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Example — A man on the Earth and on the Moon
- A man weighing 100 kg on the Earth weighs about 16.7 kg on the Moon.
Why does it happen?
- The man's body is exactly the same in both places.
- What changes is the pull acting on him.
- The Earth pulls him with a large force.
- The Moon is much smaller, so it pulls him with a much smaller force.
- The Moon pulls with about one-sixth of the Earth's pull.
- So the weighing scale shows a smaller reading on the Moon.
The same man is weighed on the Earth and on the Moon
his body does not change, the pull does
Mass
The amount of matter in his body
Same in both places, 100 kg
Example:
Measured in kilograms
Weight
The gravitational pull on him
One-sixth on the Moon
Example:
Measured in newtons
The scale reads less on the Moon because the Moon is much smaller, so it pulls with a much smaller force.
What is the mass of the man on the Earth and on the Moon?
- On the Earth his mass is 100 kg.
- On the Moon his mass is still 100 kg.
- Mass is the amount of matter in his body, and that does not change by moving him.
What is the weight of the man on the Earth and on the Moon?
- On the Earth his weight is the pull of the Earth on him.
- On the Moon his weight is the pull of the Moon on him.
- The Moon's pull is about one-sixth of the Earth's pull.
- So his weight on the Moon is about one-sixth of his weight on the Earth.
📌 Note
- In daily life we say "his weight is 100 kg". That is really his mass.
- Weight is a force, so its correct unit is the newton, not the kilogram.
- We will learn more about it later in Newton's Second Law.
What is the difference between mass and weight?
| Point | Mass | Weight |
|---|---|---|
| What it is | The amount of matter in an object | The gravitational force with which the Earth pulls the object |
| Kind of quantity | Not a force | A force |
| Unit | kilogram (kg) | newton (N) |
| Needs a direction | No | Yes, it acts downward |
| Changes with place | No, it is the same everywhere | Yes, it depends on the pull acting on the object |
How is weight a force?
- Weight is the gravitational force applied by the Earth on the object.
- It acts in the downward direction.
- It has a magnitude, a unit and a direction, like every other force.
- That is why weight can be measured with an instrument meant for forces.
How can we measure force?
- A force is measured with an instrument that the force can pull on or push against.
- The instrument used in this chapter is the spring balance.
How can we use a spring balance to measure a force?
- A spring balance was used earlier to measure the weight of objects.
- It can measure not just weight but the magnitude of a force in general.
- Pull the free end of the spring balance with your hand.
- It then shows the force with which you pull on the spring inside the balance.
📌 Note
- The spring balance has a spring inside and a hook at the free end.
- Whatever pulls on that hook is what gets measured.
GIF
Watch: a spring balance was used earlier to measure the weight of objects
![6.1.1 Measuring the Magnitude of - How Forces Affect Moti - [Teachoo] - Concepts](https://cdn.teachoo.com/a0a0d947-2269-4574-bf68-b78842eda6ba/animation-for-how-can-we-use-a-spring-balance-to-measure-a-force-.-a-short-looping-gif-three-or-four-beats-drawn-in-the-flat-classroom-st.gif)
Threads of Curiosity
- Very small forces are not written in newtons. They are written in millinewtons and yoctonewtons.
A millinewton
- 1 N = 1000 millinewtons
- 1000 millinewtons = 1 N
- 1 millinewton = 1/1000 N
- 1 millinewton = 1/10^3 N
- 1 millinewton = 10^-3 N
- The smallest forces we can directly feel are of the order of millinewtons.
- Example — A light touch is a force of this size which is measured in millinewtons.
A yoctonewton
- 1 N = 1000000000000000000000000 yoctonewtons
- 1N = 10^24 yoctonewtons
- 1 yoctonewton = 10^-24 N
- Scientists can measure forces this small in specialised experiments like Nanotechnology.
| Unit | Value in newtons | Where it is used |
|---|---|---|
| newton (N) | 1 N | Everyday forces, like holding a 100 g packet |
| millinewton | 10^-3 N | The smallest force we can directly feel, like a light touch |
| yoctonewton | 10^-24 N | Forces measured by scientists in specialised experiments |
1 N
=
1000 millinewtons
1 millinewton
=
10
−3
N — the smallest force we can feel, like a light touch
1 N
=
10
24
yoctonewtons
1 yoctonewton
=
10
−24
N — measured only in specialised experiments
📝 Important points about measuring a force
| Point | Detail |
|---|---|
| Instrument used | Spring balance |
| What it measured earlier | Weight of an object |
| What weight is | The gravitational force with which the Earth pulls the object |
| What else it can measure | The magnitude of any force applied on it |
| How it is used | Pull the free end; it shows the force on the spring inside |
| Smallest force we can feel | Of the order of 10^-3 N (Millinewtons) |
| Smallest force scientists can measure | 10^-24 N (Yoctonewtons) |
💡 Worth remembering
A spring balance was made for weighing, but the pull you give it with your own hand is measured just as well.
✅ Quick self-check
-
Which instrument measures the magnitude of a force?
View Answer
A spring balance. -
What is the weight of an object?
View Answer
The gravitational force with which the Earth pulls the object. -
In which unit is mass measured, and in which unit is weight measured?
View Answer
Mass in kilograms, weight in newtons.
Key terms and units
| Term | Meaning | Unit |
|---|---|---|
| Spring balance | Instrument that measures the magnitude of a force | - |
| Mass | The amount of matter in an object | kilogram (kg) |
| Weight | The gravitational force with which the Earth pulls an object | newton (N) |
| Millinewton | A force of 10^-3 N | newton (N) |
| Yoctonewton | A force of 10^-24 N | newton (N) |
