Notes on Pulley Systems

Introduction to Pulleys

• Pulleys are simple machines that help multiply the force exerted to lift objects.

Example Problem

• Lifting a 400 Newton crate requires a force of at least 400 Newtons in the upward direction.
• With two ropes, the tension force is the same in both ropes.
• Tension in each rope = 200 Newtons (since 200 + 200 = 400).
• Input force = 200 Newtons, Output force = 400 Newtons.
• Mechanical Advantage (MA) = Output Force / Input Force = 400 / 200 = 2.

Work and Distance

• The pulley system allows the user to lift a heavy object by applying less force over a longer distance.
• If the crate moves up by 1 meter, the rope must be pulled down by 2 meters:
  • Rope moves up by 1 meter (both ropes) = 2 meters total down pull.
• Work Calculation:
  • Work (W) = Force (F) x Displacement (d).
  • Output Work = 400 N x 1 m = 400 Joules.
  • Input Work = 200 N x 2 m = 400 Joules.
• Energy is conserved: energy is not created or lost.

Mechanical Advantage and Number of Ropes

• Mechanical Advantage is equal to the number of ropes used:
  • Example: 4 ropes for an 800 Newton crate gives MA = 4.
  • Input Force: 800 N / 4 = 200 N.
• Forces in the ropes are equal:
  • Tension in each rope is 200 N (4 ropes = 200 + 200 + 200 + 200 = 800 N total).

Distance Requirement

• To lift the crate 1 meter with 4 ropes, pull down 4 meters.
• Work Output = 800 Joules (800 N x 1 m).
• Work Input = 200 N x 4 m = 800 Joules.

Efficiency Considerations

• In ideal scenarios, input work = output work (ignoring friction).
• More ropes increase the mechanical advantage, but also require a longer pull distance:
  • Example: 10 ropes require 10 meters pull to lift 1 meter.

Practical Observations

• In real experiments, ropes may not move uniformly due to pulley tilt or alignment.

Summary Points

• Mechanical Advantage (MA) = Number of ropes.
• MA = Output Force / Input Force.
• To lift heavier objects, apply smaller input force over longer distances, resulting in larger output over shorter distances.
• Input work equals output work, assuming no energy loss.

Conclusion

• Understanding pulleys aids in comprehending force multiplication in mechanical systems.