7.4.3 Pulleys

Strings and ropes often pass over pulleys. The application might be as simple as lifting a heavy weight or as complex as the internal cable-and-pulley arrangement that precisely moves a robot arm.

FIGURE 7.24a shows a simple situation in which block B, as it falls, drags block A across a table. As the string moves, static friction between the string and pulley causes the pulley to turn. If we assume that

then no net force is needed to accelerate the string or turn the pulley. Thus the tension in a massless string remains constant as it passes over a massless, frictionless pulley.

FIGURE 7.24 Blocks A and B are connected by a string that passes over a pulley.

The figure consists of two parts labeled ("a") and (b) that illustrate two blocks labeled "A" and B connected by a rope and their free body diagrams on an x y coordinate plane.
FIGURE 7.24 Full Alternative Text

Because of this, we can draw the simplified free-body diagram of FIGURE 7.24b, in which the string and pulley are omitted. Forces T⃗A on B and T⃗B on A act as if they are an action/reaction pair, even though they are not opposite in direction because the tension force gets “turned” by the pulley.

TACTICS BOX 7.2 Working with ropes and pulleys

For massless ropes or strings and massless, frictionless pulleys:

  • If a force pulls on one end of a rope, the tension in the rope equals the magnitude of the pulling force.

  • If two objects are connected by a rope, the tension is the same at both ends.

  • If the rope passes over a pulley, the tension in the rope is unaffected.

Workbook Exercises 17–22