calculus

Consider the motion of a particle of mass m falling vertically under the earth’s gravitational field, and suppose the
downward motion is opposed by a frictional force p(v) dependent on the velocity v(t) of the particle. Then the
velocity satisfies the equation
mv0(t) = 􀀀mg+ p(v); t � 0
Let m = 1kg, g = 9:8m=sec2, and v(0) = 0. Using Euler’s, Heuns’, and Classical Runge-Kutta methods, solve the
differential equation for 0 � t � 20 and for the following choices of p(v):
1. p(v) = 􀀀0:1v
2. p(v) = 0:1v2
Find the answers to at least four digits accuracy. Graph the function v(t). Compare the solutions.

  1. 👍 0
  2. 👎 0
  3. 👁 96

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Consider the motion of a particle of mass m falling vertically under the earth’s gravitational field, and suppose the downward motion is opposed by a frictional force p(v) dependent on the velocity v(t) of the particle. Then the

    asked by help on May 18, 2014
  2. physics

    Consider the Earth and the Moon as a two-particle system. (a) Find the gravitational field of this two-particle system at the point that is exactly halfway between the Earth and the Moon. (Assume a radial direction r̂ from the

    asked by joy on February 16, 2018
  3. physics

    1. What did Newton conclude about the force that pulls apples to the ground and the force that holds the moon in orbit? 2. What does the very small value of the gravitational constant G (in standard units) tell us about the

    asked by confused on July 13, 2010
  4. Physical Science

    The frequency of circular motion for a charged particle moving around in the presence of a uniform magnetic field does not depend on ... a)The radius of the circle b)The mass of the particle c)The charge of the particle d)The

    asked by Stephanie on March 13, 2010
  5. Physics

    Calculate the electric field which must be applied vertically to hold an electron steady in the earth’s gravitational field. Assume that the charge to mass ratio of the electron is 1.758×1011 C kg-1 and that the acceleration

    asked by Olivia on May 17, 2011
  6. physics

    A PARTICLE OF MASS M IS SHOT WITH an initial velocity v making an angle b with the horizontal,the particle moves in the gravitational field of the earth. find the angular momentum of the particle about the origin when the particle

    asked by mechanics on August 22, 2013
  7. physics

    A newly-discovered plant, "Cosmo", has a mass that is 4 times the mass of the Earth. The radius of the Earth is Re. The gravitational field strength at the surface of Cosmo is equal to that at the surface of the Earth if the

    asked by Hannah on January 19, 2008
  8. Physics

    A charged particle is projected into a uniform B-field. Its velocity vector is perpendicular to the B-field vector. What type of path will the particle travel? Neglect gravity. Answer straight line motion elliptical motion

    asked by tom on July 16, 2013
  9. Solar system

    According to the theory of gravitation, the earth must be continually “falling” toward the sun. If this is true, why does the average distance between earth and sun not grow smaller? Without gravity, the Earth would go in a

    asked by Kim on January 1, 2007
  10. Physics

    The frequency of circular motion for a charged particle moving around in the presence of a uniform magnetic field does not depend on ... The radius of the circle The mass of the particle The charge of the particle The magnitude of

    asked by mm. on March 15, 2010

More Similar Questions