pounds (operator of the dolly not included). It is known that the board has a maximum load carrying capacity of 242 pounds at its center (weakest point) when horizontal. Round answers to 4 decimal places. Forced pointing down are negative. W2 < 32° = 296 lb a) What is the component of the weight of the dolly perpendicular to the ramp (wi)? 13 13

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Chapter1: Units, Trigonometry. And Vectors
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**Title: Understanding Force Components on an Inclined Ramp**

**Image Description:**

In this educational illustration, we analyze a handtruck/dolly being pulled up a board ramp inclined at 32 degrees. The combined weight of the dolly and its load is 296 pounds, excluding the operator. The board can carry a maximum load of 242 pounds at its weakest point when horizontal. All calculations should be rounded to four decimal places. Note: Forces pointing downward are considered negative.

**Diagram Explanation:**

The diagram shows a dolly on a ramp inclined at an angle of 32 degrees. The following components are visualized:

- The total weight vector (\( \vec{w} \)), with a magnitude of 296 lbs, acting vertically downward.
- Two components of the weight vector:
  - \( \vec{w}_1 \): perpendicular to the ramp.
  - \( \vec{w}_2 \): parallel to the ramp.
- The angle \( \theta \) between the weight vector and its components is shown as 32 degrees.

**Questions:**

a) **What is the component of the weight of the dolly perpendicular to the ramp (\( \vec{w}_1 \))?**

   - \( w_1 = \_\_\_\_ \) pounds

b) **What is the component of the weight of the dolly parallel to the ramp (\( \vec{w}_2 \))?**

   - \( w_2 = \_\_\_\_ \) pounds

c) **Will the board/ramp break?**

   - [ ] Yes
   - [ ] No

d) **What force is required to pull the dolly up the ramp?**

   - \( \_\_\_\_ \) pounds

This exercise aids in comprehending the forces acting on objects on inclined planes, ensuring safety and efficiency in practical applications.
Transcribed Image Text:**Title: Understanding Force Components on an Inclined Ramp** **Image Description:** In this educational illustration, we analyze a handtruck/dolly being pulled up a board ramp inclined at 32 degrees. The combined weight of the dolly and its load is 296 pounds, excluding the operator. The board can carry a maximum load of 242 pounds at its weakest point when horizontal. All calculations should be rounded to four decimal places. Note: Forces pointing downward are considered negative. **Diagram Explanation:** The diagram shows a dolly on a ramp inclined at an angle of 32 degrees. The following components are visualized: - The total weight vector (\( \vec{w} \)), with a magnitude of 296 lbs, acting vertically downward. - Two components of the weight vector: - \( \vec{w}_1 \): perpendicular to the ramp. - \( \vec{w}_2 \): parallel to the ramp. - The angle \( \theta \) between the weight vector and its components is shown as 32 degrees. **Questions:** a) **What is the component of the weight of the dolly perpendicular to the ramp (\( \vec{w}_1 \))?** - \( w_1 = \_\_\_\_ \) pounds b) **What is the component of the weight of the dolly parallel to the ramp (\( \vec{w}_2 \))?** - \( w_2 = \_\_\_\_ \) pounds c) **Will the board/ramp break?** - [ ] Yes - [ ] No d) **What force is required to pull the dolly up the ramp?** - \( \_\_\_\_ \) pounds This exercise aids in comprehending the forces acting on objects on inclined planes, ensuring safety and efficiency in practical applications.
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Component of vector at angle = A cos θ

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