# Is PUSHING a wagon mechanical advantage?

Hi all. So as we know the wheel can be a form of mechanical advantage. If I were to spin a wheel from its circumference and a rope was attached to its [smaller] axle, I would be applying less force per distance than is outputted on the axle. (I may have worded that funny but its not important for my question)

So here's my question: Does mechanical advantage and the size of the wheel vs its axle apply to when you simply push or pull a vehicle/cart with wheels. In this scenario I'm not applying any force to any part of the wheel or axle; simply pushing the back of a wagon for example. The wheels obviously reduce friction, but does the SIZE of the wheel (and its ratio to its axle) at all affect this reduction in friction in terms of mechanical advantage?

In other words: in a lab environment where a perfectly smooth floor was used, would there be any advantage in pushing a wagon with 20foot diameter wheels (and 2 inch axle) as opposed to say a wagon with 2 foot wheels (and 2 inch axle) (disregarding weight differences).

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rcgldr
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Larger radius wheels should reduce the amount of force it takes to push the wagon.

NascentOxygen
Staff Emeritus
"Perfectly smooth" implies frictionless, so your question is moot.

Rubber tyres cause "scrubbing" as they flex and scrape over a rough surface. Larger diameter tyres need to distort less as they present a flat surface to the ground.

The big advantage of large diameter tyres is that they are like a ramp--they climb over sharp undulations better than does a narrower diameter. Consider the penny farthing bicycle going up and over the curb, and compare this with a toddler's tricycle trying to do the same.

"The big advantage of large diameter tyres is that they are like a ramp--they climb over sharp undulations better than does a narrower diameter."

While this certainly is true, I am more concerned simply with mechanical advantage. That is why I phrased my question 'in a perfectly flat situation' and i don't mean to say completely frictionless.

rcgld, would you care to explain the physics behind you answer, that is where my curiosity lies:)

thanks
t

rcgldr
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rcgldr, would you care to explain the physics behind you answer, that is where my curiosity lies.
Assuming a fixed load and coefficient of friction at the axles, it takes a fixed amount of torque to keep the wagon moving at constant speed. The initial push will have to overcome the static friction at the axles, while once the wagon is moving, dynamic friction at the axles is involved, which is usually less than static friction, so less torque is required.

The amount of torque generated on the wheels, equals the horizontal force on each wheel times the radius of each wheel. The larger the radius, the greater the amount of torque for the same force, or in this case, less force is required to produce the same torque required to overcome the friction at the axles.

The "mechanical advantage" or "multiplier effect" would be the ratio of the wheel radius to the axle radius.

Ideally the friction in the bearings is very low to begin with, so you probably wouldn't feel much of a difference whether you used a wheel 5x larger or 5x smaller.

If the bearings were perfect (frictionless), then a larger wheel wouldn't make any difference.

rcgldr
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