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4. Corresponding displacement/Work absorbing displacement
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Today, we'll discuss corresponding displacement, which is the displacement occurring in the direction of the applied force. Can anyone explain why this is important?
Because it tells us how much the object moves due to the force applied.
Exactly! This is why we call it work absorbing displacement, as it directly relates to the work done by the force. Remember that this displacement is proportional to the applied force.
So, if we increase the force, the displacement must also increase?
Correct! We can summarize this relationship with the equation . Does anyone remember what represents?
The influence coefficient!
That's right! The influence coefficient shows how responsive the displacement is to the applied force.
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Next, let's discuss the energy stored in a body due to the applied force. If we apply a force , how do we express the energy stored in the body?
Is it just ?
Exactly! This is valid for a single force acting on the body. The energy stored depends on how far the body moves in the direction of this force.
What if multiple forces are at play?
"Great question! In that case, we would need to sum the energies associated with each force. So, the total energy stored would be expressed as:
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Now let's consider some real-world implications of corresponding displacement. Can anyone give me an example where this concept is essential?
Like in bridge construction? The materials must be able to absorb work without failing!
Absolutely! Engineers need to account for the displacement when designing structures to ensure they can handle the applied loads without permanent deformation.
So, understanding these concepts ensures safety in design, right?
Exactly! It’s crucial for ensuring structural integrity. Also, knowing how energy is stored can help in materials selection.
Overview
Short Summary
This section introduces the concepts of corresponding displacement and work absorbing displacement, explaining their role in energy methods related to deformation under applied forces.
Medium Summary
The section discusses the concept of corresponding displacement as the displacement parallel to the applied force and defines it as the work absorbing displacement. It explains the mathematical relationship between the displacement and the force and introduces the energy stored in an elastic body when subjected to force.
Detailed Summary
Detailed Summary
In this section, we explore the concept of corresponding displacement, defined as the displacement that occurs at the point of application of a force and in the direction of that force. This component of displacement is crucial because it is responsible for the work done by the applied force, leading to its designation as work absorbing displacement. The mathematical relationship between the force and this displacement is expressed as:
Where, is the influence coefficient, indicating how displacement at a point responds to an applied force. Further, we delve into the energy stored within a body due to this displacement when a force is applied. This is expressed initially as a simple product of force and corresponding displacement but elaborated to account for cases with multiple forces, showing that total energy stored can be represented in terms of the contribution of each force acting upon the body.
Audio Book
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Create a free accountThe displacement of the body at the point of application of force and in the same direction as the applied force is called the corresponding displacement. As this component of displacement is also responsible for the actual work done by the force, it is therefore also called the work absorbing displacement.
Detailed Explanation
Corresponding displacement refers to how much a body moves in the same direction as an applied force. This specific movement is important because it is the part of the displacement that contributes to the work done by that force. Therefore, we can think of corresponding displacement as a measure of how effectively the force is being utilized to cause movement.
Examples & Analogies
Imagine pushing a swing. The swing moves in the same direction as your push, which is the corresponding displacement. If you push directly sideways, the swing doesn't move forward or backward – it stays in place instead of doing work. The movement in the direction of your push is what counts as the work being done on the swing.
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Create a free accountSuppose we apply force at point 1 and measure the corresponding displacement δ₁, then δ₁ ∝ F or δ₁ = k₁ F.
Detailed Explanation
The relationship expresses that the corresponding displacement (δ₁) is directly proportional to the applied force (F). 'k₁' is a proportionality constant, often referred to as the influence coefficient, which relates how much displacement occurs per unit of force applied. Essentially, if you double the force, you double the displacement, highlighting a linear relationship.
Examples & Analogies
Think of a rubber band. If you pull it with a certain force and stretch it by a specific amount, the more you pull it, the more it stretches. If you double the pull, it may double the stretch. Here, the stretch of the rubber band represents the corresponding displacement, while your pulling force is what you're measuring. This relationship makes it clear how displacement responds to applied forces.
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Key concepts
Core takeaways and short definitions to help you quickly recall the key ideas from this section.
- Corresponding Displacement:
Displacement in the direction of an applied force.
- Work Absorbing Displacement:
Component responsible for the work done by a force.
- Influence Coefficient:
Proportionality constant relating force and displacement.
- Energy Stored:
The energy accumulated in a deformable body due to applied forces.
Examples
Step-by-step examples to apply the section's ideas and test your understanding.
Example of corresponding displacement can include a spring compressing under weight. The displacement caused directly corresponds to that weight.
In construction, corresponding displacement must be calculated for materials used in structures to ensure safety and performance under load.
Memory aids
Imagine a weightlifter lifting weights. Each time they lift, the barbell bends slightly. That bend is the work absorbing displacement, capturing the effort put in.
DISPLACE - Displacement In the direction of applied force Means Absorption of work done.
Flash Cards
Glossary
Corresponding Displacement
Displacement of a body at the point of application of an external force, occurring in the direction of the force.
Work Absorbing Displacement
The component of displacement responsible for the actual work done by the applied force.
Influence Coefficient (k)
A measure of the relationship between the applied force and the resulting displacement.
Energy Stored
Work done by the applied force that is stored as potential energy within the material of the body.