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 r̂ . 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 direction of the force from object #1 on object #2. Label
this F12 . Make the lengths of the force arrows proportional to their magnitudes.
6. Are these two forces a Newton’s 3rd Law force pair? Justify your answer in terms of
the expression in question #1 above and your answers to question #5 above. Reminder:
It is not enough for two forces to be equal and opposite to be a 3rd Law force pair.
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 simplified illustration 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 3rd Law force pairs by putting an equal number of slashes through the force
vectors for both forces in the pair. Use one slash for your first pair, two slashes for your
second pair, and so on. Have your TA or instructor check your diagram.
Hint: There are ten forces in five 3rd Law pairs.
package
sled
Rev. 2004 Bedrosian
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 object’s 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 expression 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
5.98x1024 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) Use 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.”
Exercise: Using the Gravitational Force Law in 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. Copy the figure to your paper. 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.
1
2
3
14. The center-to-center distance between object 1 and object 2 above is 30 cm. The
center-to-center distance between object 3 and object 2 is 50 cm. The triangle formed by
the three objects has a right angle at object 2. Object 1 has a mass of 0.5 kg, object 2 has
a mass of 1 kg and object 3 has a mass of 1.5 kg. Let +X be to the right and +Y up on the
page. 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 direction (up or down) of the Y component? What is the magnitude of the
net force acting on object 2? What angle does the net force on object 2 make relative to
the +X axis?
Rev. 2004 Bedrosian