y
*
. => x oN 2 pr)
Athy 9 |p tacet
£txz0 ov ery:o Th d
. RESP,
D5 Fm0 =2 fr sides hese -seosts- 304) 0 ERE Aree
3 Be
=? hites3dy Sudd-ad -fignbo zo p. yd
2 fon?
i
[TPR fi
Fes 107 =f Loses 4.93
Subavnere eq 3 imo eqn
[AUP NY