Physics ( Calculus & Mecahnics )

A proton with mass m moves in one dimension.The potential-energy function is where and are positive constants. The proton is released from rest a x0 = a/b.
(a) Show that can be written as

U(x) = a
--- [ ( x0/x )^2 - x0/x ]
x0^2

Graph U(x). Calculate U(x0) and thereby locate the point on
the graph. (b) Calculate v(x) the speed of the proton as a function
of position. Graph and give a qualitative description of the
motion. (c) For what value of x is the speed of the proton a maximum? What is the value of that maximum speed? (d) What is
the force on the proton at the point in part (c)? (e) Let the proton be
released instead at x1 = 3a/B Locate the point x1 on the graph of U(x)
Calculate v(x) and give a qualitative description of the
motion. (f ) For each release point ( x = x0 and x = x1 ) what are
the maximum and minimum values of x reached during the motion?

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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.

  2. electric field

    A uniform electric field of magnitude 1.0×10^2 NC^−1 exists between two conducting plates, one of which is positively charged and the other of which is negatively charged. The plates are 10 mm apart. (a) Calculate the

  3. 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

  4. Science

    Which statement is correct about the potential energy of a car moving down a ramp? A) Potential energy remains constant because total energy is constant. B) Potential energy depends on the mass and velocity of the car. C)

  1. Physics

    A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass? Mass is eliminated when equating gravitational potential energy with kinetic energy. The mass of the ball

  2. Physics

    A force of 800 N stretches a spring a distance 0.200 m horizontally. a) What is the potential energy of the spring when it is stretched 0.200m b) What is its potential energy when it is compressed 5.00cm This is a conservation of

  3. Physics

    A metal ball is placed in a device with a spring that has been compressed past its equilibrium point so that when the spring is released, it will propel the ball into the air. The device is set up on a table one meter above the

  4. physics

    If a proton is accelerated from rest through a potential difference of 1500 V, find its final velocity. proton mass = 1.67 x10−27 kg

  1. 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

  2. physics

    A proton moves in a constant electric field E from point A to point B. The magnitude of the electric field is 4.2 x10^4 N/C; and it is directed as shown in the drawing, the direction opposite to the motion of the proton. If the

  3. Biology

    When the electron moves back to lower energy levels in an electron transport chain, energy is a) stored or b) released c)converted to matter d)used to make O2 I'm not sure how to answer this cause isn't it stored as potential

  4. Physics

    A proton with mass 1.67×10−27 kg and charge 1.60×10−19 C accelerates from rest in a uniform electric field of strength 500 N/C. (a) What is the magnitude of the acceleration of the proton? (b) How long does it take the

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