For positive a, b, the potential energy, U, of a particle is given by
U = b (a^2 over x^2 - a over x) for x is greater than 0

a) find the x-intercept

b) find the asymptotes

c)compute the local minimum

d) sketch the graph

I don't know how to start this problem
Well first I'd assume that we would have to find the derivative
so u= (a^2x^-2) -ax^-1
so u' = -2a^2x^-3 - ax^-2?

and then do we have to factor and set it equal to zero to find the x-intercepts?
Are finding the x-intercepts the same thing as finding the critical points?

How do you find the asymptotes? Do we just graph what we got for the derivative and then see? But wait we can't graph the derivative because of the many unknown variables.

I am unable to find the x-intercept, asymptotes, local minimum and graph. Please help me!

  1. 👍
  2. 👎
  3. 👁
  1. U = b (a^2 over x^2 - a over x)
    or, more readably,

    U = b(a^2/x^2 - a/x)
    We can ignore b, since it does not affect where the extrema occur. It's just a scale factor.

    U = a^2/x^2 - a/x = (a^2-ax)/x^2 = a(a-x)/x^2
    clearly the asymptote is at x=0
    (asymptotes occur when the denominator is zero)

    U=0 where x=a

    dU/dx = -2a^2/x^3 + a/x^2
    = (-2a^2+ax)/x^3 = a(x-2a)/x^3
    clearly dU/dx=0 when x=2a

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science (energy)

    1. What similarities do nuclear energy and chemical energy share? Choose all that apply. A. Both are types of kinetic energy. B. Both are types of potential energy. [CORRECT!] C. Both involve magnetic energy. D. Both involve

  2. Science- Electric and Magnetic Potential Energy

    1. At which position will the bar magnets most likely experience the least magnetic potential energy between them? D - position 4 2. A positively charged test object is moving toward the positive source charge in an electric

  3. Physics

    what forms of energy are involved in the following situations? (choices: kinetic energy, potential energy - gravitational potential energy, elastic potential energy) a. a bicycle coasting along a level road b. heating water c.

  4. Science

    Classify each of the following as examples of kinetic or potential energy. a) a car driving along a level road. b) an elastic band is stretched to twice its normal length c) a book is at rest on the top shelf of a bookcase d) a

  1. Physics

    A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x + 4) N describes this force, where x is in meters. As the particle moves along the x axis from x = 1.40 m to x = 5.80 m, calculate the following. (a)

  2. Physics Please help !!

    A single conservative force = (6.0x - 12) N where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 23 J at x = 0. (a) Write an expression for U as

  3. Science(Stuff to do like with magnets!)

    1. A positively charged test object is moving toward the positive source charge in an electric field. What happens next??? A. its potential energy decreases. B. Its potential energy increases. C. Its potential energy stays the

  4. Physics

    The motion of a particle connected to a spring is described by x= 10sin(πt + π/3). At what time (in s) is the potential energy equal to the kinetic energy?

  1. Physics

    please check: Which of the following energy forms is associated with an object in motion? a. potential energy b. elastic potential energy c. nonmechanical energy d. kinetic energy i think its B Which of the following energy forms

  2. Science

    We know that the law of conservation of energy states that energy can not be created or destroyed. It only changes form. Consider this energy transformation diagram. Assume that the energy input in this case is chemical potential

  3. science(answer please)

    please answer these 1.what similarities do nuclear energy and chemical energy share?pick all that apply A.both are types of kinetic energy. B.both are types of potential energy C.both involve magnetic energy D.both involve stored

  4. Science

    The potential energy of a system of two particles is given by u(x)=a/x2-b/x. Find minimum potential energy of the system, where x is the distance of separation and a, b are positive constants.

You can view more similar questions or ask a new question.