Intraduction
The wheel and axle is a form of simple machine that uses the idea of mechanical advantage to simplify operations involving the manipulation of force. The wheel and axle are made up of a wheel, which is a round disc with a rod running through the middle of it, and an axle. This mechanism typically works against gravity to move things by using torque and rotational momentum. Gears and the wheel and axle basic machine go hand in hand.
The wheel and axle device, like all other simple machines, modifies the force by altering the distance over which the force must be applied; if the input force is decreased to 15 the output value, the force must be applied over five times the distance. Because energy is conserved, the work done is always equal to the product of the force and the distance.
The speed of rotation for the wheel and axle is the same. This indicates that the wheel will turn fully in the same amount of time as the axle (as opposed to how gears work).
Although you might not typically think of a screwdriver, it is. One of the simple machines, along with inclined planes, levers, wedges, pulleys, and screws, is the wheel and axle. All of them allow you to change the force required to finish a task by changing the distance through which the force is applied.
Non-conservative forces like friction will result in energy loss, however, wheel and axle systems frequently have very high efficiencies.
The mechanical advantage of axle and wheel
The optimal mechanical benefit of this arrangement is:
IMA=R/r
where R is the wheel’s radius and r is the axle’s radius
The force required to lift the load by a wheel and axle system can be less than the object’s weight. The distance it takes to revolve the wheel is much more than the distance the axle travels through, even though the force required to turn it may not be as great as the force it exerts on the item.
The energy transfer should be without any losses, however, in practice, there is no such thing as a system that is 100% efficient.
Calculating a Wheel and Axle’s Mechanical Advantage
A wheel and axle must be permanently attached to be regarded as a simple machine, and the wheel must by definition have a wider radius than the axle. When you turn the wheel through a full revolution, a point on the wheel travels 2 R and a point on the axle moves 2 r.
Work is energy, and since energy must be conserved, a point on the axle must be subjected to a larger force F r because it moves a shorter distance.
The equation is as follows:
W=Fr​×2πr/θ=FR​×2πR/θ
where the wheel’s angle of rotation is.
and as a result:
FR/​Fr​​=r/R​
​
The force you apply F R times the distance the point moves equals the effort W required to move a point on the wheel through one full revolution.
Mechanical Advantage and Force Calculation
The ideal mechanical advantage of the wheel and axle system is the ratio R/r. This explains that the force you impart to the wheel increases by a factor of R/r at the axle in the absence of friction. You compensate for that by advancing a point on the wheel further. Additionally, the distance ratio is R/r.
Example of Axle and Wheel
As an illustration, consider using a screwdriver with a 4 cm-diameter handle to tighten a Phillips screw. What mechanical advantage does a screwdriver have if the tip has a 1 mm diameter? What force does the screwdriver apply to the screw if you apply 5 N of force to the handle?
The screwdriver tip has a radius of 0.5 mm and a handle radius of 2 cm (20 mm). The screwdriver has a mechanical advantage of 20 mm/0.5 mm, or 40. The screwdriver exerts a force of 200 N on the screw when you apply 5 N to the handle.
By the way, a wheel and axle’s velocity ratio and mechanical advantage are related. Consider that the time it takes for point “a” on the axle to complete one full rotation (2 r) corresponds to the time it takes for point “w” to complete one full rotation (2 R). The speed of point V an is 2 r / t, while the speed of point V w is 2 R / t. Eliminating common elements and dividing V w by V a results in the connection shown below:
Va/​/Vw = r/R
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Examples of objects that can be moved by a wheel and axle include vehicle and bicycle wheels. Other examples include doorknobs and Ferris wheels. Another type of wheel is a solid pole with an axle in the middle, like a screwdriver. The assembly made up of two discs or cylinders of various diameters attached so they revolve in tandem around the same axis is referred to as a wheel and axle in the context of primitive machines. The wheel is the wider object fixed to the axle to which force is applied. The axle is the thin rod that needs to be spun. The wheel and axle are used to increase the force and make the work easier for humans. It can be used to move people, things, or intricate machine pieces as well as lifting large objects. The fundamental machine part for amplifying force is the wheel and axle. Its original purpose was probably to lift objects like weights or water buckets out of wells. The depiction at A in the drawing illustrates how its working principle is illustrated by the large and small gears mounted on the same shaft. Axle and Wheel FAQs
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