College Physics w/Calculus

(a) What is the escape speed on a spherical asteroid whose radius is 570 km and whose gravitational acceleration at the surface is 3.1 m/s2?
(b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?
(c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?

I know how to do the first question (conservation of mechanical energy): however, I have no idea how to do the other two problems

  1. 👍
  2. 👎
  3. 👁
  1. (a) Potential enegy increase = -M*Integral of g(r) dr (R to infinity) = -M*g(R)*R^2/r^2 dr
    = M*g(R)/R = (1/2) M Vo^2
    Vo = sqrt(2g(R)*R)
    = 1880 m/s
    is the escape velocity

    (b) PE change = M*[g(R)*R^2(1/R - 1/r) g(R)*R/r]
    = (1/2) M V^2

    2 g(R)* R^2 (1/R - 1/r) = V^2

    2g(R)*R - V^2 = 2g(R)*R^2/r
    = 3.53*10^6 - 10^6 m^2/s^2 = 2.53*10^6 m^2/s^2

    r = 2*(3.1 m/s^2)(570*10^3)^2 m^2/2.53*10^6 m^2/s^2
    = 7.96*10^5 m
    = 796 km. Subtract the asteroid radius (570 km) from that to get the altitude above the surface

    (c) The kinetic energy at R will equal the PE decrease in going from R + 1000 km to R altitude

    1. 👍
    2. 👎
  2. dingus

    1. 👍
    2. 👎
  3. chad

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A non-rotating spherical planet with no atmosphere has a mass M and radius R. A particle is fired off from the surface with a speed equal to 3/4 the escape speed. Calculate the farthest distance it reaches (measured from the

  2. Physics

    Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m. (a) Find the moment of inertia for each object as it rotates about the axes shown in the

  3. physics

    A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder

  4. Algebra

    The radius of the event horizon of a black hole (the point at which it is impossible to escape the black hole because the escape velocity would exceed the speed of light) is given by the formula r = 2Gm/c^2, where G is the

  1. Physics

    A ball is tossed straight up from the surface of a small spherical asteroid with no atmosphere. The ball goes to a height ewual to the asteroid's radius and then falls straight down towardd the surface of the asteroid. What forces

  2. Algebra 1

    Suppose a spherical asteroid has a radius of approximately 9.0 x 10^2m. Use the formula 4/3*pi r^3 to find the approximate volume of the asteroid. 2.57 * 10^9 m^3 1.07 * 10^4 m^3 2.54 * 10^10 m^3 4.51 * 10^10 m^3 I've worked

  3. Physics

    An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.5× 104 kg, and the force causes its speed to change from 7000 to 5000m/s. (a) What

  4. Physics Question......many thanks

    A projectile is shot directly away from Earth's surface. Neglect the rotation of Earth. (a) As a multiple of Earth's radius RE, what is the radial distance a projectile reaches if its initial speed is one-fifth of the escape speed

  1. Physics

    An asteroid revolves around the Sun with a mean orbital radius twice that of Earth's. Predict the period of the asteroid in Earth years. (6.38*10^6 radius) I don't understand how to solve this problem.

  2. Physics

    Speed of Asteroids With the same Radius? Two spherical asteroids have the same radius R . Asteroid 1 has mass M and asteroid 2 has mass 2M. The two asteroids are released from rest with distance 10R between their centers. What is

  3. Physics

    A non-rotating spherical planet with no atmosphere has a mass M and radius R. A particle is fired off from the surface with a speed equal to 3/4 the escape speed. Calculate the farthest distance it reaches (measured from the

  4. Physics

    A particle with a charge of -60.0 nC is placed at the center of a nonconducting spherical shell of inner radius 20.0 cm and outer radius 33.0 cm. The spherical shell carries charge with a uniform density of -2.02 µC/m3. A proton

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