PHYSICS 20 GRAVITATIONAL FORCES GRAVITATIONAL FIELDS
Gravitational Fields (or Acceleration Due to Gravity) Symbol:
Definition: Units:
Formula Description
• This is the formula for force due to gravity or as we call it, weight.
• This is the definition of gravitational fields. The field strength (intensity) at any point around the Earth can be found by using a test object (mass) and finding the weight to mass ratio of the test object at that point.
Relevant Mathematical Descriptions:
• In this formula we need to know the mass of the object producing the field, and the distance from the centre of that mass.
Important numbers:
mass of the Earth = 5.9742 × 1024 kilograms radius of the Earth = 6.3781 x 106 m
gravitational constant (G) = 6.67 × 10-11 Nm2/ kg2 1. Calculate the gravitational field strength on the surface
of Mars. Mars has a radius of 3.43 x 106 m and a mass
of 6.37 x 1023 kg. (3.61 N/kg)
2. At what distance from the Earth’s surface is the gravitational field strength 7.33 N/kg? (1.01 x 106 m)
3. On the surface of planet X an object has a weight of 63.5 N and a mass of 22.5 kg. What is the gravitational field strength on the surface on planet X? (2.82 N/kg)
4. On the surface of planet Y, which was a mass of 4.83 x 1024 kg, an object has a weight of 50.0 N and a mass of 30.0 kg. What is the radius of the planet? (1.3
x 107 m)
5. What is the gravitational field strength 1.27 x 107 m
(this is twice the Earth’s radius) above the Earth’s surface? (1.09 N/kg)
6. Planet B has a mass of 4.00 x 1022 kg and a radius of
6.0 x 105 m. What is the gravitational field strength
on the surface of Planet B? (7.4 N/kg)
7. Two planets A and B have the same mass. However the gravitational field strength on the surface of planet A is 1.20 times the gravitational field strength on the surface of planet B. How does the radius of Planet A compare with the radius of Planet B? (0.913 times)
8. What is the weight of a 20.0 kg object on the surface of the moon? The mass of the moon is 7.34 x 1022 kg
PHYSICS 20 GRAVITATIONAL FORCES UNIVERSAL GRAVITATION
Newton’s Law of Universal Gravitation
Formula Description
Relevant Mathematical Descriptions:
Newton’s Law of universal Gravitation States: • That the gravitational force between two masses
is directly proportional to the product of their mass.
• That the gravitational force between two masses varies inversely to the square of the distance between the centres of the masses.
Important numbers:
mass of the Earth = 5.9742 × 1024 kilograms radius of the Earth = 6.3781 x 106 m
gravitational constant (G) = 6.67 × 10-11 Nm2/ kg2 9. 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)
10. What gravitational force does the moon produce on the Earth if the centres of the Earth and moon are 3.88 x 108 m apart and the moon has a mass of 7.34 x1022 kg.
(1.94 x 1020 N)
11. 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)
12. Calculate the gravitational force on a 6.50 x102 kg spacecraft that is 4.15 x 106 m above the Earth’s
13. 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
5.5 x 101 kg, what is the mass of the other object? (3.8 x
101 kg)
14. If two objects, each with a mass of 2.0 x 102 kg, produce a gravitational force between them of 3.7 x 10 -6 N, what is the distance between them? (8.5 x10-1 m)
15. What is the gravitational force on a 70.0 kg object
standing on the Earth’s surface? (6.88 x 102 N) 16. What is the gravitational force on a 35.0 kg object standing on the Earth’s surface? (3.44 x 102 N)
17. What is the gravitational force on a 70.0 kg object that is 6.37 x 106 m above the Earth’s surface? (1.72 x102 N)
18. What is the gravitational force on a 70.0 kg object that is 3.18 x 106 m (half the radius of the Earth) above the Earth’s surface? (3.06 x 102 N)
PHYSICS 20 GRAVITATIONAL FORCES UNIVERSAL GRAVITATION
19. Three objects are all in a line, each with a mass of 10.0 kg. Each object is placed 5.00 x 10-1 m apart from each
other. What is the net gravitational force on the centre object due to the other two objects? (0)
20. Three objects are all in a line, the first and second object has a mass of 10.0 kg while the third object has a mass of 15.0 kg. Each object is placed 5.00 x 10-1 m apart from each other. What is the net gravitational force on the centre object due to the other two objects? (1.33 x 10-6 N)
21. The gravitational force between two small masses A and B when placed a short distance apart is 3.24 x 10-7 N. What is
the gravitational force between these objects if the masses of both A and B are doubled and the distance between them is tripled? (1.44 x 10-7 N)