Potential Energy: Differentiating to Find Force

In summary, potential energy is the energy stored in an object due to its position or condition. It is related to force because force is needed to change an object's position, thus affecting its potential energy. The formula for calculating potential energy is PE = mgh, and to find force, we use the formula F = -dPE/dx. Real-life examples of potential energy being differentiated to find force include roller coasters and springs.
  • #1
omarMihilmy
31
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To find the force we will differentiate the function with respect to x (dx)
My problem is with the solution
If we differentiate:
dU/dx = 9x^2 - 7

From where does the negative come from also the j component?
 
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  • #2
You should have used the homework template, then you have written the relevant equations. What equation is relevant for finding force from potential energy?
 
  • #3
F = dU/dx
 
  • #4
That is not correct.
 
  • #5
Correct me if I am wrong
 
  • #6
Why are you disregarding the y-component when you differentiate?
 

What is potential energy?

Potential energy is the energy that an object possesses due to its position or condition. It is often described as stored energy, as it has the potential to do work when it is released.

How is potential energy related to force?

Potential energy and force are related because force is required to change the position or condition of an object, which in turn affects its potential energy. For example, lifting an object to a higher position requires force and increases its potential energy.

What is the formula for calculating potential energy?

The formula for potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object.

How is potential energy differentiated to find force?

To differentiate potential energy to find force, we use the formula F = -dPE/dx, where F is the force, PE is the potential energy, and x is the position or variable that is changing. This formula allows us to calculate the force required to move an object to a specific position or height.

What are some real-life examples of potential energy being differentiated to find force?

One example is a roller coaster, where the potential energy is differentiated to find the force required to move the roller coaster cars up and down the track. Another example is a spring, where the potential energy is differentiated to find the force exerted on an object attached to the spring at different positions.

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