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Practice – Newton’s Universal Law of Gravitation
Directions: Do all work on a separate sheet of paper. For each problem you must show all steps of the GUESS
method but with this formula I am also grading you for an extra step to Simplify after you substitute (GUESSS). Answers
are in italicized parenthesis so you can check your answer.
Earth’s mass = 6.0 x 1024 kg
Sun’s mass = 1.99 x 1030 kg
Earth’s radius (surface of the earth) = 6.38 x 106 m
Distance between earth and sun = 1.5 x 1011 m
Solving for force between objects or on the surface
1) Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and the other has a mass of 52.0
kg. What is the gravitational force between them? (1.08 x 10-7 N)
2) What gravitational force does the moon produce on the earth if their centers are 3.88 x 108 m apart? (1.94 x
1020 N)
3) What is the gravitational force on a 70 kg object sitting on the earth’s surface? (6.88 x 102 N)
4) What is the gravitational force on a 35 kg object sitting on the earth’s surface? (3.44 x 102 N)
5) Calculate the gravitational force from the sun that holds the earth in orbit. (3.54 x 1022 N)
6) The force of gravity on a 60 kg woman is about 588 N. The woman also exerts a gravitational force on the
earth. How large is this force? (588 N)
7) A woman standing on the surface of the earth has a mass of 50.0 kg. How much force of gravity does that
woman feel? (491.6 N)
8) Calculate the gravitational force of attraction between a 70 kg physics student and their 1 kg physics book 1
meter away. (4.67 x 10-9 N)
9) Calculate the gravitational attraction between a proton of mass 1.67 x 10-27 kg and an electron of mass 9.11
x 10-31 kg if they are 5 x 10-11 m apart (like in a normal hydrogen atom). (4.0 x 10-47 N)
10) Copy the table and calculate the values for the last 2 columns. Make sure to use the right values for the 2
masses and distance. They’re in the table or on the worksheet somewhere.
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Solving for force above the surface
11) Calculate the gravitational force on a 6.50 x 102 kg spacecraft that is 4.15 x 106 m above the surface of the
earth. (2.34 x 103 N)
12) What is the gravitational force on a 70 kg object floating 6.38 x 106 m above the earth’s surface? (172 N)
13) What is the gravitational force on a 70 kg object floating 3.18 x 106 m above the earth’s surface? (306 N)
Solving for mass
14) The gravitational force between two objects that are 2.1 x 10-1 m apart is 3.2 x 10-6 N. If the mass of one
object is 55 kg, what is the mass of the other object? (38 kg)
15) If the gravitational force between two objects of equal mass is 2.30 x 10-8 N when the objects are 10.0 m
apart, what is the mass of each object? (1.86 x 102 kg)
Solving for distance
16) If two objects each with a mass of 200 kg produce a gravitational force between them of 3.7 x 10-6 N, what
is the distance between them? (0.85 m)
Manipulating an old force (changing mass or distance) to get a new force
17) An object weights 100 N on earth’s surface. Find its weight 1 earth radius above the surface of the earth.
(25 N)
18) The force of attraction between m1 and m2 is 26 N. What will this force become if m2 is tripled and the
distance between m1 and m2 is cut in half? (312 N)
19) The force of gravity between A and B is 100 N. When the mass of B is doubled and the distance between A
and B is quadrupled, what is the new force? (12.5 N)
20) The force of gravitational attraction between two masses is 36 N. What will the force between them be if
one mass is doubled and the distance between them is tripled? (8 N)
21) The force of gravity between two masses was 14 N when they were 10 m apart. The distance between them
was changed and the force became 56 N. What is their distance now? (5 m)
22) A mass “M1” has a force of 50 N when “R” meters away from a second mass “M2”. What is the
gravitational force between them when the distance is changed to R/2, R/3, R x 2? (200 N, 450 N, 12.5 N)
23) The gravitational force between two small masses is 3.24 x 10-7 N. What is the gravitational force between
these objects if both masses are doubled and the distance is tripled? (1.44 x 10-7 N)
Critical thinking
24) Where does gravitational force come from?
25) How is gravitational force related to the …size of an object’s mass? …distance between objects?
26) What would happen to the force of gravity on a person as…they traveled further above the surface of the
earth? …they traveled under the surface toward the center of the earth? Explain why for each.