# Is PUSHING a wagon mechanical advantage?

• Elquery
In summary: In that case, the larger wheels would require less force to overcome the friction in the bearings, leading to a greater mechanical advantage.
Elquery
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).

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

"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

Elquery said:
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.

Lsos said:
I assumed the OP was asking about pushing the wagon at constant speed on level pavement, in which cass inertia isn't an issue.

## 1. What is mechanical advantage?

Mechanical advantage is a measure of the effectiveness of a machine in multiplying the force applied to it. It is the ratio of the output force to the input force.

## 2. How is mechanical advantage calculated?

Mechanical advantage is calculated by dividing the output force by the input force. This can also be expressed as the ratio of the distance over which the output force is applied to the distance over which the input force is applied.

## 3. Is pushing a wagon considered a mechanical advantage?

Yes, pushing a wagon can be considered a mechanical advantage. This is because the force applied by the person is multiplied by the wheels of the wagon, making it easier to move the wagon.

## 4. What factors can affect the mechanical advantage of pushing a wagon?

The mechanical advantage of pushing a wagon can be affected by several factors, such as the weight and size of the wagon, the condition of the wheels and surface it is being pushed on, and the strength and technique of the person pushing.

## 5. Can the mechanical advantage of pushing a wagon be increased?

Yes, the mechanical advantage of pushing a wagon can be increased by using tools such as levers or pulleys. These tools can help to multiply the force applied, making it easier to move the wagon. Additionally, having a smoother surface or using lubrication can also increase the mechanical advantage.

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