A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 300 N and is 4.50 m long. What is the tension in each rope when the 600-N worker stands 1.30 m from one end? Make use of the situations in this scenario and tell us a story of your own that involves a similar type of static equilibrium. You may use approximate values to solve the problem that you come up with.
A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 300 N and is 4.50 m long. What is the tension in each rope when the 600-N worker stands 1.30 m from one end? Make use of the situations in this scenario and tell us a story of your own that involves a similar type of static equilibrium. You may use approximate values to solve the problem that you come up with.
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![**Problem: Static Equilibrium of a Scaffold**
**Scenario:**
A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 300 N and is 4.50 m long. What is the tension in each rope when the 600-N worker stands 1.30 m from one end?
**Task:**
Make use of the situations in this scenario and tell us a story of your own that involves a similar type of static equilibrium. You may use approximate values to solve the problem that you come up with.
**Educational Explanation:**
To solve this problem, one must apply the principles of static equilibrium. In static equilibrium, the sum of all vertical forces and the sum of all moments (torques) around any point must be zero.
Steps to solve:
1. **Identify Forces:**
- Weight of the scaffold (W_s): 300 N
- Weight of the worker (W_w): 600 N
2. **Determine Positions:**
- Length of the scaffold (L): 4.50 m
- Position of the worker from one end (d): 1.30 m
3. **Define Tensions:**
- Tension in the rope at the near end (T1)
- Tension in the rope at the far end (T2)
4. **Set up equilibrium equations:**
- Sum of vertical forces:
\[
T1 + T2 = W_s + W_w
\]
- Sum of moments about one end (taking moments about the point where T1 acts for simplicity):
\[
T2 \times L = (W_w \times d) + (W_s \times \frac{L}{2})
\]
Assuming anti-clockwise moments are positive and calculating the moments around the near end (distance to the worker and the center of the scaffold are important).
Using these equations, one can solve for the tensions T1 and T2.
**Additional Task:**
Create a similar scenario, perhaps with a painter on a ladder, a child on a seesaw, or any other example involving static equilibrium. Use approximate values to set up your problem and solve it using similar principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F219f3226-c940-46da-afab-f83d4af1a26e%2Fd007c8c9-c228-4841-9bbf-4a0a2073e8d4%2Fit3i5or_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Static Equilibrium of a Scaffold**
**Scenario:**
A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 300 N and is 4.50 m long. What is the tension in each rope when the 600-N worker stands 1.30 m from one end?
**Task:**
Make use of the situations in this scenario and tell us a story of your own that involves a similar type of static equilibrium. You may use approximate values to solve the problem that you come up with.
**Educational Explanation:**
To solve this problem, one must apply the principles of static equilibrium. In static equilibrium, the sum of all vertical forces and the sum of all moments (torques) around any point must be zero.
Steps to solve:
1. **Identify Forces:**
- Weight of the scaffold (W_s): 300 N
- Weight of the worker (W_w): 600 N
2. **Determine Positions:**
- Length of the scaffold (L): 4.50 m
- Position of the worker from one end (d): 1.30 m
3. **Define Tensions:**
- Tension in the rope at the near end (T1)
- Tension in the rope at the far end (T2)
4. **Set up equilibrium equations:**
- Sum of vertical forces:
\[
T1 + T2 = W_s + W_w
\]
- Sum of moments about one end (taking moments about the point where T1 acts for simplicity):
\[
T2 \times L = (W_w \times d) + (W_s \times \frac{L}{2})
\]
Assuming anti-clockwise moments are positive and calculating the moments around the near end (distance to the worker and the center of the scaffold are important).
Using these equations, one can solve for the tensions T1 and T2.
**Additional Task:**
Create a similar scenario, perhaps with a painter on a ladder, a child on a seesaw, or any other example involving static equilibrium. Use approximate values to set up your problem and solve it using similar principles.
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