You are here
๐ฌ Think about it
So far we applied Newton's laws to one object. But what about two boxes tied together and pulled along? Can we treat them as one? Cleverly grouping objects can make the maths much simpler. Let us see how.
How do we find the acceleration of two connected boxes?
- Treat the two boxes and the string as a single system.
- Then only external forces matter; internal forces (the tension) can be ignored.
- The force F is external; the tension T between the boxes is internal.
\( a \)
=
\( \dfrac{F}{m_1 + m_2} \)
Why is treating objects as a system useful?
- The system accelerates just like a single object of mass m 1 + m 2 .
- Analysing the boxes individually would give the same result.
- The downward weight (m 1 g + m 2 g) is balanced by the normal force (N 1 + N 2 ).
Example:
While walking, your arms and legs move in a complex way, yet your whole body can be studied as one object.
Important Points
- Connected objects can be treated as one system.
- Only external forces affect the system's acceleration.
- The system behaves like a single object of the total mass.
๐งฉ Threads of Curiosity
- While walking, your arms and legs move in a complex manner.
- Yet your overall motion can be studied by treating your body as a single object.
- Science often becomes simpler when we look at the whole rather than the parts.
โ Test Yourself
-
When two boxes are treated as a system, which forces matter?
View Answer
Only the external forces; internal forces like tension can be ignored. -
What is the acceleration of two boxes (masses mโ, mโ) pulled by force F?
View Answer
a = F / (mโ + mโ).
Important Definitions
- System of objects — two or more connected objects treated together as one, so only external forces need be considered.
- Tension — the internal pulling force in a connecting string between objects.
๐ NCERT Question 15 — A tractor pulls a
A tractor pulls a harrow (accel aโ), then a trolley (accel aโ), then both together — find the acceleration.
View Answer →
