Connected Bodies, Tension and Pulleys
Systems of bodies linked by inextensible strings share a common magnitude of acceleration, with tension transmitting force between them.
What is Connected Bodies, Tension and Pulleys?
Systems of bodies linked by inextensible strings share a common magnitude of acceleration, with tension transmitting force between them.
Key formula / rule: Inextensible string implies a constraint relation between accelerations.
Key points
- Derive the acceleration of an Atwood machine.
- Apply constraint relations to movable-pulley systems.
Common exam trap
Assuming equal tension across a pulley with mass or friction.
Definitions
- Term
Connected Bodies, Tension and Pulleys
- Meaning
Systems of bodies linked by inextensible strings share a common magnitude of acceleration, with tension transmitting force between them.
- Term
Connected Bodies, Tension and Pulleys — explanation
- Meaning
Two routes exist: write one equation per body, or treat the system as one body to get the acceleration and then return to a single body for tension. Ideal strings are massless and inextensible, so tension is uniform and accelerations are related by the constraint.
Learning objectives
Derive the acceleration of an Atwood machine.
Apply constraint relations to movable-pulley systems.
Formulae
- Key point
Inextensible string implies a constraint relation between accelerations.
- Key point
Tension is uniform in a massless string over a frictionless pulley.
- Key point
System method gives a fastest; body method gives T.
Prerequisites
PHY-U1-NLM-T1-S2-C1
Common mistakes
Assuming equal tension across a pulley with mass or friction.
Ignoring the constraint relation in movable-pulley systems.
Keywords
Connected
Bodies
Tension
Pulleys
Practice preview
Which of the following statements is INCORRECT regarding an ideal (massless and inextensible) string and a frictionless, massless pulley?…
easy
Two masses, m1 = 3 kg and m2 = 2 kg, are connected by a light inextensible string passing over a frictionless pulley. What is the acceleration of the system? (Take g = 10 m/s^2)…
easy
A block of mass m1 = 5 kg rests on a horizontal surface with a coefficient of kinetic friction mu_k = 0.2. It is connected by a light inextensible string passing over a frictionless pulley to a hanging block of mass m2 =…
medium