How Do You Apply Calculus to Determine Force in Physics?

  • Thread starter Thread starter glennpagano44
  • Start date Start date
  • Tags Tags
    Apply Calculus
AI Thread Summary
In physics, to determine force from potential energy, you take the derivative of the potential energy function. This is because force is defined as the negative gradient of potential energy, expressed mathematically as F = -dPE/dx. The relationship between energy and force is established through the units, where energy in Joules relates to force in Newtons over distance. When given a potential energy function, differentiating it with respect to position will yield the force as a function of position. Understanding these principles allows for effective application of calculus in physics problems involving force and energy.
glennpagano44
Messages
64
Reaction score
0
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 Alot
 
Physics news on Phys.org
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.
 
Thanks a lot LowlyPion that helped out. Anyone else have any input?
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top