Download Gravitation Homework Set Problem 1: In the figure, four spheres

Gravitation Homework Set
Problem 1: In the figure, four spheres form the corners
of a square whose side is 2.0 cm long. What are the
magnitude and direction of the net gravitational force
from them on a central sphere with a mass ms =250 kg?
300 kg
500 kg
ms
Draw a free body diagram here
100 kg
Show the magnitudes of the forces here
Write the x and y components here
Find the magnitude and direction here
500 kg
Gravitation Homework Set
Problem 2: Suppose a tunnel runs through Earth from pole to pole
as shown in the drawing. Assume that the Earth is a non-rotating
uniform sphere with a known density of ρ. Find the gravitational
force on a particle of mass m dropped into the tunnel when it
reaches a distance r from Earth’s center.
Write the expression of gravitational force F between two bodies m
and M’.
Find M’, the remaining amount of mass attracting the body of mass m.
Perform algebraic manipulation to solve for F as a function of r
What does this function have in common with Hooke’s Law?
Gravitation Homework Set
Problem 3. The mean diameters of Mars and Earth are 6.9 x 103 km and 1.3 x 104 km,
respectively. The mass of Mars is 0.11 times Earth’s mass.
a) What is the ratio of the mean density of Mars to that of Earth?
Describe the relationship between density, volume and mass.
What is the formula for the volume of a sphere?
Write the masses of both Earth and Mars as functions of density and radii.
Perform algebraic manipulation to find ratio
b) What is the value of g on Mars?
Show the relationship between g and the following constants: the radius of the
Earth, its mass, and the Universal Gravitational Constant, G.
Use the appropriate Martian values and solve for the Martian g. Note: A short-cut
can be used by employing the ratio of densities, the ratio of masses and the value of
g on Earth..
Gravitation Homework Set
c) What is the escape speed on Mars?
Show the relationship between escape speed of Earth, ve and the following
constants: the radius of the Earth, its mass, and the Universal Gravitational
Constant, G. It may be derived by setting the kinetic energy equal to the
gravitational potential energy at the surface of the earth.
Use the appropriate Martian values and solve for the Martian escape speed, vm.
Note: A short-cut can be used by employing the ratio of radii, the ratio of masses
and Earth’s escape speed.
Gravitation Homework Set
Problem 4: A spaceship is idling at the fringes of our galaxy, 80,000 light-years from the
galactic center. What is the ship’s escape speed from the galaxy? The mass of the
galaxy is 1.4 x 1011 times that of our sun. Assume, for simplicity, that the matter forming
the galaxy is a distributed in a uniform sphere.
Write the mass of the sun
Convert 80,000 ly to m.
Calculate mass of galaxy.
Perform algebraic manipulation and solve. Hint: See problem 3 part c.