Work, energy, and simple machines

Physical Science 112

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What is a simple machine?

Simple machines make work easier by multiplying, reducing, or changing the direction of a force. The scientific formula for work is w = f x d, or, work is equal to force multiplied by distance. Simple machines cannot change the amount of work done, but they can reduce the effort force that is required to do the work! For the inclined plane and lever, less effort (effort force) is needed to do the same work because the distance is increased. By using simple machines, the Egyptians were able to construct the pyramids.
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Inclined planes decrease the amount of force needed but more distance is required.

By pushing an object up a slanted surface, one can move the object to height h with a smaller force than the weight of the object.

The resistance force Fr =mg, the weight of the object. It takes work (Fxd = mgh) to overcome that resistance force and lift the object to height h. By doing work on it we give it gravitational potential energy mgh. By exerting force (effort) to push the object up the incline, we do the same amount of work in the ideal frictionless case. So setting the work equal FeL = Frh, we arrive at the ideal mechanical advantage Fr/Fe = L/h or Din/Dout.

Another approach to the incline is just to calculate the amount of force required to push the object up a frictionless incline. If the forces are resolved as in the standard incline problem, you find that the required force is Fe=mgsinθ = mgh/L = Fr (h/L) .

Ideal Mechanical Advantage (IMA) represents the frictionless scenario

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Actual Mechanical Advantage takes friction into account

Terms can be confusing!

As seen in the picture to the right, AMA is calculated by dividing the resistance force by the effort force. In other sources, you will see these labeled as output force and input force respectively. Resistance force is the WEIGHT of the object to be moved. It is the output force of the simple machine. The input force is the same as the effort force put into moving the object using the machine. This formula for AMA is the same for the lever and the inclined plane.

Efficiency = work out/work in x 100

Another way to calculate efficiency is AMA/IMA x 100

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A lever makes work easier by reducing the force needed to move a load by increasing the distance.

A Lever is a simple machine consisting of a rigid bar that rotates about a fixed point, called a fulcrum. The lever makes doing work easier by reducing the force needed to move an object. In order to reduce the force needed, the distance over which the force is applied must be increased. To increase this distance, the load to be moved must be close to the fulcrum and the force must be applied far from the fulcrum.

A common example of a lever is the seesaw. The human arm is also a lever, where the elbow is the fulcrum and the muscles apply the force.

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Just as with inclined planes, terms can be confusing with levers too.

As the picture to the left shows, the IMA for a lever can be calculated by taking the length of the lever arm from the fulcrum to the force (effort) divided by the length of the lever arm from the fulcrum to the load. Another way you will see this shown is effort distance/resistance difference. And still another way (as seen below), input arm length/output arm length = IMA. As with inclined planes, the object to be moved is the resistance force or load and the effort is the force put into moving the load at the other end of the fulcrum. So force=effort=in and resistance = load=out.
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