Mechanical advantage (MA) is the ratio of output force to input force: MA = output force / input force. A lever with MA = 3 multiplies your input force by three -- you push with 100 N and the lever delivers 300 N. However, conservation of energy means you must push three times the distance to move the load a given distance. The ideal mechanical advantage (IMA) is calculated from geometry (distances or radii), while the actual mechanical advantage (AMA) is measured from real forces and is always less than IMA due to friction. The ratio AMA/IMA gives the machine's efficiency.
Set up a lever with a fulcrum and measure forces with spring scales. Move the fulcrum and observe how the force ratio changes as the distance ratio changes. Calculate IMA from the lever arm lengths and AMA from the spring scale readings. Compare IMA to AMA and calculate efficiency. Repeat with an inclined plane (ramp) -- measure the force needed to push a cart up the ramp vs. lifting it straight up, and calculate both IMA and AMA.
In the Design & Build course, you learned that simple machines like levers, ramps, pulleys, and gears make work easier by reducing the force needed to accomplish a task. Mechanical advantage puts a number on exactly how much easier. If a lever lets you lift a 300 N rock by pushing with only 100 N, its mechanical advantage is 300/100 = 3. You have tripled your force.
But there is no free lunch. Conservation of energy -- one of the deepest principles in physics -- guarantees that you cannot get more work out of a machine than you put in. If a lever triples your force, it must also require you to push three times the distance. Work = force x distance, so (100 N)(3 m) = (300 N)(1 m) = 300 J either way. The machine does not create energy; it redistributes it, trading force for distance.
Engineers distinguish between ideal mechanical advantage (IMA) and actual mechanical advantage (AMA). IMA is calculated from the geometry of the machine -- the ratio of lever arms, ramp length to height, or number of supporting ropes in a pulley system. It tells you what the mechanical advantage would be if there were no friction. AMA is measured from actual forces using spring scales or load cells. It is always less than IMA because friction converts some input energy to heat, reducing the output force.
The ratio efficiency = AMA / IMA tells you how much of your input energy actually reaches the output. A well-oiled pulley system might be 90% efficient (AMA is 90% of IMA). A rusty, corroded screw jack might be only 30% efficient. Interestingly, low-efficiency machines are sometimes desirable: a screw with low efficiency is self-locking, meaning the load cannot drive it backward. That is why car jacks use screws rather than levers -- you can raise the car and it stays up.
Some machines have MA less than 1, which might seem useless -- they actually reduce force at the output. But they multiply speed and distance instead. A fishing rod has MA well below 1 at the tip: a small movement of your wrist produces a large, fast sweep of the rod tip. A baseball bat works the same way. The physics is symmetric: if MA > 1, you get more force and less speed; if MA < 1, you get less force and more speed. The right MA depends on whether your task demands force or speed.