Gravitation
Studio Physics I
The General Form of the Gravitational Force
1.The mathematical expression that describes the fundamental gravitational force is

mm
F  G 1 2 2 . State what each variable in this expression stands for.
r
2. If you did not already address this above, state precisely what distance the distance r
refers to? (Is it center to center, surface to surface or what?) Draw the figure below
on your activity sheet. Then mark the distance r on the figure.
1
2
3. On your figure above, draw the line along which the gravitation force acts.
4. The gravitational force is a “central” force. In terms of your answer to the question
immediately above, explain why this is an appropriate way to describe the gravitational
force.
5. Show on your figure the direction of the force from object #2 on object #1. Label this
F21 . Show on your figure the diction of the force from object #1 on object #2. Label
this F12 .
6. Are these two forces a Newton’s third law force pair? Justify your answer in terms of
the expression in question #1 above and your answers to question #5 above.
Comparing the General Form of the Gravitational Force to the
Gravitational Force on an Object close to earth.
7. Rewrite the expression given in question #1 for the special case of the gravitational
force from earth on an object sitting on its surface.
8. Consider the image of a stationary sled carrying a package that is shown below. Draw
free body diagrams for the earth, sled and package. Identify ALL forces acting on
each of the objects. (Hint: consider normal forces, the objects weights and
gravitational forces-which of these forces are really the same force?) Identify all
Newton’s third law force pairs by putting an equal number of slashes through the
forces vectors for both forces in the pair. Use one slash for your first pair, two slashes
for your second pair and so on.
package
sled
9. We are so familiar with the gravitational force from earth on objects near its surface
that we have given this specific case of the fundamental gravitational force a special
name. We call it an object’s weight. An object weight near earth is given by W=mg
where m is the objects mass and g is the acceleration due to gravity close to the earth.
Compare this expression to the one for the gravitational force from earth on an object on
its surface and derive an express for the acceleration due to gravity on the surface of the
earth in terms of the variables and constants that you used there.
10. The gravitational constant G is 6.67 x 10-11 Nm2/kg2, the mass of the earth M is
6x1024 kg and the radius of the earth R is 6.37 x106 m. Using these values, find the
acceleration due to gravity at the surface of the earth. What is your answer for 5000 feet
above the earth’s surface (a tall mountain)? What is your answer for 20,000 feet above
the surface (airplane flight altitude) 3.3 feet = 1 meter.
11. Consider the following two statements. Explain what is correct and what is incorrect
about both statements.
Student A: “ An object thrown up into the air does not experience a constant downward
acceleration because the acceleration due to gravity changes with height above the earth.”
Student B” “No way. The acceleration due to gravity is totally a constant.”
Using the Gravitational Force Law in Quantitative Calculations
12. What is the gravitational force of attraction between two people who are 2 meters
apart? Take the mass of each person to be 70 kg.
13. Consider the three objects shown below. Draw three arrows which show the direction
of the gravitational force on object 2 due to object 1, the direction of the force on object 2
due to object 3 and the direction of the net force on object 2.
2
1
3
14. The center-to-center distance between object 1 and object 2 above is the same as that
between object 2 and object 3 and as between object 3 and object 1. The distance in each
case is 2 x 10-4 m. Object 1 has a mass of 1 kg, object 2 has a mass of 2 kg and object 3
has a mass of 0.5 kg. What is the x component of the net force on object 2? What is the
direction (right or left) of the x component? What is the y component of the net force on
object 2? What is the magnitude of the net force acting on object 2? What is the
direction (up or down) of the y component? What angle does the net force on object 2
make relative to the positive x-axis?