Two boxes, one system
Two boxes are tied by a string with almost no mass. You pull one. How fast do both speed up?
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- A 2 kg box and a 3 kg box are joined by a string.
- Treat both boxes as one system of 5 kg.
- The string's pulls stay inside the system. Only F is unbalanced.
On a smooth floor, both boxes speed up at the same rate. That rate is the outside pull ÷ the total mass.
The rule
Boxes joined by a light, tight string move as one system. On a smooth floor, acceleration = outside pull ÷ total mass.
A system is a group of objects taken together as one.
Take a smooth floor and a light string that does not stretch. The string has almost no mass. A light string pulls both boxes equally. The pull F acts from outside, so it is an external force. The string's pulls are internal. They stay inside the system.
On a level floor, a box's weight and the floor's push balance. So only F changes the motion of the system.
| Quantity | Working | Value |
|---|---|---|
| Total mass | 3 + 2 | 5 kg |
| Acceleration of both | 10 ÷ 5 | 2 m/s² |
| String pull on the 2 kg box | 2 × 2 | 4 N |
| Check on the 3 kg box | (10 − 4) ÷ 3 | 2 m/s² |
Only the string pulls the 2 kg box along the floor. So the string's pull is 2 × 2 = 4 N.
The string pulls the 3 kg box back with 4 N too. The net force on it is 10 − 4 = 6 N. So a = 6 ÷ 3 = 2 m/s².
The check on the 3 kg box fits.