# Solving a problem

#### werehk

PHF Hall of Fame
When some objects collide with each other,
how should I define the system(i.e. what objects to be included) to determine whether a force is external or internal force?

When would earth be considered inside the system?

What is the meaning of transfer of momentum from one object to another?

#### topsquark

Forum Staff
When some objects collide with each other,
how should I define the system(i.e. what objects to be included) to determine whether a force is external or internal force?

When would earth be considered inside the system?

What is the meaning of transfer of momentum from one object to another?
What system to use can sometimes be confusing. The rule of thumb is to choose the system that makes your problem as simple as possible. For example, in most cases of projectile motion we ignore the Earth as being part of the system. The reason for this is that the motion of the Earth (toward the falling object) introduces an extra complication to the problem and is, frankly, negligible anyway.

In other cases we find that redefining the system (with care!) can be to our advantage.
Consider a string pulling with a force F a combination of two masses, M and m, which are in turn connected by a string. What is the acceleration of the two masses?
By choosing the system to be composed of both masses (and their connecting string) we can very easily find that
$$\displaystyle a = \frac{T}{m + M}$$
a result that we can verify by taking each mass and the connecting string as separate systems and solve a system of equations for taking much more time and effort.

Rule of thumb: If the Earth is not specifically mentioned in the problem, the odds are that you don't need to consider it.

A momentum transfer takes place during a collision. Typically the momentum of two (or more) objects in a collision is transfered in some way, such that the sum of the changes in the momentum of all the objects is 0 kg m/s. There is always some such transfer of momentum in a collision, no matter how small.

-Dan

#### werehk

PHF Hall of Fame
For the transfer of momentum, can it be interpreted as change in speed during collision?

#### topsquark

Forum Staff
For the transfer of momentum, can it be interpreted as change in speed during collision?
Typicaslly, yes. However, not that a change in momoentum is defined as the change in the quantity mv, so if the mass of the objects change during the collision (if they were, say, putty) then this too would affect the change in momentum. (Most Intro Physics problems do not take this into account for simplicity.)

-Dan

werehk