Work, Energy, and Simple Machines · Lesson 10 of 13
Simple Machines and Pulley
“A pulley cannot erase work, but it can persuade gravity to accept a more convenient direction.”
• Explain how simple machines make tasks more convenient. • Distinguish effort from load. • Calculate mechanical advantage. • Describe the action of fixed and movable pulleys. • Explain why an ideal machine cannot create energy or reduce total work.
Lifting a heavy load directly may require an uncomfortable upward pull. Pass a rope over a fixed pulley and the same load can be raised by pulling downward, allowing body weight and a more convenient posture to help. The machine has not removed the task or created energy. It has changed how the required force is applied.
Simple Machines
A simple machine is a device that makes a task easier or more convenient by changing the magnitude or direction of the applied force.
In an ideal machine, the total work required for a task is not reduced. If the required effort force becomes smaller, it must usually act through a greater distance. A machine may instead preserve the force magnitude but change its direction. These are force-distance trade-offs, not free energy.
Effort is the force applied to a machine by the user or another agency.
Load is the force that the machine must overcome.
Mechanical advantage is the ratio of the load to the effort.
| Mechanical Advantage | Meaning |
|---|---|
| Equal to one | Load and effort have equal magnitudes |
| Greater than one | Load is larger than effort, so force is multiplied |
| Less than one | Effort exceeds load, but another advantage such as distance or speed may be obtained |
Pulley
A pulley is a wheel with a groove that guides a rope.
Fixed Pulley
A fixed pulley is attached to a support and does not rise with the load. Pulling one end of the rope downward raises the load at the other end. In an ideal fixed pulley, the rope tension has the same magnitude on both sides, so the effort equals the load. Its mechanical advantage is one.
Although the fixed pulley does not reduce the force magnitude, it provides convenience by changing the direction. Pulling downward can be easier than lifting the same load directly upward.
Problem
A flag and its attachments exert a downward load of 40 N. Neglecting friction, find the effort and mechanical advantage of the fixed pulley.
- 1.For an ideal fixed pulley, effort equals load.
- 2.Therefore, effort = 40 N.
- 3.Mechanical advantage = load ÷ effort.
- 4.Mechanical advantage = 40 N ÷ 40 N = 1.
- 5.The benefit is the changed direction of pull, not a reduced force.
Movable Pulley and Pulley Systems
In a movable pulley, the load is attached to a pulley that rises with it. One end of the rope is fixed to a support and the free end is used to apply effort. More than one rope segment can support the moving load, allowing a smaller effort to balance a larger load. Systems combining fixed and movable pulleys are used in cranes and elevators.
The reduced effort does not mean reduced work. If two supporting rope segments share the load in an ideal arrangement, the effort may be about half the load, but the free end must move about twice the distance through which the load rises.
Problem
An ideal movable pulley has two supporting rope segments and lifts a 200 N load. Find the effort and mechanical advantage.
- 1.The load is shared equally by two supporting rope segments.
- 2.Effort = 200 N ÷ 2 = 100 N.
- 3.Mechanical advantage = load ÷ effort.
- 4.Mechanical advantage = 200 N ÷ 100 N = 2.
- 5.To raise the load by one metre, the free end must be pulled through approximately two metres in the ideal arrangement.
Machines and Energy
Ignoring friction, input work equals useful output work. Real pulleys have friction in bearings and between rope and groove, so actual effort is larger than the ideal value. Machines do not create energy; they help us transfer it in a convenient combination of force and distance.
Checking the Force-Distance Exchange
If an ideal movable arrangement has mechanical advantage two, an effort of 100 N can balance a 200 N load. Raising that load through one metre gives useful output work of 200 J. To supply the same work with 100 N effort, the free end must move through two metres. The equality 100 N × 2 m = 200 N × 1 m shows exactly where the apparent force gain is balanced.
Problem
An ideal pulley system uses 150 N effort to raise a 450 N load through 0.8 m. Find mechanical advantage, useful work and the distance moved by the effort.
- 1.Mechanical advantage = 450 N ÷ 150 N = 3.
- 2.Useful output work = load × load displacement = 450 N × 0.8 m = 360 J.
- 3.For an ideal machine, input work equals 360 J.
- 4.Effort distance = input work ÷ effort = 360 J ÷ 150 N = 2.4 m.
- 5.The effort moves three times the load distance, balancing the threefold force advantage.
Only rope segments that directly support the moving pulley and load contribute to the ideal force advantage. A fixed pulley used only to redirect the free end does not add another supporting segment.
Quiz
Which description best matches Simple Machine?
Which description best matches Effort?
Which term matches this description: A simple machine is a device that makes a task easier or more convenient by changing the magnitude or direction of the applied force.
Which term matches this description: Effort is the force applied to a machine by the user or another agency.
Which statement is a key takeaway from this lesson?
Practice Problems
- Define effort, load and mechanical advantage in a pulley system.
- Why can a fixed pulley be useful even though its mechanical advantage is one?
- An ideal machine lifts a 300 N load using 100 N effort. Find its mechanical advantage.
- Explain the force-distance trade-off in an ideal movable pulley.
Key Takeaways
• Simple machines change the magnitude or direction of effort. • Mechanical advantage is load divided by effort. • A fixed pulley changes direction and ideally has mechanical advantage one. • Movable pulley systems can provide force advantage. • Machines do not create energy or remove the total ideal work.