The Third Law & Tension
Equal and opposite, but never on the same body. Plus what a rope really does.
Lesson at a glanceShow the key points
- Third law: if A exerts F on B, B exerts −F on A. The two forces act on different bodies, so they never cancel each other.
- Only one force of an action–reaction pair can appear in a given free-body diagram.
- The tension at a point of a string is the magnitude of the pull each side exerts on the other.
- A massless string (with nothing attached in between) has the same tension throughout; a light, smooth pulley does not change it.
- A hanging string of mass m below a point, holding mass M at rest, has tension (M + m)g at that point.
You push on a wall and the wall pushes back just as hard. Yet the wall doesn’t move you backwards across the room. The third law is simple to state and surprisingly easy to misuse.
The third law, again
If body A exerts a force on body B, then B exerts a force of equal size and opposite direction on A. The crucial detail is in the subscripts: the two forces act on different bodies. So when you apply the first or second law to a chosen system (step 2 of the recipe), at most one member of any third-law pair can appear in your list.
A table pushes a book up with a normal force ; the book pushes the table down with . The first belongs in the book’s equation, the second in the table’s. The Earth pulls a falling apple down with , and the apple pulls the Earth up with . These don’t cancel: the first accelerates the apple, the second accelerates the Earth (by an immeasurably small amount, because the Earth’s mass is so huge).
What tension really means
Imagine a block hanging from the ceiling by a string, and slice the string in your mind at some point A. The part below A and the part above A are in contact there and pull on each other with equal and opposite forces (third law again).
A 3.0 kg block hangs at rest from a rope. The part of the rope below a point A has mass 0.40 kg. Find the tension at the bottom end and at A. Then find the tension at A if the whole arrangement is lowered with a downward acceleration of 2.0 m/s². (g = 9.8 m/s²)
Masses of 2.0 kg and 3.0 kg hang from a light string over a light, smooth pulley. Find their acceleration and the tension.
- 1Third-law partners act on different bodies; never put both in one free-body diagram.
- 2Tension at a point = magnitude of the pull each side of the string exerts on the other.
- 3A massless string with nothing attached in between has one tension throughout; a light smooth pulley doesn't change it.
- 4A heavy rope's tension grows toward the top: each point supports everything below it.
Check yourself
Keep exploring
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