Is mass the inertia of a body

3. Inertia and mass

3.1 Bodies are differently inert

1. In order to change the state of motion of a body, a force is required. If there is no force on the body, its state of motion cannot change.

To express that the state of motion of a body remains the same without the action of a force, one also says in physics: All bodies are sluggish.

2. But not all bodies are equally sluggish. To change the state of motion of a table tennis ball and a solid steel ball of the same size in the same way, a much greater force is required with the steel ball than with the table tennis ball. On the other hand, if an equally large force is applied to the table tennis ball or the steel ball, the speed of the steel ball changes less quickly than that of the table tennis ball. The steel ball is therefore much more sluggish than the table tennis ball.

Indolence is a property of every body. How A body is inert is determined by its physical size Dimensions specified. A body that is very inert has great mass; a body with less inertia has a smaller mass.

The mass is measured in the unit 1 kilogram (1 kg) (see introduction).


Exercises

1. What should you watch out for when towing a vehicle using a rope?

2. Explain what happens in each case using the terms inertia and Dimensions.

a) A block of wood is loosely placed on a carriage.
a1) The car is given a push so that it starts off suddenly.
a2) The wagon with the block of wood on it hits an obstacle.
a3) The wagon and block of wood are pulled straight ahead at a constant speed and then drive through a tight curve.

b) Dynamometers, which are connected to one another by a rod, are attached to two carriages of different weights. If you pull the bar evenly, both carriages change their state of motion in the same way. Compare the readings on the dynamometers.

c) Place a sheet of paper under a paper cup that is on the edge of the table. Can you pull the paper away without the cup tipping over? The cup should be filled once and empty once.

d) Two steel balls of different sizes are pushed away with the same force - e.g. by a curved plastic ruler. Which of the balls reaches the higher speed?

3. Stack twenty 5 cent pieces on top of each other. The bottom one is meant to be removed without lifting or tipping the stack ...

4. A plate filled with water is pushed jerkily or moved at a constant speed and then stopped abruptly. Think about which side the water spills over.

5. During which maneuvers of buses and trams is it important that standing passengers hold on tightly?

6. If a plate falls on a stone floor, it is more likely to break than if it falls on a carpeted floor. Why?


3.2 Mass and weight

A single 5-cent coin and two 5-cent coins stuck together are dropped from the same height at the same time. Do the stuck coins hit the ground sooner than the single coin?

Twice the weight acts on the stuck together coins as on the single coin. So one might think that the stuck coins actually hit the ground first. The observation shows, however, that this is not the case: single and double coins hit at the same time. From this it can be concluded that the inertia of the double coin must also be twice as great as the inertia of the single coin. Expressed differently:

The weight and inertia of a body are proportional to each other,
and therefore weight and mass are also proportional.

This is nothing new, because when the unit of force was introduced, the weight of a body became mass m detected:

.

Since the moon landings, it has also been experimentally proven that all bodies on the moon are "lighter" - i.e. the weight of a body on the moon is less than the weight that acts on the same body on earth:

.

Does that mean that the mass of a body on the moon is smaller than on earth?

The answer to this is the observation that bodies fall more slowly on the moon than on earth. An example: If a stone is dropped from a height of 10 m on the earth, it hits after a fall time of 1.43 s. On the other hand, the fall time on the moon is 3.51 s.

If the inertia - and thus the mass - of the stone were smaller on the moon than on earth, then it would have to fall just as quickly as on earth under the effect of the smaller weight force. But since it falls more slowly, it can be concluded that its inertia - and thus its mass - is the same on the moon as on earth.

Also on the moon (as on every celestial body) it applies that weight and mass of bodies are proportional to each other. Only is the proportionality factor, which is also called Location factor is called another.
 

Celestial bodies
G in N / kg
Earth: equator
Central Europe
North, South Pole
9,78
9,81
9,83
moon
1,62
Mercury
3,7
Venus
8,87
Mars
3,93
Jupiter
23,31
Saturn
9,28
Uranus
9
Neptune
11,6
Pluto
0,57


Exercises

1. A horizontally directed force of 1 N is exerted on a body weighing 1 kg, once on the earth and once on the moon. After a certain period of time, is the body faster on the moon than on earth?

2. An astronaut's equipment has a mass of 84 kg. How great is the weight on earth and on the moon?

3. Calculate the weight forces that act on a person (70 kg) in Central Europe, at the equator and at the North Pole.

4. What force would be required to carry a bag with a mass of 4 kg on the different planets?

5. Sugar is often offered in 1 kg packs. You could also make the sugar packs a little bigger and write ā€œ10 Nā€ on the pack. Why wouldn't that make sense?

6. How can you use a beam balance to determine which of two objects has the larger one on? Weight force works?
Can you also use the beam balance to measure how great the weight is on the two bodies?

7. On the moon it is measured that a packet of sugar has a mass of 5 kg. Another pack is hung there on a dynamometer; it shows 25 N. Which pack contains more sugar?
What would the answer be if the same measurement results had been obtained on Earth?

8. A spaceship moves through space without any propulsion. The objects in it seem to be completely weightless. Inside the spaceship there is a massive iron cylinder and a hollow iron cylinder. Outwardly, both look completely the same. An astronaut takes one of the two cylinders in each hand, shakes it - and immediately knows which one is the massive one ... Why?