Forces inside, forces outside

The idea

Connected objects can be treated as one system: forces between its parts, such as the tension in a connecting string, are internal and need not be considered, and only external forces acting from outside matter.

Two boxes on a string

Two boxes are joined by a string. You pull one of them, and the other follows.

Which forces would you need to count to find how the boxes move together?

• Only the force pulling from outside
• The string's tension and the pull, both
• Only the string's tension

Draw the boundary

Treat both boxes and the string as one system.

Only outside forces

The string pulls on both boxes, but these forces are between the parts of the system. When we look at the two boxes as one system, we do not need them. Only the force F from outside matters.

Connected objects can be treated as one system: forces between its parts, such as the tension in a connecting string, are internal and need not be considered, and only external forces acting from outside matter.

Notes

Connected objects form a system. Internal forces (like string tension) can be ignored; only external forces matter.

Check yourself

Two boxes are joined by a string and Box 1 is pulled by a force F. Which force is internal to the system of both boxes?

Which forces matter when two connected boxes are treated as one system?

Box 1 pulls Box 2 through the string. What does Box 2 do to Box 1?

Why is it useful to treat connected objects as one system?

• The tension in the string — correct. Yes!
• The force F. F acts from outside the system, so it is an external force.
• Both F and the tension. The tension acts between the parts of the system, but F acts from outside.
• The internal forces. Forces between the parts of the system need not be considered.
• The external forces — correct. Yes!
• All the forces, internal ones included. The internal forces need not be considered, only the forces acting from outside matter.
• Nothing, because the string is light. By the third law, Box 2 applies an equal and opposite force on Box 1 through the string.
• It pushes Box 1 forward. The force of Box 2 on Box 1 is opposite to the force of Box 1 on Box 2.
• It pulls back with an equal and opposite force, the tension — correct. Yes!
• The forces inside need not be considered, which makes the analysis simpler — correct. Yes!
• It makes the external force zero. The external force still acts. Only the internal forces need not be considered.
• It removes the third law. The third law still holds. It is just that the internal forces need not be considered.