S2.7 Tension
[A] About the force
- A stretched string (or wire, rod …) is said to be under tension.
- The force such a string exerts on an object to which it is attached has magnitude T, the tension, and acts along the string, away from the object.
- If the string is light enough the tension is uniform (the same at both ends).
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Tension does not really have the credentials of a force: it has a ‘magnitude’ (of the right ‘units’!), but not a direction. It is best to think of it as something which can be used to specify a force–namely the force which a stretched object exerts on the point to which it is attached. The example that follows may help.
Commentary

About the ‘F-symbols’
We could think of all the forces that feature in this argument as ‘one-dimensional vectors’ whose sign prescribes their direction (see S0.4). But here it is clearer if we use the ‘F-symbols’ to represent only the magnitudes of the forces and put in the appropriate signs (plus or minus) explicitly, when we come to combine the forces.- Apply Newton’s 2nd law to the string:
FSB-FSA=ma
- The RHS is zero if string is light.
- Then FSA=FSB
- Invoke the 3rd law (twice):
- So string exerts forces of equal magnitude on each end:
FAS=FBS≡T
[B] Example problem
Two masses m1 and m2 are suspended over a light and frictionless pulley. Find the accelerations of the masses and the string tension. |
Results
string tension:
![\[ T= \frac{2m_1 m_2}{m_1 +m_2} g \]](mastermathpng-4.png)
![\[ a= \frac{m_1- m_2}{m_1 +m_2} g \]](mastermathpng-5.png)
Check It!
- Are the units OK?
- Does it make sense?
Learning Resources
![]() | HRW Chapter 5.7,5.9 |
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