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what minimum horizontal force is needed to pull a wheel of radius R and mass M over a step of height H. force is supplied at center of wheel.
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The verticle component of the force exerted by the step upon the wheel must counteract gravity, so that it lifts off of the ground.
Originally posted by himanshu121
Given force is horizontal
The wheel will roll over the step when the reactive force from the step has a verticle component equal and opposite to the gravitaional effect upon the wheel.
To calculate the horizontal force needed to pull a wheel, you will need to know the weight of the wheel, the coefficient of friction, and the angle between the ground and the direction of motion. The formula for calculating this force is F = μmgcosθ, where F is the force, μ is the coefficient of friction, m is the mass of the wheel, g is the acceleration due to gravity, and θ is the angle.
The coefficient of friction is a measure of the amount of friction between two surfaces in contact. It is represented by the symbol μ and is a dimensionless number. A higher coefficient of friction means there is more resistance to motion between the two surfaces.
The weight of the wheel directly affects the horizontal force needed to pull it. The heavier the wheel, the greater the force needed to overcome its inertia and move it horizontally. This is represented in the formula as the variable m (mass).
The angle, represented by θ in the formula, is the angle between the ground and the direction of motion. This angle determines the direction of the force needed to pull the wheel. If the angle is 0 degrees, meaning the wheel is being pulled along a flat surface, the horizontal force needed will be equal to the weight of the wheel multiplied by the coefficient of friction. However, as the angle increases, the horizontal force needed will also increase.
Knowing how to calculate the horizontal force needed to pull a wheel can be useful in various real-life situations. For example, it can help in determining the force needed to pull a cart or a sled, or in designing machinery that requires pulling or pushing of heavy objects. It can also be useful in understanding the physics behind everyday activities, such as pulling a suitcase or pushing a shopping cart.