### Sand Excavator Force Analysis**Problem Statement:**The sand excavator depicted is in equilibrium. It experiences a horizontal force of 30 N on the bucket. The task is to determine the horizontal forces $ F_1 $ and $ F_2 $ applied to the handles. The weight of the members is neglected.**Diagram Explanation:**The diagram illustrates a mechanical system with the following components and force details:- **Lever and Forces:** - The point $ E $ is acted upon by force $ F_1 $, directed horizontally to the right. - The point $ D $ experiences force $ F_2 $, directed horizontally to the left. - The bucket at point $ B $ is subjected to a 30 N horizontal force.- **Geometrical Setup:** - The entire setup is based around point $ A $, which acts as a pivot or base. - Distance from point $ C $ to $ D $ vertically is 47.38 cm. - Distance from point $ B $ to $ C $ vertically is 8.82 cm. - Distance from point $ A $ to $ B $ vertically is 26.22 cm. - The lever arm inclined at 10° starts from point $ F $ down to the bucket at $ G $, a vertical distance of 8 cm to a support at point $ H $. - Point $ H $ is vertically 20 cm below point $ G $ where the 30 N force is applied.- **Angles:** - The angle between the lever AB and the horizontal line at point $ B $ is 80°.**Calculation Approach:**To find forces $ F_1 $ and $ F_2 $, use principles of static equilibrium where sum of forces and moments around any pivot should be zero. Consider torque calculations around point $ A $ and apply equilibrium conditions to resolve unknown forces. Take into account the angles given for precise computation.

Answered: Image /qna-images/answer/652d1ec8-f3a4-4b2a-820f-f441082def22.jpgF1 = 33.403 NF2 = 31.885 N

The sand excavator is in equilibrium. The horizontal force on the bucket is 30 N. Find the horizontal forces F₁ and F2 applied to the handles. Ignore the weight of the members. 8 cm 20cm H 10° $10⁰ 30N R E 80° B D F₂ C A 47.38cm 8.82cm 26.22cm

The sand excavator is in equilibrium. The horizontal force on the bucket is 30 N. Find the horizontal forces F₁ and F2 applied to the handles. Ignore the weight of the members. 8 cm 20cm H 10° $10⁰ 30N R E 80° B D F₂ C A 47.38cm 8.82cm 26.22cm

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

Question

### Sand Excavator Force Analysis

**Problem Statement:**
The sand excavator depicted is in equilibrium. It experiences a horizontal force of 30 N on the bucket. The task is to determine the horizontal forces $ F_1 $ and $ F_2 $ applied to the handles. The weight of the members is neglected.

**Diagram Explanation:**
The diagram illustrates a mechanical system with the following components and force details:

- **Lever and Forces:**
- The point $ E $ is acted upon by force $ F_1 $, directed horizontally to the right.
- The point $ D $ experiences force $ F_2 $, directed horizontally to the left.
- The bucket at point $ B $ is subjected to a 30 N horizontal force.

- **Geometrical Setup:**
- The entire setup is based around point $ A $, which acts as a pivot or base.
- Distance from point $ C $ to $ D $ vertically is 47.38 cm.
- Distance from point $ B $ to $ C $ vertically is 8.82 cm.
- Distance from point $ A $ to $ B $ vertically is 26.22 cm.
- The lever arm inclined at 10° starts from point $ F $ down to the bucket at $ G $, a vertical distance of 8 cm to a support at point $ H $.
- Point $ H $ is vertically 20 cm below point $ G $ where the 30 N force is applied.

- **Angles:**
- The angle between the lever AB and the horizontal line at point $ B $ is 80°.

**Calculation Approach:**
To find forces $ F_1 $ and $ F_2 $, use principles of static equilibrium where sum of forces and moments around any pivot should be zero. Consider torque calculations around point $ A $ and apply equilibrium conditions to resolve unknown forces. Take into account the angles given for precise computation.

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