Levers: force and travel

A bar turns about a fixed point

Imagine a stiff bar resting on a support, with a load on its right end. Pushing the left end down turns the bar and raises the load. This simple machine is a lever

1. 1Pivot The fixed point or support about which the bar turns. It is also called the fulcrum
2. 2Input The force supplied to operate the lever. Here it is the person’s downward push on the bar. Input force is also called effort
3. 3Output The useful force the lever applies. Here the bar pushes up on the load. The load is the object being raised; its weight is a downward force on it
4. 4This arrangement The pivot is between the input end and the load end. This is called a first-class lever. The two ends move in opposite directions

Compare three setups with the same load

The next display keeps the bar and the 12 N load the same. Force is measured in newtons (N). Read the distances from the pivot in centimetres (cm). The input arm runs from the pivot to the input end; the load arm runs from the pivot to the load end

1. 1Separate setups Changing Pivot position chooses a different setup. The pivot stays fixed during each lift. Start and Raised are two poses, not a timed animation
2. 2Read the arrows Both solid arrows use the same force scale. One is the person’s push on the bar; the other is the bar’s push on the load. They act on different objects, so this is not a complete force diagram of one object
3. 3Ideal model The bar is rigid and weightless, the pivot has no friction, the forces are vertical and the lift is slow. Support and gravity are not drawn. This model does not give a safe load rating for a real machine

Keeping the load the same, what do you predict happens to the required input force when the pivot is nearer the load?

Compare the input force at Near input, Middle and Near load. Then use Near load and switch Start to Raised. The dashed bar marks the start. Compare how far each end moves. Which statement matches both observations?

What happens in the Near load setup?

Distance from the pivot changes the force

For the same load, a longer input arm and shorter load arm need a smaller input force. The total bar length alone does not tell you the effect: check where the pivot divides it

1. 1Input arm longer The required input force is smaller than the output force on the load
2. 2Equal arms The force sizes are equal in this ideal model. The lever still changes the force direction
3. 3Input arm shorter The required input force is larger. Not every lever reduces the input force

A person pushes down on one end of a bar, and the other end raises a load. Which statement names the output force and its receiving object?

The output is the lever’s useful force on the object being moved

An ideal first-class lever has a 15 cm input arm and a 30 cm load arm. Forces are vertical and the load is lifted slowly. How does the required input compare with the output force?

Compare the two distances from the pivot. Here the input arm is shorter

A smaller force, over a longer path

Both ends turn through the same angle. The end farther from the pivot follows a longer curved path. In the Near load setup, the smaller input force comes with longer input travel

1. 1Equal-arm boundary Equal arms have equal end travel and equal force sizes in this ideal model
2. 2Reverse trade-off A shorter input arm moves through a shorter path, but needs a larger input force
3. 3No free energy The machine passes on energy supplied at the input; it does not create energy. Reducing the force does not remove the need to move the input end farther

A different ideal first-class lever has a 42 cm input arm and a 21 cm load arm. It turns slowly through a small angle, with vertical input and output forces. Which comparison is correct?

Explain a comparison with evidence

Two ideal setups lift the same 20 N load with the same 60 cm bar. Setup A has 20 cm from input to pivot and 40 cm from pivot to load; its input is 40 N. Setup B has 40 cm and 20 cm; its input is 10 N. These are supplied model observations

1. 1Principle For the same load, a longer input arm and shorter load arm reduce the required input force
2. 2Evidence The load and total bar length stay fixed. In B the input arm is longer and the load arm shorter; the required input falls from 40 N to 10 N
3. 3Conclusion These observations support that force comparison for the stated ideal setups. The longer input path is the trade-off. They do not establish the strength or safe rating of a real bar

Two setups need the same input force. The pivot position changes, but so does the load. Does this show that pivot position has no effect?

Check the pivot, force targets and travel

A first-class lever has its pivot between input and load. A longer input arm can reduce the required force, but that end travels farther. Equal arms give equal force sizes and equal travel in the ideal model

1. 1Explain independently Explain why moving the pivot nearer the same load can reduce the required input force, and name the travel trade-off. Compare your explanation with the worked example. The app does not mark your prose
2. 2Sketch the mechanism Sketch a bar, a fixed pivot between its ends, an input push and a load. Label the source and receiving object of each selected force. This drawing is not automatically assessed
3. 3Keep the boundary These checks cover a fixed-pivot first-class lever, not every lever arrangement or simple machine. Practical construction, measurement and safety assessment need separate evidence