Physics 11 Gizmo – Universal Gravitation
History reports that Sir Isaac Newton was pondering the question of what keeps the Moon in orbit
around Earth when he witnessed an apple fall from a tree. It occurred to Newton that, if it was
possible for gravity to exert its influence at the top of a tree, it might also exert its influence as far
away as the Moon. Could it be, Newton wondered, that the Moon was in a sense "falling" to Earth
under the influence of the same forces that caused the apple to fall?
Newton's theory was absolutely correct, even if the story might not be. Historians have suggested
that Newton might have made up this tale to date his discovery of the Law of Universal Gravitation
twenty-five years earlier than his own notes seem to indicate that it actually occurred. Nevertheless,
even though others may have proposed components of the law before him, it was Newton who fully
stated it and Newton that presented the strongest arguments in its favor.
The Direction of Gravitational Force
Isaac Newton realized that any two objects, no matter how large or how small, exert forces upon
one another. In this activity, you will examine the direction of the gravitational forces between two
objects.
1.
The Gizmotm shows two objects, A and B. Check Show force vector for object A
and examine the purple vector. This represents the force that acts on object A due
to object B.
a.
b.
Describe the direction of the force that acts on object A.
Drag object A to a different location and describe the direction of
the force with A at this location.
c.
Drag object B to a different location and watch the force vector for
object A as you drag. What is always true of the direction of the force
on A?
2.
With Show force vector for object A selected, turn on Show force vector for
object B. A green vector appears representing the force that acts on object B.
a.
b.
Describe the direction of the force acting on object B.
Drag both A and B to different locations. What is always true about
the directions of the forces acting on objects A and B?
c.
Select Show connecting line. Move the objects around in the
Gizmo. How do the gravitational forces acting on the objects relate to
the connecting line?
The Relationship Between Force and Distance
In this activity, you will explore how the distance between the two objects affects the magnitude of
the forces that act on each.
1.
Check Show force vector for object A and Show force vector for object B.
Make sure all other options are unselected. Drag objects A and B to opposite ends
of the Gizmo.
a.
The length of each arrow represents the magnitude of that force.
(Longer arrows represent stronger forces.) How does the length of the
arrow on A compare to the length of the arrow on B? What does this tell
you about the forces acting on A and B?
b.
Move object A slightly closer to object B. How does this affect the
two forces? Are the magnitudes still equal?
c.
Experiment moving the objects closer together and further apart.
Watch the magnitudes of the forces as you do. How does distance
between the objects affect the magnitude of the forces on them?
2.
Turn off Show force vector for both objects. Then select Show distance, Show
grid, and Show vector notation for both objects. Be sure that m A and m B are
equal. The distance between the two objects is displayed near the top of the Gizmo.
Displayed below Show vector notation are the forces that act on each object, F A
and F B , and the magnitudes of those forces, |F A | and |F B |, in Newtons (N). The
magnitude of a force is always positive.
a.
Position object A at (−1, 0) and object B at (1, 0) . What is the
distance between the two objects? What is |F A |, the magnitude of the
force acting on A? What is |F B |?
b.
Drag object A to (−2, 0) and object B to (2, 0) . (Note that the
distance between A and B has been doubled.) What are |F A | and |F B |?
How does this compare with |F A | and |F B | in the previous step? (What
were the forces divided by when the distance was doubled?)
c.
Repeat the experiment with the objects at positions (−4, 0) and
(4, 0) , and then again at (−8, 0) and (8, 0). Record the distance
and magnitude of forces in each case.
d.
You should have noticed that whenever the distance between objects
(A and B) is multiplied by two, |F A | and |F B | are divided by four (two
squared). This is called the inverse square relationship. How do you
think |F A | and |F B | would change if the distance between objects A
and B were cut in half? What if the distance were tripled? Check your
answers in the Gizmo.
e.
On a sheet of paper, plot a graph with distance between the two
objects on the horizontal axis and |F| on the vertical axis. Then use the
Gizmo to find |F| when the objects are distances of 2, 3, 4, 5, 6, 7, and
8 m apart. Plot these points on the graph and connect them with a
smooth curve. What is the shape of the graph?
The Relationship Between Force and Mass
In this activity, you will explore how the masses of the two objects affect the magnitude of the
forces acting on each object.
1.
Check all of the options in the Gizmo except for Show connecting line. Note that the
masses of the objects (m A and m B ) are displayed in the center pane. Set each of
these values to 10. (To set the mass to a specific number, click in the text box, type
the number, and hit Enter.) Note that the actual mass is 10 • 10 5 kg, or
1,000,000 kg.
a.
Place object A near the center of the left half of the screen and
object B near the center of the right half. What are |F A | and |F B |?
b.
Without moving either object, double the mass of object A (m A =
20 • 10 5 kg, or 2,000,000 kg). How does |F A | change? Is |F B |
affected? In what way?
c.
What would you expect to happen to |F A | and |F B | if you doubled
mB (set m B = 20 • 10 5 kg, or 2,000,000 kg) while m A = 20 • 10 5
kg also? Check your expectation using the Gizmo.
d.
Set m A = 10 • 10 5 kg and m B = 40 • 10 5 kg. What are |F A |
and |F B |? How do those values compare to |F A | and |F B | when m A =
20 • 10 5 kg and m B = 20 • 10 5 kg?
2.
Set both m A and m B to 10 • 105 kg. On paper, create a graph with m A on the
horizontal axis and |F A | on the vertical axis. In the Gizmo, vary m A while keeping
m B constant. Plot a graph of |F A | vs m A . Describe the graph. What kind of
relationship does this indicate between force and mass?