# The 7 Rules That Determining Motion After Collision

##### 4 minutes • 760 words

## Table of contents

#### 45. The rules for determining how much the motion of each body is changed because of the collision of other bodies

Collisions with other bodies cause bodies to:

- increase or decrease their motions, or
- turn elsewhere

In order to calculate such changes, we only need to:

- subtract the amount of force in each, either to move or to resist motion, and
- establish for certain that which is stronger always achieves its effect.

This could easily be deduced by calculation if:

- only 2 bodies encountered each other mutually
- they were perfectly hard, and separated from all others.
- In this way, their motions were not impeded by any other surrounding bodies, nor assisted.

They then would follow the following rules.

#### 46. Rule 1

Assume Body `B`

and `C`

, were perfectly equal and moving at equal speeds. `B`

is moving from right to left, and `C`

from left to right.

When they encountered each other, they would be reflected and then continue to move, `B`

to the right, and `C`

to the left, without any loss of their speed.

#### 47. Rule 2

If `B`

were just slightly larger than `C`

, then only `C`

would be reflected. Both would move to the left with the same speed.

#### 48. Rule 3

If they were equal in mass, but `B`

moved slightly faster than `C`

, they would both continue moving to the left. Some of `B`

’s excess speed would be transferred to `C`

.

If:

- B had 6 units of speed
- C had 4 units

After the collision, each would move to the left with 5 units of speed.

#### 49. Rule 4

Assume body `C`

were completely at rest and slightly larger than B. No matter how fast `B`

moved towards `C`

, it would never move `C`

.

Instead, it would be repelled by `C`

in the opposite direction.

This is because a stationary body resists high velocity more than low velocity, in proportion to the excess of one over the other.

Therefore, the force in `C`

to resist would always be greater than in B to propel.

#### 50. Rule 5

Assume that body `C`

were stationary and smaller than `B`

.

No matter how slowly `B`

moved towards `C`

, it would move `C`

with it, transferring a portion of its own motion to it, so that both would subsequently move at the same speed.

Specifically, if `B`

were twice as large as `C`

, it would transfer to `C`

1/3 of its motion.

This is because that 1/3 would move the body `C`

as quickly as the remaining 2/3 would move the body `B`

, which is twice as large.

So, after `B`

had encountered `C`

, it would move 1/3 slower than before. It would take the same amount of time to move through a space of 2 feet as it did before to move through a space of 3 feet.

Similarly, if `B`

were 3 times larger than `C`

, it would transfer to `C`

1/4 of its motion, and so on for the rest.

#### 51. Rule 6

If the mass of stationary body `C`

were precisely equal to that of the moving body `B`

, when `B`

approached `C`

with 4 units of speed, it would:

- transfer 1 unit of speed to
`C`

- be reflected with the remaining 3 units in the opposite direction.

#### 52. Rule 7

Assume `B`

and `C`

were moving towards the same direction.

`C`

was moving slower, with`B`

eventually catching up to it`C`

were larger than`B`

- The speed of
`B`

was greater than the excess of size in`C`

Then `B`

would transfer just enough of its motion to `C`

so that both would subsequently move at the same speed and direction.

However, if the excess of speed in `B`

were less than the excess of size in `C`

, then `B`

would be reflected in the opposite direction and retain all of its motion.

These excesses are calculated as follows:

- If
`C`

were twice as large as`B`

and`B`

did not move twice as fast as`C`

, it would not propel`C`

but would be reflected in the opposite direction. - If it moved more than twice as fast, it would propel
`C`

.

For instance, if `C`

had only 2 units of speed and `B`

had 5, subtracting 2 units from `B`

would transfer only 1 unit to `C`

.

This would make both bodies move with 3 units of speed thereafter. This is because `C`

is twice as large as `B`

.

This would result in both bodies, `B`

and `C`

, moving with 3 units of speed.

This reasoning applies similarly to other cases.