How do things that provide mechanical advantage by being levers or acting like levers (gears) fit into the F=m•a formula? I.e. do they increase force in the formula by increasing either the acting mass of an object or the acceleration.
In: Engineering
I think you need the equation work = force x distance. Simple machines change the ratio of force and distance for the same work. So if you use a lever to pry something, you apply less force over a greater distance on one end and get more force over a smaller distance on the other end. But the same amount of work (a form of energy) remains the same.
F = m*a applies to each individual object. Different objects can have different forces applied to them, so it’s not the right formula if you want to understand how a lever works.
If a lever provides you with a mechanical advantage then the acceleration at the point where you apply the (smaller) force is larger than the acceleration of the object you move with a larger force.
If I recall it’s a matter of trading off range of motion for increased lifting power/torque etc. Across the whole system energy is conserved but you sacrifice a certain amount of range or velocity to overcome gravitational or inertial forces.
For example you use a large gear range of 5 or 6:1 to apply the torque to start a car from a standing start, overcoming it’s own inertia, in first gear; but you can only go 15 or 20mph in that first gear without redlining the engine. After that you shift thru smaller and smaller gear ranges in order to keep propelling the already moving car to higher and higher speeds; in other words trading higher range of (rotational) motion for a reduction in the advantage of higher output torque:input torque.
When accounting for the mechanical advantage you have to bear in mind that we are more nearly talking about WORK not FORCE, work in this case being a force across distance. Mechanical advantage is trading a large force applied across a small distance (1-2 gear in a car at <20mph), instead of a small force across a large distance (6th gear in a car at 80mph). Throughout the gear ranges the input & output energy remains the same.
Hope this helps! This is half remembered from physics classes 30 years ago and slightly researched so if ANYBODY wants to correct or clarify anything please do so
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