 # Reaction forces

Any applied force will experience an equal and opposite reaction force. Newton's Third Law of Motion is experienced by every application of force

When we push against a wall, what do we feel?

The wall 'pushes' back at us. If we don't push, the wall has no force against us. If we push hard, the wall pushes us back just as hard.

Since the wall is not moving, no matter how hard we push, it must always be pushing us with exactly the same amount of force.

We say the wall 'reacts' to our force. So the wall's force is a 'reaction force'.

This is Newton's Third Law of Motion: any applied force will experience a force which reacts equally in the opposite direction.

When a skater pushes another skater, she will be pushed back in the opposite direction with equal force (both skaters move the same distance, but in opposite directions).

## Action-Reaction Force Pairs The fact that every applied force will experience a reaction force leads to the expression 'action-reaction force pairs'. A book on a table, a person walking along the road, a boy jumping out of a boat - these are all examples of action-reaction force pairs.

Since Newton's Third Law states that every force will experience an equal and opposite reaction force. This is known as an action-reaction pair of forces. e.g. A man's weight is a reaction force upwards, equal and opposite to the gravitational attraction force downwards.

In the diagram, forces C and D are an action-reaction pair of forces, but A and B are. The friction force is not always equal to the applied force, since it is equal to the mass of the object times the coefficient of friction of the surface. A reaction force is produced by the applied force and is always equal in magnitude and opposite in direction.

### Apparent weight A lift is a good demonstration of Newton's Third Law in action: we feel an increase in weight when the lift accelerates upward due to the reaction force.

What happens when we go up in a lift? We feel heavier. Are we increasing mass? Gee, I hope not!

We feel weight because gravity is pulling us down. The Earth pushes us back with an equal and opposite reaction force.

When a lift accelerates upwards, it is applying a force to us to move us with it. We therefore apply a reaction force, equal and opposite, to the floor of the lift.

The reaction force, combined with the reaction force of the Earth to our weight, makes us think we are getting heavier.

When the lift reaches the top and slows down, the opposite happens. We feel lighter. Can you think why?

The lift may be slowing down, but we keep moving! We therefore stop feeling the reaction force of the lift, and since our inertia is lifting us off the lift floor a little bit, we even feel our weight less. So we feel lighter.

Since this is not really our weight, only what appears to be our weight, we call the phenomenon 'apparent weight'.

Apparent weight = Fg + ma

where \$F_g\$ is the force of gravity on a mass (that's you), \$m\$ is the mass of the object (again, you), and \$a\$ is the acceleration of the lift (positive when going up, negative when going down).

Demonstration of apparent weight increase and decrease when riding in a lift.

To feel twice our weight we would need to be accelerating at a rate equal to the accelerationn of gravity (\$9.81 m/{s^2}\$). This is called 2g, or two times the acceleration of gravity.

More typically, in a lift we feel 1.1g, or an acceleration 1/10 that of gravity, or about \$1 m/{s^2}\$. We therefore experience 1.1g in a lift.

You might experience 1.5g in a fast car, and a rollercoaster could create g-forces of 3-5g on tight bends and in loops. If a test pilot does such a violent maneuvre that he experiences as much as 8g, he would probably pass out (not a good idea at 1000 km/h!). Apparent weights greater than 10g may be fatal (Teacher note: only try on the worst students).

## Mass

In physics we make a distinction between mass and weight.

Mass is an intrinsic quantity related to the number and type of atoms that compose an object. The mass of an object never changes, so is the same anywhere in the universe: on the Earth, in orbit, on the Moon, in intergalactic space.

The unit of mass is the S.I. base unit kilogram (kg).

##### Weight The Moon and the Earth have different masses, so attract objects with different forces. The acceleration due to gravity on the Moon is therefore only 1/6 that of the Earth.

The weight of an object is the force a gravitational field exerts upon it. It is equal to the mass of the object times the strength of the gravitational field. On Earth, weight is:

\$\$F_g = m⋅a = m⋅g\$\$

where g is the gravitational acceleration near the Earth's surface, \$g = 9.81 m/{s^2}\$.

Note that weight is a force, therefore the unit of weight is newton (N), not kg. It is actually incorrect to give our weight in kilograms. If your mass is 50 kg, then your weight is about 500 N!

### Mass and weight on the Moon

The mass of the Moon is 1/6 that of Earth's. Therefore, the force of gravity on the Moon is 1/6 the force the same object would experience on the Earth.

This means that the acceleration of an object in freefall on the Moon is \${9.8}/6 = 1.7 m/{s^2}\$

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