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What is the minimum force that we need to lift our body to walk up a flight of stairs?

Let's say I weigh 50 kg and I walk up a flight of stairs. What the minimum force I need to apply to stand straight on flat ground and to climb the stairs?

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The minimum amount of work required to lift a stationary object of mass $m$ through a height $h$ is $mgh$ where $g$ is the acceleration due to gravity - this is the difference in potential energy between height $0$ and height $h$.

This can be achieved with a force that is as small as you like. This is because work is force times distance (where we measure distance parallel to the direction of the force). So you can do the same amount of work by moving a small force through a large distance as by moving a larger force through a smaller distance.

A device that magnifies force, converting a small force over a large distance into a larger force over a smaller distance is called a mechanical advantage device. Examples are levers, block and tackle systems, and probably the simplest example, the inclined plane.

So if you built a long, smooth inclined plane to the top of the stairs, and you made the angle of the plane to the horizontal very shallow, then you could climb the stairs by exerting very little force (although it might take you a long time). This is, of course, the principle behind wheelchair ramps.

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To climb stairs, you need to start with an upward force slightly greater than your weight to produce an upward acceleration (and velocity). Once you get moving, the upward force must support your weight (in Newtons) (shifted from leg to leg). As you go up, this force is acting through a vertical distance and doing work (which it does not do on a horizontal walk).

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While you are climbing at a uniform velocity, the force is exactly the same as if you were standing still. As you begin the climb, you accelerate, which requires a force applied in the direction of the climb (inclined at the stair's angle); this force vector adds to the vertical force vector due to gravity to create a net force vector. Once you have established the climbing velocity, the angled force goes away; only the vertical gravity force remains.

What you feel while climbing stairs which you do not feel while standing still is the work being done as the force against gravity is being applied over the height you are climbing. It is not an increase in force but an expenditure of energy.

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