Introducing Forces

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Purpose

This is a level (2+ to 3+) mathematics in science contexts activity from the Figure It Out series.
A PDF of the student activity is included.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Student Activity

Click on the image to enlarge it. Click again to close. Download PDF (846 KB)

Specific Learning Outcomes

Students will:

  • work with constants and variables (mass is constant regardless of gravity; weight is variable)
  • investigate proportional relationships – when one quantity varies directly according to another (for example, the force of gravity and mass).

Students should discover that:

  • force is proportional to mass.
Required Resource Materials
FIO, Forces, Levels 2+-3+, Introducing Forces, page 1

a classmate

science books on forces and/or access to the Internet

Activity

Preparation and points to note

Make sure the students have access to computers and/or reference books to fi nd good data. You may wish to suggest some age-appropriate websites (see the section on related information). Set ground rules about pushing and pulling, for example, We’re studying forces, not experiencing them! Note that action and reaction will be explored in the next activity, Rocket Balloon.

This activity is ideal for focusing on the key competency thinking because students will be exploring forces* by using their own experiences and ideas and the information that they research.

Your students will have a variety of prior knowledge, ideas, and misconceptions about mass, weight, and force. Encourage them to test and argue their ideas and fi nd evidence or counter-arguments through their investigations. Force is a subtle idea. People had incorrect ideas about force for thousands of years before Newton – and after. Students need to be explicitly taught the norms of mathematical argumentation and that it’s the ideas that are competing and being evaluated, not them.

Most students will have intuitive knowledge of forces, so questioning strategies that prompt the students to probe deeper into their own thinking will probably be more valuable than direct explanation.

Although the term weight is commonly used in general conversation to mean mass, mass and weight are not the same thing. In mathematics and science, the terms have specifi c and very different meanings. Weight is the force of gravity acting on mass. A good way to help the students understand the difference is to ask them to imagine trying to weigh a rocket ship in outer space. Even if they had a scale large enough, there would be no way to put the rocket ship on it and no force pressing it down onto the scale. It would weigh nothing, even though it clearly has a lot of mass. Body mass is another good example. On Earth, a student might have a body mass of 40 kg. On the Moon, that same student would still have the same body mass but their weight would be 1/6 of their weight on Earth. (See the answers for questions 2 and 3 for more on mass and weight.)

Points of entry: Mathematics

Encourage the students to have conversations about the nature of constants and variables: some things don’t vary with location or motion, while other things do. (The mass of an object doesn’t change whether it’s in a pool, on Earth, or in outer space. Weight varies in moving escalators, on swings, in water, or in outer space.)

Prompt the students to think about relationships and proportions. Ask: Will a tennis ball knock down as many pins as a bowling ball? Why does the bowling ball knock down the pin and not vice versa? Which has more gravity, the Earth or the Moon? (Hint: Where do you weigh more?)

Note that, for this Figure It Out book, we have avoided the use of a newton as a unit of measure because it is not a commonly used measurement in mathematics. (For your information, mass is measured in kilograms, force in newtons. You may wonder why, if weight is a measure of force, we describe weight in terms of kilograms … in fact, we should talk about weight in newtons, but kilograms is commonly used as shorthand.)

Points of entry: Science

Mass, force, gravity, and weight can be difficult concepts for students to understand. Most will need multiple examples or representations of each idea to construct a robust defi nition. Challenge the students to test their definitions across many contexts to see if they can be applied universally (for example, ask: How is the force of a bowling ball similar to the force of gravity? What is the force of a bowling ball?).

Concrete and counter-intuitive representations of mass are helpful. For example, bring in a cricket ball, a tennis ball, a bowling ball, and a beach ball and ask the students to rank them in terms of the size of the balls and which has the most mass. Have the students conduct actual or imagined experiments with the force transferred by the different balls when they hit something.

Group and regroup the students strategically so that they are exposed to a variety of examples and are asked to justify their thinking to a variety of classmates. In this way, they are using and developing the key competency relating to others.

Gravity is a function of mass and distance. A large object far away has relatively less force of gravity than a smaller, closer object. It’s because the Moon is so far away that it barely affects your weight on Earth.

Some students will quickly grasp the fact that if gravity is a function of mass, their own bodies create a (small) force of gravity. Not only is Earth pulling at them, but they are also pulling at Earth. Ask What would happen if everyone moved to New Zealand: would the Earth get pulled into a shape that isn’t as round? (If everyone on Earth did move to New Zealand, the Earth would get pulled into a shape that was only very slightly less round. Essentially, we would create a bit of a dip in the ocean on the other side of the planet and a slightly higher tide in New Zealand because water moves in response to gravity much more than rock does.)

Answers

1. a. When you bowl a tenpin bowling ball, you put force on the ball. The momentum of the
ball (the moving object) will push against anything it hits, in this case, the pins.

b. Examples could include: pushing a supermarket trolley, pulling your shoelaces tight, pushing someone over, or pulling a weed out of the garden. (Examples of inanimate objects could include a boat pulling a water skier or a machine pulling a post out of the ground.)

c. When you pull on a rope (for example, in a tug of war or using a rope to help you climb a  mountain), you exert a force on your end of the rope.

The more force you use to push or pull, the more energy you use and the greater the effect on the object being pushed or pulled. For example, when you gently push off the ground on a skateboard, you roll a little bit, but if you push off hard,  you go much faster.

2. a. The mass of objects causes the force of gravity. Massive objects, like Earth and the Moon,  exert a lot of force. Earth pulls on the Moon, and the Moon pulls on Earth. The Moon’s force  causes the tides. The Earth’s force keeps the Moon locked in orbit around Earth instead of flying  into outer space.

b. An apple falls to the ground because of the force of gravity exerted by the mass of the Earth. It’s the same force that keeps the Moon from flying away.

c. The Earth’s gravity is a pull that draws everything to the ground. The force of gravity is what gives us weight. Weight is a force; mass isn’t.

3. In everyday life, most people use “weight” to mean weight or mass. But in science, weight and
mass have different meanings. Mass refers to the amount of material in an object (for example,
the amount of matter in a 10 tonne truck) and weight refers to how that object is being pulled
by gravity (for example, if a 10 tonne truck fell over a cliff, its weight would be the force with which gravity pulled it down).

The Earth has more gravity than the Moon so a 10 tonne truck on the Moon has less weight than the same truck on Earth, even though the mass is the same. A 10 tonne truck floating in outer space would have no weight at all! Another way to think about the difference between mass and weight is to imagine going for a swim. Buoyancy counteracts the effects of gravity and you float, even though you still have the same mass as you have on land.

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Level Two