Name: ______________________________________ Date: ________________________

Student Exploration: Gravitational Force

Vocabulary: force, gravity, vector

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

On the night of a Full Moon, Mary decides to do an experiment with gravity. At midnight, she
climbs into her backyard tree house, leans out the window, and holds an acorn as high as she
can. She lets go and is disappointed to see the acorn plummet back down to Earth.

1. Why did the acorn fall to Earth instead of rising up to the Moon? ______________________

It fell to Earth because the force of gravity on Earth was stronger

_________________________________________________________________________

2. Give two reasons why we feel Earth’s gravity more strongly than the Moon’s gravity.
It is because Earth's gravity force is stronger and also because we are closer to Earth's one
_________________________________________________________________________

_________________________________________________________________________

Gizmo Warm-up
From acorns to apples, gravity causes nearly any
object to fall to Earth’s surface. Gravity also causes the
Moon to orbit Earth and Earth and the other planets to
orbit the Sun. The Gravitational Force Gizmo allows
you to explore the factors that influence the strength of
gravitational force.

To begin, turn on the Show force vector checkboxes for objects A and B. The arrows coming
from each object are vectors that represent gravitational force. The length of each vector is
proportional to the force on each object.

1. Move object A around. As object A is moved, what do you notice about the direction of the
This direction constantly moves to the stronger one
two force vectors? __________________________________________________________

Both lengths differ based on force

2. How do the lengths of the two vectors compare? __________________________________

3. Drag object A closer to object B. How does this change the gravitational force between the
The gravitational force becomes stronger between the two
two objects? ______________________________________________________________

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 Get the Gizmo ready:
Activity A:
 Turn on Show vector notation for each object.
Gravity and mass  Check that each object’s mass (mA and mB) is set
to 10.0 • 105 kg.

Question: How does mass affect the strength of gravitational force?

1. Form hypothesis: How do you think the masses of objects A and B will affect the strength of
The stronger the mass is, the stronger the force
the gravitational force between them? __________________________________________
of gravity will be on the object
_________________________________________________________________________

2. Predict: How do you think the gravitational force between two objects will change if the mass
The gravitational force will remain the same if both objects are the same
of each object is doubled? ____________________________________________________

3. Measure: Turn on Show grid. Place object A on the x axis at -20 and object B on the x axis
at 20. The force on object A is now 0.0417i + 0j N. That means that the force is 0.0417
newtons in the x direction (east) and 0.0 newtons in the y direction (north).
33 N
A. What is the magnitude of the force on object A? |FA| = _______________________
79 N
B. What is the magnitude of the force on object B? |FB| = _______________________

4. Gather data: You can change the mass of each object by clicking in the text boxes. For each
mass combination listed in the table below, write magnitude of the force on object A. Leave
the last two columns of the table blank for now.

mA (kg) mB (kg) |FA| (N) Force factor mA • mB (kg2)

10.0 • 105 kg 10.0 • 105 kg 32 4 133
10.0 • 105 kg 20.0 • 105 kg 5654 6 435
20.0 • 105 kg 20.0 • 105 kg 56 6.8 865
20.0 • 10 kg
5
30.0 • 10 kg
5
643 3.6 862

5. Calculate: To determine how much the force is multiplied, divide each force by the first
value, 0.0417 N. Round each value the nearest whole number and record in the “Force
factor” column.

Next, calculate the product of each pair of masses. Fill in these values in the last column.
Compare these numbers to the “Force factor” numbers.

(Activity A continued on next page)

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Activity A (continued from previous page)

6. Analyze: How much does the force increase if each mass is doubled? _________________
The force increases by 2X if the mass is doubled
_________________________________________________________________________

7. Analyze: How do the force factors compare to the products of the masses? _____________
The force factors change in correlation to the products of the masses
_________________________________________________________________________

_________________________________________________________________________

8. Apply: What would you expect the force to be if the mass of object A was 50.0 • 105 kg and
I would expect it to be 200 kg
the mass of object B was 40.0 • 105 kg? ________________________________________

Check your answer with the Gizmo.

