5.8 Ropes and Pulleys

Ropes and Tension

• Objects are connected by ropes, cables, etc.

• Tension force (T) is the force exerted by the rope on the box.

• Tension and box's force on the rope are equal in magnitude (action-reaction pair).

• Assumption: mass of the ropes is negligible (massless).

Forces Acting on the Rope

• Forces acting include hand's force (F) and the box pulling back on the rope (Fboxeson_rope).

• From Newton's second law: $\sum F<em>x = F - F</em>{box<em>on</em>rope} = 0$ implies $T = F$.

• Tension remains the same throughout a massless rope.

Examples of Tension

• Example scenario: 100 N force on one end creates 100 N tension.

• Tug of war scenario: 100 N pull from each side results in equal tension on both sides (100 N).

• Whether a wall or person pulls, the tension is constant.

Pulleys

• Ideal pulleys (massless and frictionless) do not change tension but change direction of tension force.

• Tension remains constant across pulley.

Practical Applications of Ropes and Pulleys

• Example with spring scale shows it reads equal to weight when static (not accelerating).

• For traction applications (e.g., leg injuries), angle of the rope impacts force:

  • $T = mg$ (where m is mass).

  • For a mass of 4.2 kg, $T = 41.2 N$.

• Equation for angle of traction: $2T \cos(\theta) - F<em>{leg</em>on_pulley} = 0$, leading to calculation of angle θ.

Newton's Laws

• Fundamental principles governing motion and mechanics.

• Importance in understanding everyday physical phenomena and future developments in physics (e.g., Einstein's theories).

In the context of the notes on "Ropes and Tension," "massless" refers to an object, such as a rope or a pulley, whose mass is considered negligible. This means its mass is so small that it can be ignored in calculations, simplifying the analysis of forces and tension in a system. For example, a massless rope implies that the tension remains the same throughout its length, and ideal massless pulleys do not change the tension's magnitude.