How to Calculate the Force of Gravity: 10 Steps

Table of contents:

How to Calculate the Force of Gravity: 10 Steps
How to Calculate the Force of Gravity: 10 Steps

Video: How to Calculate the Force of Gravity: 10 Steps

Video: How to Calculate the Force of Gravity: 10 Steps
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Gravity is one of the fundamental forces in physics. Its most important aspect is that it is universal: all bodies have a gravitational force that attracts other bodies to them. The gravitational force acting on any body is independent of the masses of both bodies and the distances between them.

Steps

Part 1 of 2: Calculating the gravitational force between two bodies

Calculate Force of Gravity Step 1
Calculate Force of Gravity Step 1

Step 1. Define the equation for the force of gravity that attracts a body, Fserious = (Gm1m2)/d2.

In order to correctly calculate the gravitational force of a body, the equation takes into account the mass of both bodies and the distance between them. The variables are defined below:

  • Fserious is the force of gravity.
  • G is the universal gravitational constant 6, 673 x 10-11 No2/kg2.
  • m1 is the mass of the first body.
  • m2 is the mass of the second body.
  • d is the distance from the center of the two bodies.
  • Sometimes you will see the letter r instead of the letter d. Both symbols represent the distance between bodies.
Calculate Force of Gravity Step 2
Calculate Force of Gravity Step 2

Step 2. Use the proper measurement units

For this specific equation, you need to use the metric system. Body masses must be in kilograms (kg) and distance in meters (m). You need to convert these units before proceeding with the calculation.

Calculate Force of Gravity Step 3
Calculate Force of Gravity Step 3

Step 3. Determine the mass of the body in question

For smaller bodies, you can weigh them on a scale to find out the weight in kilograms (kg). For larger bodies, it is necessary to check a table of approximate weights on the internet. In Physics exercises, body mass is usually given in the statement.

Calculate Force of Gravity Step 4
Calculate Force of Gravity Step 4

Step 4. Measure the distance between the two bodies

If you're trying to calculate the force of gravity between a body and the Earth, you need to determine how far the body is from its center.

  • The distance from the Earth's surface to its center is approximately 6.38 x 106 m.
  • You can find tables and other resources online that give approximate distances to the Earth's center and bodies at various surface elevations.
Calculate Force of Gravity Step 5
Calculate Force of Gravity Step 5

Step 5. Solve the equation

After defining the equation's variables, you can assemble and solve it. Remember that all units must be in the metric system and in the correct scale. The mass must be in kilograms and the distance in meters. Solve the equation using the correct order of operations.

  • For example: determine the force of gravity of a 68 kg person on the Earth's surface. The Earth's mass is 5.98 x 1024 kg.
  • Remember to use the variables in the correct units m1 = 5.98 x 1024 kg, m2 = 68 kg, G = 6, 673 x 10-11 No2/kg2, and d = 6.38 x 106 m.
  • Write the equation: Fserious = (Gm1m2)/d2 = [(6, 67 x 10-11) x 68 x (5, 98 x 1024)]/(6, 38 x 106)2.
  • Multiply the masses of the two bodies together. 68 x (5, 98 x 1024) = 4.06 x 1026.
  • Multiply the product of m1 in2 by the gravitational constant G (4.06 x 1026) x (6.67 x 10-11) = 2.708 x 1016.
  • Square the distance between the two bodies: (6, 38 x 106)2 = 4.07 x 1013.
  • Divide the product of G x m1 x m2 by square distance to find the gravitational force in Newtons (N). 2, 708 x 1016/4, 07 x 1013 = 665 N.
  • The force of gravity is 665 N.

Part 2 of 2: Calculating the gravitational force on Earth

Calculate Force of Gravity Step 6
Calculate Force of Gravity Step 6

Step 1. Understand Newton's Second Law, F = ma

According to Newton's second law: "The net force acting on a body is proportional to the product of the mass and the acceleration acquired by it". In other words, if a force acts on a body that is greater than forces acting in the opposite direction, the body will accelerate in the direction of the greater force.

  • This formula can be summarized by the equation F = ma, where F is the force, m is the mass of the body, and a is the acceleration.
  • Using this law, it is possible to calculate the force of gravity of any body on the Earth's surface using the known gravity acceleration.
Calculate Force of Gravity Step 7
Calculate Force of Gravity Step 7

Step 2. Know the acceleration of Earth's gravity

On Earth, the force of gravity of bodies causes bodies to accelerate at a rate of 9.8 m/s.2. On the Earth's surface, we can use the simplified equation Fserious = mg to calculate the force of gravity.

If you want a more accurate approximation of force, you can still use formula Fserious = (GMEarthm)/d2 to determine the force of gravity.

Calculate Force of Gravity Step 8
Calculate Force of Gravity Step 8

Step 3. Use the proper measurement units

For this specific equation, you need to use the metric system. The mass of bodies must be in kilograms (kg) and the acceleration in meters per second squared (m/sec2). You need to convert these units before proceeding with the calculation.

Calculate Force of Gravity Step 9
Calculate Force of Gravity Step 9

Step 4. Determine the mass of the body in question

For smaller bodies, you can weigh them on a scale to find the weight in kilograms (kg). For larger bodies, you will need to check a table of approximate weights on the internet. In physical exercises, body mass is usually given in the statement.

Calculate Force of Gravity Step 10
Calculate Force of Gravity Step 10

Step 5. Solve the equation

After defining the equation's variables, you can assemble and solve it. Remember that all units must be in the metric system and in the correct scale. The mass must be in kilograms and the distance in meters. Solve the equation using the correct order of operations.

  • Let's use the same equation as above and see the level of approximation. Discover the force of gravity of a 68 kg person on the Earth's surface.
  • Remember to use the variables in the correct units: m = 68 kg, g = 9, 8 m/s2.
  • Write the equation: Fserious = mg = 68*9, 8 = 666 N.
  • Using the formula F = mg the force of gravity is 666 N. Using a more exact equation, the result is 665 N. As you can see, these values are pretty much identical.

Tips

  • These two formulas should give the same result, but the shorter formula is simpler to use when working with bodies on the planet's surface.
  • Use the first formula if you don't know the planet's acceleration of gravity or if you're trying to find the force of gravity between two very large bodies, like the Moon and a planet.

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