In a frictionless pulley system, is the tension the same on both sides of the rope? Why?

In a frictionless pulley system, is the tension the same on both sides of the rope? Why?

• A. No; the heavier side has greater tension.
• B. Yes; the tension is the same on both sides because the rope is massless and the pulley is frictionless.
• C. Only if the masses are equal.
• D. Only if the rope stretches.

Answer: (B)

In an ideal frictionless pulley system, the tension is the same on both sides because the rope is massless and the pulley is frictionless. A massless rope cannot support a net force at any tiny segment; if the tensions on its ends differed, that segment would experience a net force and would need infinite acceleration, which isn’t possible for a massless rope. The pulley being frictionless means the rope can change direction without any loss or gain in tension magnitude, so the same tension pulls on both sides. If the rope had mass or the pulley weren’t frictionless, tensions could differ along the rope.

In an ideal frictionless pulley system, the tension is the same on both sides because the rope is massless and the pulley is frictionless. A massless rope cannot support a net force at any tiny segment; if the tensions on its ends differed, that segment would experience a net force and would need infinite acceleration, which isn’t possible for a massless rope. The pulley being frictionless means the rope can change direction without any loss or gain in tension magnitude, so the same tension pulls on both sides. If the rope had mass or the pulley weren’t frictionless, tensions could differ along the rope.