Gravitational Forces

Gravitational Forces

Activity 1. Mass and weight of bodies

 

Explore the textual information below:

Mass (m) is the amount of matter in a body. The more matter contained in a body, the greater its mass. It is measured in grams and kilograms. It is a constant quantity and does not change with location. For example, an object with a mass of 1 kilogram on Earth will have the same mass on the Moon and any other place in space. The greater the mass of an object, the greater the force needed to accelerate or stop it.

Weigh (G) is a physical quantity defining the force of gravity (gravitational force) with which a body of a given mass is attracted to the centre of another body of greater mass. The weight of any object represents the mass of the object and the force of gravity acting on the object. Or, put another way, weight is a measure of the gravitational force acting on the object. Weight is a force and is therefore measured in Newtons (N).

Unlike mass, weight is not a constant quantity and can vary depending on where a body is in the universe, i.e. it depends on the strength of the gravitational field. For example, the same body will weigh less on the Moon than on Earth because the gravity (g) on the Moon is weaker than on Earth.

Mass and weight are two different but related concepts. According to Newton’s second law, weight is proportional to the mass of the body and the acceleration of free fall (g) and is expressed by the formula G = m.g

This means that the greater the mass of a body, the greater its weight at a given acceleration of free fall.

Example: to clarify the difference between mass and weight, consider an astronaut who is soon going on a mission to the Moon. While the astronaut is still on Earth, his measured mass is 100 kg. With Earth’s gravity at 9.8 m/s², the astronaut’s weight would be 980 N.

After landing on the Moon, the astronaut’s mass will still be 100 kg. However, the Moon’s gravitational acceleration is only 1.6 m/s², so the astronaut’s weight will be 162 N.

 

Questions and tasks to be performed

Each body in our solar system has a different mass, and a different radius (i.e. size). Therefore, there is a different gravitational acceleration on the surface of each body.

 

  1. Take a look at the pictures and the table that shows data about the different planets in our Solar System.

Source: https://k8schoollessons.com/wp-content/uploads/2013/05/solar-system.jpg

 

Source: https://www.pixelstalk.net/wp-content/uploads/2016/08/3D-Solar-System-Wallpaper-620×467.jpg

 

mass

m (kg)

 radius

r (km)

 gravitational acceleration

 g (m/s )2

weight of a person

G (N)
Earth’s Moon 7,342 . 1022 1 737 1,62 129,85
Mercury 3,301 . 10 23 2 440 3,7 296,0
Venus 4,8675 . 1024 6 052 8,87 709,6
The Earth 5,9742 . 1024 6 378 9,81 784,8
Mars 6,4171 . 1023 3 390 3,72 297,6
Jupiter 1,8982 . 1027 69 911 24,79
Saturn 5,6834 . 1026 58 232 10,44 835,2
Uranus 8,6810 . 1025 25 362 8,87 709,6
Neptune 1,024 . 1026 24 622 11,15 892,0

 

  1. Based on the data in the table, answer the questions and solve the problems.

 

Questions and tasks:

    1. Which planet in the solar system has the greatest mass?
    2. Which planet in the solar system has the least mass?
    3. What is the largest planet in the solar system?
    4. What is the smallest planet in the solar system?
    5. Which body has the least acceleration of gravity at the surface?
    6. Which body has the greatest gravitational acceleration at the surface?
    7. How many times less is the gravitational acceleration on the surface of the Moon?
    8. Calculate the weight of a person on the surface of Jupiter.
    9. Discuss the effect of the mass of a body on the magnitude of the gravitational acceleration of its surface.

 

    1. Complete the interactive exercise: