Understanding Work with Conservative Forces | Physics

In summary, the concept of work and energy can be confusing when dealing with conservative forces. The work-energy theorem states that the net work equals the change in kinetic energy, but in situations where both potential and kinetic energy seem to increase, it is important to consider all external forces acting on the system. In the example given, the external force from muscles adds energy to the system, resulting in an increase in both potential and kinetic energy. However, in order to conserve total energy, some other form of energy, such as biochemical energy, must decrease. Including the entire body in the system can help clarify the changes in potential and kinetic energy. Overall, understanding the role of non-conservative forces is key to fully grasping the concept of work and
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pokemon123
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so the concept of work I've never really understood (even after a year and a half of physics classes rip). What mainly confuses me is when the work done is positive or negative. From what I understand the net work=deltaKE or net work=-PE assuming energy is conserved (so if an external force was in the system this thereom does NOT hold true). But I get confused by this in situations where you seemingly are able to gain kinetic energy and potential energy despite having conservative forces.

For example: I define the system as the Earth, my hand, and a rock. If I lift the rock up and accelerate it shouldn't it gain KE because vf>vi (my hand is accelerating too so it gains KE) but isn't my hand and the rock also gaining PE because we are higher than before. Someone tried to explain this to me by saying that the reason why we're accelerating is because the overall potential energy is less at the top than at the bottom (i.e other PE like spring, electric) but I can't think of another significant type of PE in this scenario.

So yeah I'm confused how you seemingly can gain both PE and KE with conservative forces despite the work energy theorem stating the contrary.

note: I have only taken algebra so i would not understand calculus.
 
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pokemon123 said:
If I lift the rock up and accelerate it shouldn't it gain KE because vf>vi (my hand is accelerating too so it gains KE) but isn't my hand and the rock also gaining PE because we are higher than before
Yes. Note that this is not an isolated system. There is an external force from your muscles acting on your hand. That external force adds energy to the system resulting in an increase of both PE and KE.

The easiest way to fix that is to include your whole body as part of the system instead of just your hand. When you do that you find that the PE of your body goes down. The gravitational PE goes up, but the chemical PE goes down more. In the end the system has the same energy, but some of the energy has changed from chemical PE to gravitational PE and KE.
 
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The work-energy theorem says Δ(KE) = WNet and always holds true. In your example, when you accelerate your hand holding a rock up, the system gains both potential and kinetic energy. The sum of the two increases in time, which means that mechanical energy is not conserved. This increase in mechanical energy is accounted for by the expenditure of biochemical energy. The rest of you arm that is attached to your hand and is not part of the system exerts a non-conservative force that does work on the system. You burn calories in order to increase the mechanical energy of the rock and your hand so that the total energy change, biochemical plus mechanical, is zero. Total energy is always conserved so that if you see that the mechanical energy of a system increases and you have accounted for all the conservative forces that do work on the system, you have to conclude that there must be some non-conservative force at play. A rocket shot up in space gains mechanical energy at the expense of the chemical energy in the rocket fuel.
 
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Dale said:
Yes. Note that this is not an isolated system. There is an external force from your muscles acting on your hand.

The easiest way to fix that is to include your whole body as part of the system instead of just your hand. When you do that you find that the PE of your body goes down. The gravitational PE goes up, but the chemical PE goes down more.

ah I see, Thanks! this definitely makes me understand the concept of work energy thereom better.

thank you too kuruman!
 
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What is work and how is it related to conservative forces?

Work is a physical concept that measures the transfer of energy from one object to another. In the context of conservative forces, work is done when an object is moved against a conservative force, such as gravity or a spring. The amount of work done is equal to the product of the force and the displacement of the object.

How can I determine if a force is conservative?

A force is considered conservative if the work done by or against it is independent of the path taken. In other words, if the work done by a force is the same regardless of the path taken, then the force is conservative. This can be determined using a mathematical concept known as the line integral.

What is potential energy and how is it related to conservative forces?

Potential energy is the energy possessed by an object due to its position or configuration. In the context of conservative forces, potential energy is closely related to work. When work is done against a conservative force, the energy is stored as potential energy. This potential energy can be converted back to kinetic energy when the object moves in the opposite direction.

How do conservative forces affect the motion of an object?

Conservative forces do not affect the overall motion of an object, but they do affect the potential energy of the object. As an object moves against a conservative force, its potential energy increases, and as it moves in the direction of the force, its potential energy decreases. This exchange between potential and kinetic energy results in the object oscillating around a stable equilibrium position.

What are some examples of conservative forces?

Some common examples of conservative forces include gravity, elastic forces, and electrostatic forces. These forces are conservative because the amount of work done against them is independent of the path taken. Other examples include magnetic forces, frictional forces, and tension forces, which are considered non-conservative because they dissipate energy as heat or sound.

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