How Do You Apply Calculus to Determine Force in Physics?

[glennpagano44]

Right now I am in AP physics in High School, while also taking calculus and I need some assitance on when and how to apply the calculus (once I know to do calculus I can go from there)

Example

If Potential Energy is 5x^2+3x+7 what function is the force.

- I know you have to take derivative of the PE equation because my teacher told me.

Also because -PE=Fdcos the you get -PE/d=F. From there how do you know to put dPE/dd =F. Also how do you know not to integrate.

Thanks a lot

 

[LowlyPion]

You can look at the units if nothing else.

Forces are in Newtons N and energy is in Joules which are N-m

If you have Joules then the rate of changes in Joules by x should yield Newtons.

If you have Newtons exerted over a distance x, the integral of F⋅X (F as a function of x) yields you Joules - energy.

In your problem you're wanting to know the F as a function of x and you are given the energy potentials PE as a function of x. Hence dPE/dx should yield you your Force as a function of x.

 

[glennpagano44]

Thanks a lot LowlyPion that helped out. Anyone else have any input?