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Understanding Work Done
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Yesterday, we talked about work in a mechanical context. Can anyone explain how 'work done' can differ in physics compared to how we use it in day-to-day language?
In everyday life, work can mean any effort, like studying or cleaning, but in physics, it has a precise definition.
Great! That's called the difference between colloquial and scientific definitions. Since work is *defined as force times distance*, can someone give me a scenario where this applies?
When pushing a box across the floor, if I apply a force and it moves, I do work.
Exactly! Remember, work can be calculated as W = FΒ·dΒ·cos(ΞΈ), where ΞΈ is the angle between the force and displacement. This brings us to a fun mnemonic: 'Work is done When you Push and Move.'
What about cases when no work is done?
If there's no displacement, or the force is perpendicular to motion, work done is zero. Letβs summarize: In physics, 'work done' is a specific term calculated as the force multiplied by distance and specifically applies in scenarios where displacement occurs. Everyone understood?
Nature of Forces in Work Done
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Now, let's discuss forces that can do 'negative work.' Who can give me an example?
When friction opposes motion, it does negative work, right?
Precisely! So if you have a constant pushing force, but friction is acting against it, how would we calculate the net work done?
We would consider both the applied force and frictional force to find the net force and then apply that over the distance.
Correct! And this leads us to understand conservation laws. We know that the work-energy principle states that the work done equals the change in kinetic energy. Keep this in mind as it ties into why mechanical systems often focus on forces and work.
Can negative work affect the kinetic energy?
Absolutely! Negative work would reduce the kinetic energy of an object. Reviewing our concepts: when considering work, always define the forces acting and remember that energy can be lost to negative work. Letβs review what we learned today.
Conservation and Calculation
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To wrap up, we should consider the conservation of momentum and energy. How do they relate to the work done?
If forces acting are conservative, the mechanical energy in the system stays the same, right?
Correct! When only conservative forces act, total mechanical energy remains constant. However, if non-conservative forces are present, like friction, how can we summarize energy considerations?
The net work done by non-conservative forces equals the change in the total mechanical energy.
Perfect! Additional note: the work done can also sometimes reveal information about forces acting even when not all forces are known. This is the essence of the work-energy theorem. Letβs recap our learning today about forces, energy, and momentum conservation, ensuring we grasp their ties to work done.
Introduction & Overview
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Quick Overview
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Points to Ponder highlights the nuances of calculating work done, the nature of forces in relation to work, and the conservation of energy principles. It brings attention to misconceptions and clarifies essential definitions within the realm of physics.
Detailed
Detailed Summary
This section focuses on the intricacies of interpreting and calculating work and energy in physical contexts. It outlines the incomplete nature of phrases like 'calculate the work done' without specific references to forces and contexts. The definition of work as a scalar quantity that can be either positive or negative is discussed, emphasizing that work done by forces such as friction is negative, affecting energy calculations. Important principles regarding the conservation of energy and momentum are reiterated, along with the nuances of calculating work for specific forces. Moreover, this section highlights the relationship between the work-energy theorem and Newton's laws, indicating how these concepts guide our understanding of physical interactions.
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Completeness of Work Calculation
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- The phrase βcalculate the work doneβ is incomplete. We should refer (or imply clearly by context) to the work done by a specific force or a group of forces on a given body over a certain displacement.
Detailed Explanation
When calculating work, it's important to specify which force is doing the work and over what distance. For example, if someone lifts a box, we need to clarify that we're talking about the gravitational force acting on the box while it is lifted a certain height. Clarifying these details ensures that the calculation is accurate and meaningful.
Examples & Analogies
Imagine telling someone to calculate how much energy they used while doing housework. Without specifics, they might not realize they need to consider the force of their own muscles in lifting, the weight of the vacuum cleaner, or even how far they vacuumed.
Nature of Work as a Scalar
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- Work done is a scalar quantity. It can be positive or negative unlike mass and kinetic energy which are positive scalar quantities. The work done by the friction or viscous force on a moving body is negative.
Detailed Explanation
In physics, work is a scalar quantity, which means it has magnitude but no direction. Work can be positive when it enhances energy (like lifting a ball), and negative when it opposes energy (like friction slowing down a sliding object). This is significant because it can imply loss of energy in systems where work done is negative.
Examples & Analogies
Think of pushing a heavy box across a floor. If the box is heavy and you push it, you are doing positive work. However, if there's friction, it might slow down despite your efforts, which can be thought of as negative work. It's akin to running against a strong wind β while you're exerting effort, the wind makes it harder for you to move forward.
Mutual Forces and Work Done
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- For two bodies, the sum of the mutual forces exerted between them is zero from Newtonβs Third Law, F12 + F21 = 0. But the sum of the work done by the two forces need not always cancel, i.e., W12 + W21 β 0. However, it may sometimes be true.
Detailed Explanation
According to Newtonβs Third Law, if body A exerts a force on body B, body B exerts an equal and opposite force on body A. While this law dictates the balance of forces, the work done by each force on the other can differ significantly. This means one force could do positive work while the other does negative work, depending on the situation.
Examples & Analogies
Imagine two ice skaters pushing off each other. They exert equal forces, but if one skater moves further than the other, the work done by the pushing force is not the same. One skater gets pushed back farther, implying that one has traveled more distance than the other, highlighting the imbalance in work done.
Calculating Work Done
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- The work done by a force can be calculated sometimes even if the exact nature of the force is not known. This is clear from Example 5.2 where the WE theorem is used in such a situation.
