Is Work the Same as Kinetic Energy?

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• ForceBoy
In summary, the work-energy theorem states that if you put energy into an object, the object's energy increases by that much.
ForceBoy
Kinetic Energy is defined as the product of half the mass of an object multiplied by the square of its velocity. Using this I derived the end formula. Work is as follows:

KE = ½(m⋅v2)

Because v = vi +at, if vi = 0,

KE = ½(m⋅(at)2)

KE = ½(m⋅a2⋅t2)

KE = ½(m⋅a⋅a⋅t2)

Substituting F for m⋅a (force is equal to mass by acceleration),

KE = ½(F⋅a⋅t2)

Displacement is equivalent to vi⋅t +½⋅a⋅t2
It was stated that vi = 0, therefore s = ½⋅a⋅t2
Making this replacement in the equation yields:

KE = F⋅ s

Where F is a force and s is a displacement. This is also the formula for work. Then, is work the same thing as Kinetic Energy? Can the formula for work be used to calculate Kinetic Energy?

Yes, that's often called the "Work-Energy Theorem". It's just conservation of energy. If you put work into the motion of an object, that object's kinetic energy increases by the amount of work you put in.

Your derivation used some formulas that assume straight line motion, constant force and constant acceleration. But it's a more general result than that. If you put energy into an object, the object's energy increases by that much.

That concept can be used in all sorts of situations. Suppose you throw a ball up in the air. How high will it go? Answer: It will rise until its initial kinetic energy (1/2)mv^2 has all been turned into work against gravity mg * h. So you set those two things equal and solve for h. KE = work.

If you have an object moving with velocity v and a frictional force F acts on it, how far does it slide before friction stops it? It takes until the work Fd done by friction is equal to the amount of energy (1/2)mv^2 that the object started with. Again, set KE = work.

ForceBoy
Thank you. Have a good day.

1. Is the derived formula always valid?

The validity of a derived formula depends on the accuracy of the assumptions and data used in its derivation. It is possible for a formula to be valid in certain situations but not in others.

2. How can I determine if a derived formula is valid?

To determine the validity of a derived formula, one must carefully examine the assumptions and data used in its derivation and compare it to real-world observations or experimental results. It is also important to consider the limitations and potential sources of error in the derivation process.

3. Can a derived formula be valid if it does not match experimental results?

No, a derived formula should accurately reflect real-world observations or experimental results in order to be considered valid. If a derived formula does not match experimental results, it may indicate that the assumptions or data used in its derivation were not accurate.

4. Can a derived formula become invalid over time?

Yes, a derived formula can become invalid over time if the assumptions or data used in its derivation are no longer accurate. This could be due to changes in technology, new discoveries, or updated data.

5. What should I do if I suspect a derived formula is not valid?

If you have reason to believe that a derived formula is not valid, it is important to thoroughly review the assumptions and data used in its derivation. You may also want to consult with other experts in the field to get their opinions and potentially conduct further experiments or research to validate or refine the formula.

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