Newton's Law of Gravitation
Earth and Space

Tin of beans

Classroom Activity for 11-14 Supporting Physics Teaching

What the Activity is for

The aims are to establish the strength of the gravitational field at the Earth's surface and to appreciate that the strength of the gravitational field will be different at the surface of other planets.

According to Newton's model, all objects with mass exert a gravitational force on all other objects with mass.

At any point the strength of the gravitational field due to any object with mass (such as the Earth) is given by the gravitational force per kilogram.

At the surface of the Earth the strength of the gravitational field is about 10 N on each kilogram (10 newton / kilogram). On the surface of the Moon the strength of the gravitational field is about one-sixth of what it is on the Earth (2 newton / kilogram). The strength of the gravitational field is different at the surface of all of the other planets because they have different masses.

What to Prepare

  • spring balances 0–10 newton
  • 1 kilogram of 100 g slotted masses
  • selection of 200 g baked bean tins (with labels retained) of different masses

To prepare the tins use 200 gram tins, with the labels kept on. Drill a large hole (30 mm diameter) in the base, drain the contents, wash thoroughly and add sand and masses as required. Reseal the hole with a metal or plastic patch attached with epoxy resin adhesive (a false patch can be added to the Earth can of beans as well!).

Combinations of 100 gram masses and sand can be used to obtain the appropriate masses, as follows:

Venus 180 gram

Earth 200 gram

Mars 80 gram

Jupiter 520 gram

Label the top of each tin with a letter so that the order is not obvious.

Safety note: If can openers are used, all sharp edges must be sealed effectively. If tins are not washed out thoroughly, decomposition of the food residue will introduce a health hazard. Alternatively, discard the tins after use.

What Happens During this Activity

In this activity, pupils measure the strength of the Earth's gravitational field, and begin to explore the difference between the mass of an object and the gravity force acting on the object. After this activity, they should also begin to appreciate that placing the same mass on other planets will result in different gravity forces acting on those masses.

Instructions:

  1. With a spring balance and a 1 kilogram set of 100 gram slotted masses in front of them, ask the class to measure the strength of the force with which the Earth pulls on 100 gram (the wording is important here). Confirm that it is about 1 newton, the gravity force (as it happens) of a typical apple. To get a feel for the gravity force of a 100 gram mass encourage the pupils to hold it in their hand. Explain that since gravity force is a force, we say that its gravity force is about 1 N.
  2. Ask pupils to then predict what the force of the Earth will be on 200 gram, and then perhaps 600 gram.
  3. Next ask pupils to measure the strength of the force with which the Earth pulls on 1 kilogram. Confirm that this is about 10 newton. This is a special value, which we call the gravitational field strength of the Earth.
  4. The gravitational field strength at the surface of the Moon is different, because the Moon has a smaller mass. It is about one sixth of the value, around 1.7 newton / kilogram. Ask the pupils to put just 200 gram on the spring balance and feel the gravity force acting on that mass with their eyes closed. If they were on the Moon, this is roughly how heavy a kilogram would feel.
  5. Attention should now be drawn to the selection of baked bean tins, all nominally 200 gram. The pupils should be told that one of them is how a can of baked beans would feel on Earth, one on Venus, one on Mars and one on Jupiter. They should identify which is which (it is likely you will need to share sets of tins between several pairs).

The whole activity should take no more than 40 minutes.

The important thing is for the pupils to get a feel for the concept of gravitational force and an appreciation of what gravitational field strength means and how it varies from place to place.

For reinforcement, a set of simple calculations could be performed:

Teacher: Calculate the gravity force acting on an object of mass Z on planet Y, where the gravitational field strength is X newton / kilogram.

Here's an example:

Calculate the gravity force acting on an object of mass 12 kilogram on Neptune, where the gravitational field strength is 14 newton / kilogram.

Answer: the gravity force is 12 kilogram  ×  14 newton / kilogram, which is 168 newton.

As an extension, you might mention the effect of distance on the value of the gravitational field strength – nothing quantitative, just an appreciation that it will decrease with distance. So, in the case of the Earth, as you go into space gravity gets weaker.

However, you have to go a very long way from the Earth for gravity to become insignificant. At the height of most orbits for spacecraft, there is still an appreciable gravitational field. That is what holds the spacecraft in orbit.

Newton's Law of Gravitation
is expressed by the relation F=G(m_1)(m_2)/r^2
can be used to derive Kepler's First Law

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