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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. Answers are in italicized parenthesis so you can check your answer.
Earth’s mass = 6.0 x 1024 kg Earth’s radius (surface of the earth) = 6.4 x 106 m
Sun’s mass = 1.99 x 1030 kg 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 with a mass of 7.36x 1022 kg 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 with a mass of 1.99 x 1030 kg that holds the earth in orbit a distance of 1.5 x 1011 m. (3.54 x 1022 N)
6)A woman standing on the surface of the earth has a mass of 60.0 kg. How much force of gravity does that woman feel? (586 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? (488.5 N)
8)Calculate the gravitational force of attraction between a 70 kg physics student and their 1 kg physics book 1 meter away. (4.66 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). (4.05 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.
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? (171.50 N)
13)What is the gravitational force on a 70 kg object floating 3.18 x 106 m above the earth’s surface? (305.24 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? (38.46 kg)
15)The gravitational force between two objects that are 3.8 x 10-2 m apart is 8.2 x 10-3 N. If the mass of one object is 95 kg, what is the mass of the other object? (1868.66 kg)
16)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? (1.85 x 102 kg)
Solving for distance
17)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)
18)If two objects each one with a mass of 100 kg and the other with a mass of 75 kg produce a gravitational force between them of 3.7 x 10-4 N, what is the distance between them? (0.03 m)
ULG- Relationships: Manipulating an old force (changing mass or distance) to get new force
19)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 doubled? (19.5N)
20)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)
21)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)