Physics – Newton’s Law of Universal Gravitation
Dr. Lu
11/21/2018
Learning targets
I can determine the magnitude of attractive force between two objects by Newton’s Law of Universal
Gravitation which depends on the mass of the objects and inverse square of the distance between them.
Unpacking
- Attractive force
- Mass dependence
- Inverse square dependence of distance between the objects
Mini Lesson
Newton’s Law of Universal Gravitation
Where m1 and m2 are the mass of the objects; r = the distance between these two objects.
G=6.67x10-11 Nm2/kg2
Example 1: Two objects with mass of 5 kg and 8 kg are separated at a distance of 20 cm. Find the
gravitational force between them
F= GM1M2 / r2 = 6.67x10-11 (5kg)(8kg)/ (0.2 m)2
= 66.7 x10 – 9 N= 6.67 x10- 8 N
Group work
1.The graph below represents the relationship
between gravitational force and mass for objects
near the surface of Earth.
The slope of the graph represents the
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(1) acceleration due to gravity
(2) universal gravitational constant
(3) momentum of objects
(4) weight of objects
2. A space probe is launched into space from Earth’s surface. Which graph represents the
relationship between the magnitude of the gravitational force exerted on Earth by the space probe
and the distance between the space probe and the center of Earth?
3.. Calculate the magnitude of the average gravitational force between Earth and the Moon.
[Show all work, including the equation and substitution with units.]
4.Two masses are attracted to each other by a force of 3.4 X 10-2 N. What would be the force of
attraction if the masses of each were doubled and the distance between them kept constant?
5.Referring to problem 4, what would be the force if one mass was doubled, the other mass
tripled and the distance between them 1/2 the original separation distance?
6.What would be the mass of the man in problem 5; a.) on the earth b.) on planet Z?
7.How is the acceleration due to gravity affected if the distance from the center of gravity is
doubled?
8. How is the acceleration due to gravity affected if the distance from the center of gravity is
double tripled?
9. How is the acceleration due to gravity affected if the distance from the center of gravity is
doubled 1/4?
10.. Calculate the acceleration due to gravity at an altitude of 6.37 X 10 6 m above the
earth's surface.
11. What is the gravitational force between two 800 kg cars that are 5 m apart? What
would the gravitational force between these two cars be if the distance between them
was changed to 10 m?
The whole class Sharing
Each group shares their answer to the whole class.
Exit Ticket
Which graph represents the relationship between the magnitude of the gravitational force
exerted by Earth on a spacecraft and the distance between the center of the spacecraft and center
of Earth? [Assume constant mass for the spacecraft.]
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Homework
Review problem on friction force
1. A force of 10. newtons toward the right is exerted on a wooden crate initially moving to the
right on a horizontal wooden floor. The crate weighs 25 newtons.
(a) Calculate the magnitude of the force of friction between the crate and the floor. [Show all
work,including the equation and substitution with units.] [2]
(b) Draw and label all vertical forces acting on the crate. [1]
© On the diagram in your answer booklet, draw and label all horizontal forces acting on the
crate. [1]
(d) What is the magnitude of the net force acting on the crate? [1]
(e) Is the crate accelerating? Explain your answer. [1]
Review problem on Newton’s 1st Law of Motion
2. Which graph best represents the motion of an object in equilibrium?
Problems related to Gravitational force
3. The distance between an electron and a proton is varied. Which pair of graphs best represents
the relationship between gravitational force, Fg, and distance, r, and the relationship between
electrostatic force, Fe, and distance, r, for these particles?
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4. The mass of moon is about 7.35 x 1022 kg. The mass of the earth is about 5.98 x 1024
kg. If the centers of the two are 3.84 x 108 m apart, what is the gravitational force
between them?
5. The mass of an electron is 9.11 x 10-31 kg. The mass of a proton is 1.67 x 10-27 kg. They are
about 1.0 x 10-10 m apart in a hydrogen atom. What is the gravitational force between
these two particles in the hydrogen atom?
6. The acceleration of gravity at Hartford, Connecticut, is 9.80336 m/s2. What is the
gravitational force acting on a .25000 kg mass at this location?
7. What happens to the force of gravity between two objects if you double the mass of one of
the objects?
8. What happens to the force of gravity between two objects if you double both masses and
make the distance between them 1/2 what it originally was?
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