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9.5 Simple Machines
Simple machines are devices that can be used to increase or decrease a force that we apply, often at the expense of a distance through which we apply the force.
Machines include levers, gears, pulleys, wedges, and screws.
The machine cannot do more work than the energy put into it.
The input force that is needed to perform the job can be reduced by machines.
One of the simplest machines is the lever, which is a rigid bar pivoted at a fixed place.
There is a rotation about a pivot point.
We can get a useful expression for the MA in terms of the distances from the pivot of the lever.
A nail puller has a mechanical advantage.
Solid arrows show the external forces on the nail puller.
The force that the nail puller applies to the nail is not the same as the force on the nail puller.
The force that the nail exerts back on the puller is an external force.
The lever arms of the input and output forces are parallel.
The lever type shown in Figure 9.22 is used for nail pulling.
The levers that are similar to this one are crowbars, seesaws, and other levers.
The system of interest consists of three vertical forces acting on the nail puller.
The distance from the pivot point to the point where the input force is applied and the distance from the pivot point to the point where the output force is applied are not labeled on the diagram.
The figure shows the distances from where the input and output forces are applied to the pivot.
The magnitude of the force applied to the nail puller is much greater than the force applied to the other end.
The equation is true for levers in general.
The MA is greater than one.
The longer the handle is, the more force you can exert with it.
The input and output forces are on the same side of the pivot, so the wheelbarrow and shovel are different.
In the case of the wheelbarrow, the load is between the pivot and the applied force.
In the case of the shovel, the input force is between the pivot and the load, but the input lever arm is shorter than the output lever arm.
The MA is less than one.
The pivot is the center of the wheel.
The output force is greater than the input force.
A wheelbarrow allows you to lift heavier loads than you could with your body alone.
The handle is held by the right hand.
The output force is less than the input force because the input is closer to the pivot.
The concept of mechanical advantage is used here.
The force needed to lift the load would be reduced by an even longer handle.
The MA is here.
The inclined plane is a very simple machine.
Pushing a cart up a plane is easier than lifting the same cart straight up to the top using a ladder because the applied force is less.
The work done in both cases is the same.
During the construction of the Egyptian pyramids, inclined lanes or ramps were used to move large blocks of stone to the top.
The physics of such a machine are the same even though it doesn't look like a lever.
The ratio of the radii is what the MA for a crank is.
The simple expression for their MAs can be found in wheels and gears.
As shown, the MA can be greater than 1, as it is for the crank, or less than 1, as it is for the simplified car axle driving the wheels.
If the wheel's radius is greater than the axle's, then the wheel would have to exert a force on the ground.
A large MA is what the cranks are usually designed to have.
The MA is not very high.
The force that the cord exerts is not changed by the pulley.
This machine has an MA of 1.
The MA of an ordinary pulley is 1 and it only changes the direction of the force.
The force output is an integral multiple of the tension in the cable if the pulleys are friction-free.
The number of cables pulling upward on the system of interest is roughly the MA of the pulley system.
They say that since each attachment applies an external force in approximately the same direction as the others, it creates a total force that is nearly an integral multiple of the input force.
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