Math Problem Statement
What is the work done by the weight of the crate?
Solution
Let's analyze the problem step by step.
Problem Summary:
- A 321-kg crate hangs from a rope of length 11.4 m.
- You apply a horizontal force to move the crate 3.8 m to the right.
- The applied force required was 1108.4 N.
- We're interested in calculating:
- Work done by the weight of the crate.
- Work done by the force applied on the crate.
To solve for the work done by the weight of the crate:
-
Weight of the Crate: The weight of the crate is given by: where is the mass of the crate, and is the acceleration due to gravity.
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Vertical Displacement: In this scenario, the force of gravity acts vertically downward. The crate, however, is only displaced horizontally by . There is no vertical movement of the crate, so the vertical displacement () is zero. Since work is defined as , and in this case, between the weight (vertical) and displacement (horizontal):
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Work Done by Weight: Therefore, the work done by the weight of the crate is:
Conclusion: The work done by the weight of the crate is 0 J.
Would you like me to help calculate the work done by the applied force or discuss any other details?
Related Questions:
- How is the work done calculated when the force is not aligned with displacement?
- What is the difference between conservative and non-conservative forces in terms of work done?
- How does gravitational potential energy change if the crate moves vertically?
- What happens to the work done if the crate were moved diagonally instead of horizontally?
- Can you explain how tension in the rope changes as the crate is displaced horizontally?
Tip: In problems involving forces, always remember to decompose forces into components that are parallel and perpendicular to the direction of movement to correctly determine the work done.
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Math Problem Analysis
Mathematical Concepts
Work and Energy
Forces
Trigonometry
Formulas
W = F \cdot d \cdot \cos(\theta)
W = F \cdot displacement
Weight (W) = mg
Theorems
Work-Energy Theorem
Suitable Grade Level
Grades 10-12 (Physics)
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