Detailed Explanation
In certain contexts, such as when the work-energy theorem is applied, one can calculate the work done even without knowing all details about the forces involved. The theorem states that the work done is equal to the change in kinetic energy. Therefore, we can make calculations based on the energies before and after an event, irrespective of intermediary forces. It simplifies situations where complex dynamics are present.
Examples & Analogies
If you know how fast a car was going before a crash and how fast it was going after, you can still calculate the work done in that crash without needing all the specifics of the forces acting on it. Itβs like calculating how much a hill increased your speed on a bike ride without knowing the exact incline.
Work-Energy Theorem Relationship
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- The WE theorem is not independent of Newtonβs Second Law. The WE theorem may be viewed as a scalar form of the Second Law. The principle of conservation of mechanical energy may be viewed as a consequence of the WE theorem for conservative forces.
Detailed Explanation
The work-energy theorem links work done to changes in kinetic energy, which is essentially an extension of Newton's Second Law. The conservation of energy, which states that total mechanical energy remains constant when only conservative forces act, derives from this relationship because it implies that any work done transforms energy forms but doesn't create or destroy energy.
Examples & Analogies
Think of a rollercoaster. As it climbs (doing work against gravity), it gains potential energy. When it comes down, that potential energy converts back into kinetic energy as it speeds up. Both principles of force application and energy conservation hand-in-hand describe the ride experience.
Valid Frames of Reference
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- The WE theorem holds in all inertial frames. It can also be extended to non-inertial frames provided we include the pseudoforces in the calculation of the net force acting on the body under consideration.
Detailed Explanation
The work-energy theorem applies universally in all inertial frames where laws of motion are straightforward. Even in accelerated (non-inertial) frames, we can still use it by accounting for fictitious forces, like considering how the feeling of being pushed back in your seat in a speeding car is just a result of acceleration.
Examples & Analogies
Imagine you're in a moving elevator. You feel heavier when it accelerates upward. If you want to calculate how hard youβre pushing against the floor, itβs more complex because that acceleration needs to be considered as an additional force acting on you.
Potential Energy Assumptions
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- The potential energy of a body subjected to a conservative force is always undetermined up to a constant. For example, the point where the potential energy is zero is a matter of choice. For the gravitational potential energy mg h, the zero of the potential energy is chosen to be the ground. For the spring potential energy kx2/2, the zero of the potential energy is the equilibrium position of the oscillating mass.
Detailed Explanation
Potential energy depends on reference points. When calculating gravitational or spring potential energy, we choose where this energy is considered 'zero'. This means that potential energy is relative β it can change based on the chosen reference point, allowing us flexibility based on the problem being addressed.
Examples & Analogies
Think about a book on a shelf. If we say the shelf is two meters above the ground, then the potential energy is based on that height. If we move the shelf up to three meters and don't adjust our zero-point, the energy would increase without ever adding any additional height from the perspective of the book itself β itβs simply a product of where we define our reference point.
Existence of Conservative Energy
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- Every force encountered in mechanics does not have an associated potential energy. For example, work done by friction over a closed path is not zero and no potential energy can be associated with friction.
Detailed Explanation
Not all forces allow for potential energy calculations. Non-conservative forces like friction convert mechanical energy to thermal energy, and thus do not allow for a simple potential energy description since thereβs energy loss to heat. The energy lost in overcoming friction cannot be stored as potential energy.
Examples & Analogies
Imagine sliding down a hill. If there's friction, you lose energy as heat β thatβs energy that canβt be recovered like potential energy could be if you were at the top of the hill before descending. That loss from friction is akin to taking one step forward in your uphill battle only to slide back down again.
Collision Energy Conservation
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- During a collision: (a) the total linear momentum is conserved at each instant of the collision; (b) the kinetic energy conservation (even if the collision is elastic) applies after the collision is over and does not hold at every instant of the collision. In fact, the two colliding objects are deformed and may be momentarily at rest with respect to each other.
Detailed Explanation
In collisions, momentum is always conserved, which means total momentum before the collision equals total momentum afterward. However, kinetic energy may not be conserved, particularly in inelastic collisions where objects may deform and energy is dissipated. This means while they might briefly stop moving relative to one another, momentum remains unchanged throughout the interaction.
Examples & Analogies
In a car crash, while the cars may crumple and energy is lost, the total momentum of both vehicles before and after the crash can still be accounted for. Itβs like a dance where partners may lose sync but still keep the rhythm of the dance overall!
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Work: Defined as force multiplied by displacement.
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Conservation of Mechanical Energy: Total energy remains constant for conservative forces.
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Net Work: The work done by all forces acting on an object.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Calculating work done when pushing a box across the floor against friction.
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Finding the net work done in a pendulum motion considering air resistance.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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When you push and you move, work is done, it grooves!
π Fascinating Stories
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Imagine a strong person trying to lift a heavy box. If they can't move it at all, even if they're trying hard, they haven't done any work. But once they manage to lift it, they've done work!
π§ Other Memory Gems
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Think of W=FΒ·d as 'Work for Force on Distance.'
π― Super Acronyms
WFD = Work, Force, Distance - Remember this for calculating work!
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Work
Definition:
The product of force and displacement in the direction of the force.
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Term: Conservative Force
Definition:
A force that does not change the total mechanical energy of a system.
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Term: NonConservative Force
Definition:
A force that results in a change of mechanical energy; e.g., friction.