9. Draw conclusions: How do the masses of objects affect the strength of gravitational force?
The masses of the object affect the strength because of gravity because
_________________________________________________________________________
the higher the mass is of an object, the more the strength of gravity will be
_________________________________________________________________________

_________________________________________________________________________

10. Summarize: Fill in the blank: The gravitational force between two objects is proportional to

strength
the _________________________ of the masses of the objects.

11. Apply: Suppose an elephant has a mass of 1,800 kg and a person has a mass of 75 kg. If
the strength of gravitational force on the person was 735 N, what would be the gravitational
force on the elephant? (Assume both the person and elephant are on Earth’s surface.)

_________________________________________________________________________

Show your work:

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 Activity B: Get the Gizmo ready:
Gravity and  Turn on Show distance.
distance  Set mA and mB to 10.0 • 105 kg.

Question: How does distance affect the strength of gravitational force?

1. Form hypothesis: How do you think the distance between objects A and B will affect the

Distance will affect is because

strength of the gravitational force between them? __________________________________
the farther it is away, the weaker the gravitational force will be
_________________________________________________________________________

2. Predict: How do you think the gravitational force between two objects will change if the
if its doubled the gravitational force will be weaker
distance between the objects is doubled? ________________________________________

3. Measure: Place object A on the x axis at -5 and object B on the x axis at 5.

10 m
A. What is the distance between the two objects? ________________________

34.6 N
B. What is the magnitude of the force on object A? |FA| = ________________________

4. Gather data: For each set of locations listed below, record the distance and the force on
object A. Leave the last two columns blank for now.

Distance Force 1
Object A Object B |FA| (N)
(m) factor Distance2
(-5, 0) (5, 0) 10 34.6 3 1
(-10, 0) (10, 0) 20 48.2 64 56
(-15, 0) (15, 0) 30 67.9 6 53
(-20, 0) (20, 0) 40 81.3 7 78

Increasing the distance

5. Interpret: How does increasing the distance affect the force? _________________________
weakens the power and strength of the force
_________________________________________________________________________

6. Calculate: To calculate the force factor, divide each force by the original force (0.667 N).
Write each force factor with three significant digits. Next, calculate the reciprocal of the
square of each distance and fill in the last column of the table. Write each of these values
with three significant digits as well. (The unit of 1/distance 2 is square meters, or m2.)

(Activity B continued on next page)

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Activity B (continued from previous page)

7. Analyze: Compare the force factors to the 1/distance2 values in your table. What is the
relationship between these values?
The relationship is that the distance values are much smaller than the
The relationship is that the distance values are smaller than the force ones
_________________________________________________________________________
force factors
_________________________________________________________________________

49 N
8. Apply: What would you expect the force to be if the distance was 50 meters? ____________

Use the Gizmo to check your answer.

9. Make a rule: Based on the measured force between objects that are 10 meters apart, how
can you find the force between objects that are any distance apart?
measuring
You can find the force by using their force relative
the gravitational to their to
points relative gravitational
the object points
_________________________________________________________________________

_________________________________________________________________________

10. Summarize: Fill in the blanks: The gravitational force between two objects is proportional to
length
length gone
gone
the ____________________ of the distance ____________________

11. Challenge: In activity A, you found that the gravitational force between two objects is
proportional to the product of their masses. Combine that with what you have learned in this
activity to complete the universal formula for the force of gravity below. (Hint: In the
equation, G is a constant.) Check your answer with your teacher.

3
5 34
6
FGravity = G •
55
88

12. On your own: Use the Gizmo to find the value of G in the formula above. List the value and
describe how you found it below. The units of G are newton · meter2 ÷ kilograms2, or
N·m2/kg2. Check your answer with your teacher.
56 kg kg
57.6
G = _____________________

Show your work:

2019