The figure gives the potential energy function U(r) of a projectile, plotted outward from the surface of a planet of radius. What least kinetic energy is required of a projectile launched at the surface if the projectile is to “escape” the planet
Minimum kinetic energy required to escape from the surface of planet is
Potential energy at Rs is J
The total energy of a particle is the sum of the kinetic and potential energies of the particle. To escape from the gravitational field, the supplied kinetic energy should be equal to the gravitational potential energy of the particle.
Total energy= Kinetic Energy+ Potential Energy
TE = U + KE
Minimum kinetic energy required to escape from the surface of the planet
To escape from the surface of earth TE = 0
But, from the graph, the potential energy on surface of earth is
So, the least kinetic energy of the particle is
The Sun, which is from the center of the Milky Way galaxy, revolves around that center once every . Assuming each star in the Galaxy has a mass equal to the Sun’s mass of , the stars are distributed uniformly in a sphere about the galactic center, and the Sun is at the edge of that sphere, estimate the number of stars in the Galaxy.
Planet Roton, with a mass of and a radius of , gravitationally attracts a meteorite that is initially at rest relative to the planet, at a distance great enough to take as infinite.The meteorite falls toward the planet. Assuming the planet is airless, find the speed of the meteorite when it reaches the planet’s surface.
Figure 13-43 gives the potential energy function U(r) of aprojectile, plotted outward from the surface of a planet of radius . If the projectile is launched radially outward from the surfacewith a mechanical energy of , what are (a) its kineticenergy at radius and (b) its turning point (see Module 8-3)in terms of ?
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