Something wrong with the equations of work

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In summary, the conversation revolved around the equation F*d=1/2*mv2 and the speaker's attempts to manipulate it. However, it was pointed out that their assumption that v=d/t was incorrect, leading to an incorrect result of 1=1/2. This was explained by the fact that the force, F, was assumed to be constant, causing the velocity, v, to change and making the initial assumption invalid.
  • #1
nhmllr
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Ok, so recently I was introduced work, being
F*d=1/2*mv2
So, naturally I started playing around with it
m*d*v/t = 1/2*m*d/t*d/t
m*d2/t2 = 1/2 * m*d2/t2
1 = 1/2
What did I do wrong here? Did I divide by zero somewhere or something?
(I know that these equations are not relativistically correct but this seems ridiculous)
 
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  • #2
You assume that v=d/t which isn't correct unless v is constant which is not the case since you assume a (constant) force F is acting which changes v. If we assume F is constant then d=1/2 * v * t or v=2d/t where v here represents the final velocity after distantce d has been traveled. If you replace that v then you finally get 1=1.
 

What is work and how is it calculated?

Work is the measure of energy transfer that occurs when a force is applied to an object and the object moves in the direction of the force. It is calculated by multiplying the magnitude of the force by the displacement of the object in the direction of the force.

What are the basic equations of work?

The most basic equation of work is W = F * d, where W is work, F is force, and d is displacement. There are also variations of this equation, such as W = F * cos(theta) * d, which takes into account the angle between the force and displacement.

What could be wrong with the equations of work?

There are a few common errors that can occur when working with the equations of work. One possible mistake is using the wrong units for force and displacement, which can result in incorrect calculations. Another error could be not taking into account the direction of the force and displacement, which can lead to a negative value for work.

How can I check if my work calculations are correct?

To check if your work calculations are correct, you can use the principle of conservation of energy. This states that the total amount of energy in a system remains constant, so the work done on an object should equal the change in its kinetic or potential energy. If your calculated work does not match the change in energy, then there may be an error in your equations.

What are some real-life applications of the equations of work?

The equations of work have many real-life applications, including calculating the power output of machines, determining the amount of force needed to move an object, and understanding the work done by muscles in the human body. They are also used in various fields of engineering and physics, such as in designing and analyzing mechanical systems.

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